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y(the)h(sp)q(eci\014cation)h(of)e(the)h(surface)h(and)f(errors.)22 b(If)15 b(this)g(allo)q(cated)f(space)i(is)f(to)q(o)f(small,)f(the)262 1104 y Fp(k)q Fr(-)p Fp(d)j Fr(tree)i(division)d(is)i(truncated)h(and)f(a)f (w)o(arning)g(message)h(sen)o(t)g(up.)27 b(In)17 b(some)f(cases)i(the)262 1154 y(problem)9 b(is)h(extreme)h(enough)f(that)h(the)g(\014t)f(is)g(not)h (carried)g(out;)g(this)f(necessitates)j(increasing)262 1204 y(the)h(v)n(alue)f(of)h Fp(\013)p Fr(.)262 1341 y Fn(5)69 b(Bibliographic)20 b(Notes)262 1432 y Fr(Lo)q(cal)10 b(regression)i(mo)q(dels)e(are)h(treated)h (in)f(detail)f(in)g(a)h(new)g(b)q(o)q(ok)g(b)o(y)g(Clev)o(eland)f(and)h (Grosse)262 1482 y(\(forthcoming\).)16 b(But)f(metho)q(ds)e(of)h(lo)q(cal)f (\014tting)g(date)i(bac)o(k)f(at)g(least)g(to)g(the)g(1920s.)k(Initial)262 1532 y(applications)c(w)o(ere)i(to)f(smo)q(oth)f(a)h(time)f(series)j (\(Macauley)m(,)e(1931\).)21 b(An)15 b(early)h(use)g(of)e(lo)q(cal)262 1581 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Fp(g)q Fr(\()p Fp(x)p Fr(\))11 b(is)f(directly)h(computed)f(at)h(the)g(v)o (ertices.)19 b(By)11 b(\\v)o(ertex,")262 1802 y(w)o(e)e(just)h(mean)f(a)g (corner)i(of)e(a)h(cell;)g(\\v)o(ertex")g(seems)g(a)g(b)q(etter)h(term)e (than)h(\\corner")g(b)q(ecause)i(a)262 1851 y(v)o(ertex)f(of)g(one)g(cell)g (t)o(ypically)e(lies)i(in)g(the)g(middle)e(of)i(a)f(side)i(of)e(an)h(adjacen) o(t)g(cell.)17 b(In)11 b(addition)262 1901 y(to)k(computing)g(^)-22 b Fp(g)q Fr(\()p Fp(x)p Fr(\))16 b(at)f(a)h(v)o(ertex,)g(a)f(deriv)n(ativ)o (e)g(of)i(^)-23 b Fp(g)17 b Fr(at)f(the)g(v)o(ertex)h(is)e(appro)o(ximated)f (b)o(y)262 1951 y(the)h(deriv)n(ativ)o(e)g(of)f(the)i(lo)q(cally-\014tted)e (surface.)22 b(This)15 b(deriv)n(ativ)o(e)g(is)g(a)f(natural)h(b)o(y-pro)q (duct)262 2001 y(of)e(the)h(least-squares)h(computation)e(and)g(costs)i (nothing)e(extra)i(to)e(obtain.)324 2051 y(T)o(ypically)m(,)i(the)j(n)o(um)o (b)q(er)e(of)h(v)o(ertices,)h Fp(v)q Fr(,)g(will)e(b)q(e)i(m)o(uc)o(h)e (smaller)f(than)i Fp(n)p Fr(.)28 b(This)17 b(is)g(at)262 2100 y(least)e(true)i(asymptotically)m(,)12 b(b)q(ecause)18 b(the)e(n)o(um)o(b)q (er)f(of)g(cells)h(needed)h(to)f(ac)o(hiev)o(e)g(a)f(certain)262 2150 y(accuracy)f(of)e(appro)o(ximation)e(dep)q(ends)15 b(on)e(the)g(smo)q (othness)h(of)f(^)-22 b Fp(g)q Fr(\()p Fp(x)p Fr(\),)13 b(not)g Fp(n)p Fr(.)18 b(In)13 b(Figure)g(28)262 2200 y(there)i(are)f(66)g(v)o (ertices,)h(so)f(w)o(e)g(solv)o(e)g(66)f(least-squares)j(problems)d(instead)h (of)g(one)g(problem)262 2250 y(p)q(er)20 b(ev)n(aluation)d(of)j(^)-22 b Fp(g)q Fr(\()p Fp(x)p Fr(\).)34 b(\(Recall)18 b(that)i(for)f(the)g(galaxy)f (surface)i(w)o(e)g(carried)f(out)g(5841)262 2300 y(ev)n(aluations)14 b(to)i(mak)o(e)e(a)h(con)o(tour)h(plot.\))22 b(The)16 b(amoun)o(t)e(of)h(w)o (ork)g(in)h(general)f(to)h(construct)262 2350 y(the)d Fp(k)q Fr(-)p Fp(d)f Fr(tree,)i(including)e(v)o(ertex)i(co)q(e\016cien)o(ts,)g(is)f Fp(O)q Fr(\()p Fp(v)q Fr(\(\(1)p Fp(:)p Fr(5)7 b(+)g Fp(\013\034)e Fr(\))p Fp(n)i Fr(+)h Fp(\034)1426 2334 y Fl(3)1444 2350 y Fr(\)\).)18 b(After)c(building)262 2399 y(the)g(tree,)h(eac)o(h)g(in)o(terp)q (olation)e(costs)i Fp(O)q Fr(\(log)7 b Fp(v)q Fr(\).)19 b(Since)c Fp(\034)k Fr(is)14 b(\014xed)g(and)g Fp(v)i Fr(is)e(asymptotically)262 2449 y(b)q(ounded,)g(the)g(total)f(running)h(time)e(is)i(linear)g(in)f(the)h (size)h(of)e(the)i(input)f(and)f(output.)991 2574 y(49)p eop %%Page: 48 7 bop 262 307 a Fm(Symme)o(tri)o(c)16 b(Errors)262 384 y Fr(When)g(the)h(error) g(distribution)f(is)g(sp)q(eci\014ed)i(to)e(b)q(e)h(symmetric,)e(inferences)j (are)f(based)g(on)262 434 y Fq(pseudo-values)p Fr(.)h(Let)13 b(the)f(robustness)i(w)o(eigh)o(ts)e(and)g(the)g(median)f(absolute)h (residual)g(used)h(in)262 483 y(the)d(\014nal)g(up)q(date)h(of)f(the)h (\014t,)h(^)-23 b Fp(g)r Fr(\()p Fp(x)p Fr(\),)10 b(b)q(e)h Fp(r)899 489 y Fo(i)923 483 y Fr(and)f Fp(m)p Fr(,)h(resp)q(ectiv)o(ely)m(,)h (and)e(let)g Fp( )q Fr(\()p Fp(u)p Fr(;)d Fp(b)p Fr(\))12 b(=)f Fp(uB)r Fr(\()p Fp(u)p Fr(;)c Fp(b)p Fr(\).)262 533 y(The)14 b(pseudo-v)n(alues)g(are)885 583 y(\177)-24 b Fp(y)902 589 y Fo(i)928 583 y Fr(=)15 b(^)-24 b Fp(y)992 589 y Fo(i)1015 583 y Fr(+)10 b Fp(cr)1094 589 y Fo(i)1110 583 y Fr(^)-24 b Fp(")1126 589 y Fo(i)262 658 y Fr(where)17 b(^)-23 b Fp(y)402 664 y Fo(i)430 658 y Fr(are)14 b(the)g(\014tted)h(v)n(alues,)h(^)-24 b Fp(")835 664 y Fo(i)863 658 y Fr(are)15 b(the)f(residuals,)g(and)820 757 y Fp(c)e Fr(=)1030 729 y Fp(n)p 898 748 288 2 v 898 755 a Fj(P)942 765 y Fo(n)942 799 y(i)p Fl(=1)1005 786 y Fp( )1033 774 y Ff(0)1045 786 y Fr(\()s(^)-24 b Fp(")1080 792 y Fo(i)1095 786 y Fr(;)7 b(6)p Fp(m)p Fr(\))1191 757 y Fp(:)262 873 y Fr(Inferences)21 b(are)f(carried)g(out)f(b)o(y)g(applying)f(the)h(inference)i(pro)q(cedures)h (of)c(the)i(Gaussian)262 923 y(case)14 b(but)g(replacing)g(the)g(observ)n (ations)g(of)g(the)g(resp)q(onse)i Fp(y)1218 929 y Fo(i)1246 923 y Fr(b)o(y)d(the)i(pseudo-v)n(alues)i(\177)-24 b Fp(y)1657 929 y Fo(i)1671 923 y Fr(.)18 b(F)m(or)262 973 y(example,)8 b(supp)q(ose)j(w)o(e)e(w)o(an)o(t)g(to)g(compute)g(a)g(con\014dence)i(in)o (terv)n(al)e(for)g Fp(g)q Fr(\()p Fp(x)p Fr(\))h(ab)q(out)f(the)h(robust)262 1023 y(estimate,)16 b(^)-23 b Fp(g)r Fr(\()p Fp(x)p Fr(\).)22 b(Using)15 b(the)h(pseudo-v)n(alues)g(as)f(the)h(resp)q(onse,)i(w)o(e)d (compute)g(a)g(Gaussian-)262 1072 y(error)g(estimate,)g Fp(\032)p Fr(,)g(and)f Fp(s)p Fr(\()p Fp(x)p Fr(\))i(as)f(describ)q(ed)i(ab)q(o)o(v)o (e.)k(The)15 b(con\014dence)i(in)o(terv)n(al)d(for)g Fp(g)q Fr(\()p Fp(x)p Fr(\))i(is)262 1122 y(the)h(^)-23 b Fp(g)q Fr(\()p Fp(x)p Fr(\))15 b(plus)g(and)g(min)o(us)f Fp(s)p Fr(\()p Fp(x)p Fr(\))h(times)f(a)h Fp(t)g Fr(v)n(alue)f(with)h Fp(\032)g Fr(degrees)i(of)e (freedom.)20 b(The)c(true)262 1172 y(co)o(v)o(erage)g(using)g(this)g(pro)q (cedure)i(is)e(w)o(ell)g(appro)o(ximated)e(b)o(y)i(the)g(nominal)e(co)o(v)o (erage.)25 b(F)m(or)262 1222 y(the)18 b(analysis)f(of)g(v)n(ariance,)h(w)o(e) g(pro)q(ceed)h(in)e(a)g(similar)f(fashion)g(using)i(the)g(pseudo-v)n(alues) 262 1272 y(from)d(the)k(alternativ)o(e)e(mo)q(del)f(and)h(carrying)h(out)f (the)i(Gaussian-error)e(pro)q(cedures.)32 b(F)m(or)262 1322 y(small)16 b(samples,)j(the)g(appro)o(ximation)d(is)j(not)f(as)h(go)q(o)q(d)f (as)h(for)g(con\014dence)h(in)o(terv)n(als)f(and)262 1371 y(pro)q(duces)f (optimistic)d(results,)j(but)f(w)o(ork)f(is)h(under)g(w)o(a)o(y)f(to)h (\014nd)f(metho)q(ds)h(for)f(adjusting)262 1421 y(degrees)f(of)e(freedom)h (that)f(will)g(impro)o(v)o(e)f(the)i(appro)o(ximations.)262 1537 y Fm(Errors)k(with)g(Unequal)g(Scales)262 1614 y Fr(Supp)q(ose)12 b(w)o(e)g(ha)o(v)o(e)f(sp)q(eci\014ed)i(that)f(the)g(random)e(errors)j Fp(")1181 1620 y Fo(i)1207 1614 y Fr(in)e(the)h(mo)q(del)e(ha)o(v)o(e)h(the)i (prop)q(ert)o(y)262 1664 y(that)g Fp(a)373 1670 y Fo(i)387 1664 y Fp(")406 1670 y Fo(i)433 1664 y Fr(are)h(iden)o(tically)e(distributed) i(where)g(the)g Fq(a)h(priori)e(weights)p Fr(,)f Fp(a)1434 1670 y Fo(i)1448 1664 y Fr(,)h(are)h(p)q(ositiv)o(e)f(and)262 1714 y(kno)o(wn.)k(Then)e(v)n(arious)e(mo)q(di\014cations)f(are)i(made)f(to)g (the)i(metho)q(ds)e(of)h(inference.)324 1763 y(F)m(or)i(the)h(Gaussian-error) f(estimate,)g(the)h(op)q(erator)g(matrix)d Fp(L)j Fr(is,)f(of)g(course,)i (di\013eren)o(t)262 1813 y(from)d(that)j(in)f(the)h(equal-v)n(ariance)f (case,)i(but)f Fp(\016)1062 1819 y Fl(1)1098 1813 y Fr(and)f Fp(\016)1200 1819 y Fl(2)1237 1813 y Fr(are)h(de\014ned)g(in)g(terms)f(of)g Fp(L)g Fr(as)262 1863 y(b)q(efore.)h(The)d(estimate)e(of)g Fp(\033)i Fr(b)q(ecomes)858 1990 y Fp(s)d Fr(=)933 1912 y Fj(s)p 975 1912 191 2 v 980 1930 a(P)1023 1941 y Fo(n)1023 1974 y(i)p Fl(=1)1086 1962 y Fp(a)1108 1968 y Fo(i)1125 1962 y Fr(^)-24 b Fp(")1141 1947 y Fl(2)1141 1973 y Fo(i)p 980 1981 181 2 v 1051 2019 a Fp(\016)1069 2025 y Fl(1)262 2112 y Fr(and)13 b(the)i(estimate)e (of)g(the)i(standard)f(deviation)f(of)i(^)-23 b Fp(g)r Fr(\()p Fp(x)p Fr(\))14 b(b)q(ecomes)803 2256 y Fp(s)p Fr(\()p Fp(x)p Fr(\))e(=)g Fp(s)953 2171 y Fj(v)953 2194 y(u)953 2219 y(u)953 2244 y(t)p 997 2171 212 2 v 1017 2204 a Fo(n)997 2216 y Fj(X)1000 2305 y Fo(i)p Fl(=1)1064 2256 y Fp(l)1077 2241 y Fl(2)1076 2267 y Fo(i)1096 2256 y Fr(\()p Fp(x)p Fr(\))p Fp(=a)1195 2262 y Fo(i)1208 2256 y Fp(:)262 2393 y Fr(F)m(or)g(the)i(analysis)e(of)h(v)n (ariance,)g(all)f(residual)h(sum-of-squares)f(are)i(mo)q(di\014ed)e(b)o(y)h (adding)f(the)262 2443 y(terms)h Fp(a)399 2449 y Fo(i)413 2443 y Fr(,)g(as)h(done)g(ab)q(o)o(v)o(e)g(for)g Fp(s)p Fr(.)991 2574 y(48)p eop %%Page: 47 8 bop 282 307 a Fr(\(1\))14 b Fp(\013)376 292 y Fl(\()p Fo(n)p Fl(\))436 307 y Fk(\025)e Fp(\013)p Fr(.)282 390 y(\(2\))i Fp(\025)373 375 y Fl(\()p Fo(n)p Fl(\))433 390 y Fk(\024)e Fp(\025)p Fr(.)282 473 y(\(3\))k(If)f(the)h(square)h(of)e(a)g(factor)h(is)f (dropp)q(ed)h(from)e(the)j(alternativ)o(e)e(mo)q(del,)f(then)i(it)g(m)o(ust) 365 523 y(not)e(b)q(e)h(presen)o(t)g(in)f(the)g(n)o(ull)f(mo)q(del;)f(the)i (con)o(v)o(erse)i(need)e(not)g(b)q(e)h(true.)282 606 y(\(4\))e(The)h(mo)q (dels)e(m)o(ust)g(ha)o(v)o(e)h(the)g(same)f(factors)i(with)f(the)g(follo)o (wing)e(exception:)18 b(a)13 b(condi-)365 656 y(tionally)h(parametric)g (factor)i(in)f(the)h(alternativ)o(e)f(need)h(not)f(b)q(e)h(presen)o(t)h(in)e (the)h(n)o(ull;)365 706 y(if)d(presen)o(t,)i(though,)f(it)f(m)o(ust)g(also)g (b)q(e)i(conditionally)d(parametric.)262 789 y(Conditions)i(\(2\))i(to)g (\(4\))f(can)h(b)q(e)h(expressed)h(in)d(a)g(di\013eren)o(t)i(w)o(a)o(y)m(.)22 b(T)m(o)15 b(explain,)g(w)o(e)h(need)h(to)262 839 y(di\013eren)o(tiate)i Fq(neighb)n(orho)n(o)n(d)g(variables)p Fr(|the)f(factors)h(used)g(to)g (determine)f(the)h(neigh)o(b)q(or-)262 888 y(ho)q(o)q(ds)c(in)g(the)h(lo)q (ess)f(\014tting|and)g Fq(\014tting)h(variables)p Fr(|the)e(factors)i(that)f (are)h(\014tted)g(lo)q(cally)262 938 y(b)o(y)f(w)o(eigh)o(ted)h(least)g (squares.)24 b(Let's)16 b(tak)o(e)g(a)f(sp)q(eci\014c)i(example.)22 b(Supp)q(ose)17 b(there)g(are)f(three)262 988 y(factors:)h Fp(u)p Fr(,)12 b Fp(v)q Fr(,)h(and)g Fp(w)q Fr(.)k(Supp)q(ose)d Fp(\025)e Fr(=)h(2,)f Fp(u)g Fr(is)h(tak)o(en)f(to)h(b)q(e)g(conditionally)e (parametric,)h(and)262 1038 y(the)j(square)h(of)f Fp(w)h Fr(is)f(dropp)q(ed.) 23 b(The)16 b(neigh)o(b)q(orho)q(o)q(d)f(v)n(ariables)g(are)g Fp(v)i Fr(and)e Fp(w)q Fr(.)22 b(The)16 b(\014tting)262 1088 y(v)n(ariables)d(are)i(a)f(constan)o(t,)h Fp(u)p Fr(,)e Fp(u)792 1073 y Fl(2)811 1088 y Fr(,)h Fp(v)q Fr(,)g Fp(v)905 1073 y Fl(2)925 1088 y Fr(,)g Fp(w)q Fr(,)f Fp(uv)q Fr(,)i(and)f Fp(v)q(w)q Fr(.)20 b(No)o(w)14 b(w)o(e)h(can)f(reexpress)j(\(2\))e(to)262 1137 y(\(4\))e(b)o(y)h(the)h(follo)o(wing:)282 1220 y(\(2\))335 1193 y Fd(0)362 1220 y Fr(The)g(n)o(ull)e(and)g(alternativ)o(e)h(mo)q(dels)f (ha)o(v)o(e)h(the)g(same)f(neigh)o(b)q(orho)q(o)q(d)h(v)n(ariables.)282 1303 y(\(3\))335 1276 y Fd(0)363 1303 y Fr(The)i(\014tting)e(v)n(ariables)g (of)g(the)h(n)o(ull)f(mo)q(del)f(are)j(a)e(subset)i(of)e(the)i(\014tting)e(v) n(ariables)g(of)365 1353 y(the)h(alternativ)o(e)e(mo)q(del.)262 1469 y Fm(The)18 b(Equiv)m(alen)n(t)f(Num)n(b)r(er)g(of)i(P)n(arameters)262 1546 y Fr(Let)898 1596 y Fp(\026)12 b Fr(=)g(tr\()p Fp(L)1055 1568 y Fd(0)1069 1596 y Fp(L)p Fr(\))p Fp(:)262 1671 y Fr(If)h(the)k(^)-23 b Fp(y)395 1677 y Fo(i)423 1671 y Fr(are)14 b(the)g(\014tted)h(v)n(alues,)e (then)796 1786 y Fp(\026)e Fr(=)881 1727 y Fj(P)925 1737 y Fo(n)925 1770 y(i)p Fl(=1)988 1758 y Fr(V)m(ariance)o(\()s(^)-24 b Fp(y)1180 1764 y Fo(i)1195 1758 y Fr(\))p 881 1777 330 2 v 1024 1815 a Fp(\033)1049 1803 y Fl(2)1216 1786 y Fp(:)262 1889 y Fr(W)m(e)16 b(will)f(call)g Fp(\026)i Fr(the)g Fq(e)n(quivalent)h (numb)n(er)f(of)g(p)n(ar)n(ameters)f Fr(since)i(if)d(the)20 b(^)-24 b Fp(y)1461 1895 y Fo(i)1492 1889 y Fr(w)o(ere)18 b(the)f(\014tted) 262 1939 y(v)n(alues)d(for)h(a)g(linear)g(mo)q(del,)e(the)j(righ)o(t)f(side)g (of)g(the)h(last)f(equation)f(w)o(ould)h(b)q(e)g(the)h(n)o(um)o(b)q(er)262 1989 y(of)h(estimated)h(parameters.)32 b Fp(\026)18 b Fr(is)h(greater)g(than) g(or)f(equal)g(to)g Fp(\034)5 b Fr(,)19 b(the)g(n)o(um)o(b)q(er)f(of)g (\014tting)262 2039 y(v)n(ariables,)d(and)h(approac)o(hes)i Fp(\034)j Fr(as)16 b Fp(\013)g Fr(tends)i(to)e(in\014nit)o(y)m(.)24 b(The)17 b(equiv)n(alen)o(t)e(n)o(um)o(b)q(er)h(of)g(pa-)262 2089 y(rameters)d(is)h(one)g(measure)f(of)g(the)i(amoun)o(t)c(of)i(smo)q (othing.)j(Strictly)e(sp)q(eaking,)f Fp(\026)h Fr(dep)q(ends)262 2138 y(on)k Fp(\013)p Fr(,)h(on)g(the)g(v)n(alues)g(of)f(the)h(factors,)h (and)f(on)f(the)i(c)o(hoices)f(of)g(the)g(neigh)o(b)q(orho)q(o)q(d)g(and)262 2188 y(\014tting)12 b(v)n(ariables.)17 b(Ho)o(w)o(ev)o(er,)c(ha)o(ving)f (selected)i(all)e(of)g(these)i(factors)f(except)h Fp(\013)p Fr(,)f(w)o(e)g(can)g(get,)262 2238 y(appro)o(ximately)m(,)e(a)j(desired)i(v)n (alue)d Fp(\026)i Fr(b)o(y)f(taking)g Fp(\013)g Fr(to)g(b)q(e)h(1)p Fp(:)p Fr(2)p Fp(\034)5 b(=\026)p Fr(,)13 b(where)j Fp(\034)j Fr(is)14 b(the)h(n)o(um)o(b)q(er)262 2288 y(of)e(\014tting)g(v)n(ariables.) 991 2574 y(47)p eop %%Page: 46 9 bop 262 307 a Fr(W)m(e)13 b(estimate)g Fp(\033)q Fr(\()p Fp(x)p Fr(\))h(b)o(y)831 410 y Fp(s)p Fr(\()p Fp(x)p Fr(\))e(=)g Fp(s)981 325 y Fj(v)981 348 y(u)981 373 y(u)981 398 y(t)p 1025 325 155 2 v 1045 358 a Fo(n)1025 370 y Fj(X)1028 459 y Fo(i)p Fl(=1)1092 410 y Fp(l)1105 395 y Fl(2)1104 421 y Fo(i)1124 410 y Fr(\()p Fp(x)p Fr(\))p Fp(:)262 530 y Fr(Let)943 596 y Fp(\032)g Fr(=)1025 568 y Fp(\016)1045 553 y Fl(2)1043 578 y(1)p 1025 587 39 2 v 1026 625 a Fp(\016)1044 631 y Fl(2)1068 596 y Fp(:)262 689 y Fr(The)i(distribution)f(of)910 724 y(^)-22 b Fp(g)q Fr(\()p Fp(x)p Fr(\))9 b Fk(\000)h Fp(g)q Fr(\()p Fp(x)p Fr(\))p 909 743 206 2 v 974 781 a Fp(s)p Fr(\()p Fp(x)p Fr(\))262 849 y(is)j(w)o(ell)g (appro)o(ximated)e(b)o(y)j(a)f Fp(t)h Fr(distribution)f(with)g Fp(\032)h Fr(degrees)h(of)e(freedom;)f(w)o(e)i(can)g(use)g(this)262 899 y(result)g(to)g(form)d(con\014dence)16 b(in)o(terv)n(als)d(for)g Fp(g)q Fr(\()p Fp(x)p Fr(\))h(based)h(on)g(^)-23 b Fp(g)q Fr(\()p Fp(x)p Fr(\).)18 b(Notice)c(that)g(the)g(v)n(alue)f Fp(\016)1742 905 y Fl(1)262 949 y Fr(b)o(y)i(whic)o(h)g(w)o(e)h(divide)f(the)h (sum-of-squares)f(of)g(residuals)h(is)f(not)h(the)g(same)e(as)i(the)g(v)n (alue)f Fp(\032)262 998 y Fr(used)c(for)g(the)g(degrees)i(of)d(freedom)g(of)g (the)i Fp(t)f Fr(distribution.)16 b(F)m(or)11 b(classical)f(parametric)g (\014tting,)262 1048 y(these)15 b(t)o(w)o(o)f(v)n(alues)f(are)i(equal.)j(F)m (or)13 b(lo)q(ess,)i(they)f(are)h(t)o(ypically)d(close)j(but)f(not)g(close)g (enough)262 1098 y(to)e(ignore)h(the)g(di\013erence.)19 b(W)m(e)13 b(will)e(refer)j(to)e Fp(\032)i Fr(as)e(the)i Fq(lo)n(ok-up)g(de)n(gr)n(e)n (es)f(of)h(fr)n(e)n(e)n(dom)e Fr(since)i(it)262 1148 y(is)g(the)h(degrees)i (of)d(freedom)g(of)g(the)h(distribution)f(that)h(w)o(e)g(lo)q(ok)e(up)i(to)g (get)f(the)i(con\014dence)262 1198 y(in)o(terv)n(al.)262 1314 y Fm(Analysis)i(of)h(V)-5 b(ariance)19 b(for)f(Nested)g(Mo)r(dels)262 1390 y Fr(W)m(e)13 b(can)g(use)i(the)f(analysis)f(of)f(v)n(ariance)i(to)f (test)i(a)e(n)o(ull)f(lo)q(cal)h(regression)i(mo)q(del)d(against)h(an)262 1446 y(alternativ)o(e)h(one.)19 b(Let)14 b(the)h(parameters)f(of)g(the)h(n)o (ull)e(mo)q(del)g(b)q(e)i Fp(\013)1334 1431 y Fl(\()p Fo(n)p Fl(\))1382 1446 y Fr(,)f Fp(\025)1432 1431 y Fl(\()p Fo(n)p Fl(\))1480 1446 y Fr(,)g Fp(\016)1526 1424 y Fl(\()p Fo(n)p Fl(\))1524 1457 y(1)1575 1446 y Fr(,)f(and)h Fp(\016)1701 1424 y Fl(\()p Fo(n)p Fl(\))1699 1457 y(2)1750 1446 y Fr(.)262 1496 y(Let)j(the)g(parameters)g(of)g(the)g(alternativ)o(e)g(mo)q(del)e(b)q(e)j Fp(\013)p Fr(,)f Fp(\025)p Fr(,)g Fp(\016)1280 1502 y Fl(1)1299 1496 y Fr(,)h(and)e Fp(\016)1430 1502 y Fl(2)1449 1496 y Fr(.)28 b(F)m(or)16 b(the)i(test)g(to)262 1546 y(mak)o(e)13 b(sense,)k(the)e(n)o(ull) f(mo)q(del)g(should)h(b)q(e)h Fq(neste)n(d)f Fr(in)g(the)g(alternativ)o(e;)g (w)o(e)h(will)d(de\014ne)j(this)262 1595 y(concept)h(shortly)m(.)26 b(Let)17 b Fp(r)q(ss)h Fr(b)q(e)f(the)g(residual)g(sum-of-squares)f(of)g(the) h(alternativ)o(e)f(mo)q(del,)262 1645 y(and)d(let)h Fp(r)q(ss)460 1630 y Fl(\()p Fo(n)p Fl(\))523 1645 y Fr(b)q(e)h(the)f(residual)g (sum-of-squares)f(of)h(the)g(n)o(ull)f(mo)q(del.)324 1695 y(The)h(test)h (statistic,)f(whic)o(h)g(is)g(analogous)f(to)h(that)g(for)g(the)h(analysis)e (of)g(v)n(ariance)h(in)g(the)262 1745 y(parametric)f(case,)h(is)728 1829 y Fp(F)j Fr(=)820 1801 y(\()p Fp(r)q(ss)894 1785 y Fl(\()p Fo(n)p Fl(\))953 1801 y Fk(\000)10 b Fp(r)q(ss)p Fr(\))p Fp(=)p Fr(\()p Fp(\016)1126 1779 y Fl(\()p Fo(n)p Fl(\))1124 1812 y(1)1184 1801 y Fk(\000)g Fp(\016)1244 1807 y Fl(1)1263 1801 y Fr(\))p 820 1819 459 2 v 991 1857 a Fp(r)q(ss=\016)1088 1863 y Fl(1)1284 1829 y Fp(:)262 1925 y(F)20 b Fr(has)15 b(a)f(distribution)g (that)h(is)g(w)o(ell)f(appro)o(ximated)f(b)o(y)i(an)f Fp(F)20 b Fr(distribution)15 b(with)f(denomi-)262 1975 y(nator)f(lo)q(ok-up)f (degrees)k(of)c(freedom)h Fp(\032)p Fr(,)h(de\014ned)g(earlier,)f(and)h(n)o (umerator)e(lo)q(ok-up)h(degrees)262 2025 y(of)g(freedom)858 2101 y Fp(\027)h Fr(=)941 2072 y(\()p Fp(\016)977 2051 y Fl(\()p Fo(n)p Fl(\))975 2084 y(1)1035 2072 y Fk(\000)c Fp(\016)1095 2078 y Fl(1)1114 2072 y Fr(\))1130 2057 y Fl(2)p 941 2091 208 2 v 967 2139 a Fp(\016)987 2118 y Fl(\()p Fo(n)p Fl(\))985 2150 y(2)1045 2139 y Fk(\000)f Fp(\016)1104 2145 y Fl(2)1154 2101 y Fp(:)324 2208 y Fr(The)16 b(concept)g(of)f(a)g(n)o(ull)g(mo)q(del)e(b) q(eing)j(nested)h(in)e(the)h(alternativ)o(e)f(expresses)j(the)e(idea)262 2258 y(that)c(the)g(alternativ)o(e)g(is)g(capable)g(of)f(capturing)h(an)o(y)g (e\013ect)h(that)f(the)h(n)o(ull)e(can)h(capture,)h(but)262 2308 y(the)k(de\014nition)g(is)h(more)e(precisely)i(a)f(sp)q(eci\014cation)i (of)d(when)i(it)f(mak)o(es)f(sense)j(to)f(use)g(the)262 2358 y(analysis)12 b(of)h(v)n(ariance)g(to)g(compare)g(t)o(w)o(o)g(mo)q(dels.)j (The)e(n)o(ull)e(is)i(nested)g(in)f(the)h(alternativ)o(e)f(if)262 2408 y(the)h(follo)o(wing)d(conditions)j(hold:)991 2574 y(46)p eop %%Page: 45 10 bop 262 307 a Fm(4.1)55 b(Statistical)18 b(Inference)262 384 y Fr(Initially)m(,)9 b(w)o(e)j(will)f(supp)q(ose)i(that)f(the)h(errors)g(ha)o (v)o(e)f(b)q(een)h(sp)q(eci\014ed)h(to)e(b)q(e)g(Gaussian)g(and)g(the)262 434 y(v)n(ariances)i(ha)o(v)o(e)f(b)q(een)i(sp)q(eci\014ed)h(to)d(b)q(e)i (constan)o(t.)324 483 y(One)j(imp)q(ortan)o(t)d(prop)q(ert)o(y)j(of)f(a)g (Gaussian-error)h(lo)q(ess)f(estimate,)i(^)-23 b Fp(g)r Fr(\()p Fp(x)p Fr(\),)17 b(is)g(that)h(it)f(is)262 533 y(linear)c(in)g Fp(y)445 539 y Fo(i)460 533 y Fr(|that)g(is,)855 614 y(^)-22 b Fp(g)q Fr(\()p Fp(x)p Fr(\))11 b(=)1006 562 y Fo(n)986 575 y Fj(X)989 663 y Fo(i)p Fl(=1)1053 614 y Fp(l)1065 620 y Fo(i)1079 614 y Fr(\()p Fp(x)p Fr(\))p Fp(y)1155 620 y Fo(i)262 719 y Fr(where)21 b(the)f Fp(l)477 725 y Fo(i)492 719 y Fr(\()p Fp(x)p Fr(\))f(do)h(not)g(dep)q(end)h(on)f(the)h Fp(y)1023 725 y Fo(i)1037 719 y Fr(.)36 b(This)20 b(linearit)o(y)f(results)i(in)f(distribution)262 769 y(prop)q(erties)f(of)f(the)h(estimate)f(that)g(are)h(v)o(ery)g(similar)d (to)i(those)h(for)f(classical)g(parametric)262 819 y(\014tting.)324 869 y(Supp)q(ose)f(that)g(the)g(diagnostic)f(metho)q(ds)g(ha)o(v)o(e)g(b)q (een)i(applied)e(and)g(ha)o(v)o(e)h(rev)o(ealed)g(no)262 919 y(lac)o(k)e(of)g(\014t)h(in)g(^)-22 b Fp(g)q Fr(\()p Fp(x)p Fr(\);)16 b(w)o(e)g(will)e(tak)o(e)i(this)g(to)f(mean)g(that)g Fp(E)t Fr(^)-23 b Fp(g)r Fr(\()p Fp(x)p Fr(\))10 b Fk(\000)h Fp(g)q Fr(\()p Fp(x)p Fr(\))16 b(is)f(small.)22 b(Supp)q(ose)262 968 y(further)14 b(that)f(diagnostic)f(c)o(hec)o(king)i(has)f(v)o(eri\014ed)h (the)g(sp)q(eci\014cations)g(of)f(the)h(error)g(terms)f(in)262 1018 y(the)h(mo)q(del.)262 1132 y Fm(Estimation)i(of)j Fe(\033)262 1209 y Fr(Since)c(^)-22 b Fp(g)q Fr(\()p Fp(x)p Fr(\))14 b(is)g(linear)f(in)h Fp(y)687 1215 y Fo(i)701 1209 y Fr(,)f(the)i(\014tted)f(v)n(alue)g(at)f Fp(x)1090 1215 y Fo(i)1118 1209 y Fr(can)h(b)q(e)g(written)862 1320 y(^)-24 b Fp(y)879 1326 y Fo(i)904 1320 y Fr(=)968 1268 y Fo(n)948 1280 y Fj(X)950 1369 y Fo(j)r Fl(=1)1015 1320 y Fp(l)1027 1326 y Fo(j)1045 1320 y Fr(\()p Fp(x)1085 1326 y Fo(i)1099 1320 y Fr(\))p Fp(y)1135 1326 y Fo(j)1153 1320 y Fp(:)262 1442 y Fr(Let)14 b Fp(L)g Fr(b)q(e)g(the)h(matrix)d(whose)i(\()p Fp(i;)7 b(j)r Fr(\)th)15 b(elemen)o(t)e(is)h Fp(l)1108 1448 y Fo(j)1126 1442 y Fr(\()p Fp(x)1166 1448 y Fo(i)1180 1442 y Fr(\))g(and)f(let)924 1509 y(\026)919 1520 y Fp(L)f Fr(=)g Fp(I)h Fk(\000)c Fp(L)262 1598 y Fr(where)15 b Fp(I)i Fr(is)d(the)g Fp(n)9 b Fk(\002)h Fp(n)k Fr(iden)o(tit)o(y)f(matrix.)j(F)m(or)e Fp(k)g Fr(=)g(1)g(and)g(2,)f(let)882 1676 y Fp(\016)900 1682 y Fo(k)932 1676 y Fr(=)f(tr\()1029 1665 y(\026)1024 1676 y Fp(L)1052 1661 y Ff(0)1070 1665 y Fr(\026)1065 1676 y Fp(L)p Fr(\))1109 1661 y Fo(k)1129 1676 y Fp(:)262 1754 y Fr(W)m(e)h(estimate)g Fp(\033)i Fr(b)o(y)f(the)g(scale)h(estimate)870 1875 y Fp(s)d Fr(=)945 1797 y Fj(s)p 987 1797 155 2 v 992 1816 a(P)1035 1826 y Fo(n)1035 1859 y(i)p Fl(=1)1101 1847 y Fr(^)-24 b Fp(")1117 1832 y Fl(2)1117 1858 y Fo(i)p 992 1866 145 2 v 1045 1904 a Fp(\016)1063 1910 y Fl(1)1141 1875 y Fp(:)262 2017 y Fm(Con\014dence)18 b(In)n(terv)m(als)g(for)h Fe(g)r Fs(\()p Fe(x)p Fs(\))262 2094 y Fr(Since)849 2167 y(^)-22 b Fp(g)q Fr(\()p Fp(x)p Fr(\))12 b(=)1000 2115 y Fo(n)980 2127 y Fj(X)984 2216 y Fo(i)p Fl(=1)1047 2167 y Fp(l)1059 2173 y Fo(i)1074 2167 y Fr(\()p Fp(x)p Fr(\))p Fp(y)1150 2173 y Fo(i)1164 2167 y Fp(;)262 2272 y Fr(the)i(standard)g (deviation)f(of)i(^)-22 b Fp(g)q Fr(\()p Fp(x)p Fr(\))14 b(is)826 2403 y Fp(\033)q Fr(\()p Fp(x)p Fr(\))d(=)h Fp(\033)987 2318 y Fj(v)987 2341 y(u)987 2366 y(u)987 2391 y(t)p 1031 2318 155 2 v 1051 2351 a Fo(n)1031 2363 y Fj(X)1034 2452 y Fo(i)p Fl(=1)1098 2403 y Fp(l)1111 2388 y Fl(2)1110 2414 y Fo(i)1130 2403 y Fr(\()p Fp(x)p Fr(\))p Fp(:)991 2574 y Fr(45)p eop %%Page: 44 11 bop 262 307 a Fr(can)14 b(try)g(this)g(on)f(the)i(gas)f(data:)324 386 y Fi(struct)37 b(loess_str)o(uc)o(t)76 b(gas_slow)o(er;)324 477 y(loess_set)o(up\()o(E,)16 b(NOx,)i(n,)h(p,)g(&gas_slow)o(er)o(\);)324 523 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pop /uy exch def /ux exch def /ly exch def /lx exch def uy ly sub ux lx sub Landscape {exch} if /Width exch def /Height exch def lx ly translate Landscape {90 rotate 0 Height neg translate} if 1 RastersPerPoint div dup scale} bd /SetPchSize { Pch 0 get 254 ne { gsave newpath 0 0 moveto Pch false charpath flattenpath pathbbox exch 3 1 roll add 2 div neg /Pch-y exch def add 2 div neg /Pch-x exch def grestore } if } bd /TextShow {CharRot StringRot sub dup 0 eq {pop SimpleShow} {FancyShow} ifelse} bd /SimpleShow {0 Text-y 2 div neg rmoveto Show} bd /FancyShow { /RotDiff exch def /Cos RotDiff cos abs def /Sin RotDiff sin abs def { ( ) dup 0 4 -1 roll put dup stringwidth pop /CharWidth exch def Cos 0 eq { Text-y Sin div } { Sin 0 eq { CharWidth Cos div } { /H Text-y Sin div def /W CharWidth Cos div def H W lt {H} {W} ifelse } ifelse } ifelse 2 div /CharDist exch def CharDist 0 translate 0 0 moveto gsave RotDiff rotate CharWidth 2 div neg Text-y 2 div neg rmoveto Outline {false charpath stroke} {show} ifelse grestore CharDist 0 translate 0 0 moveto } forall } bd /Show {Outline {false charpath stroke} {show} ifelse} bd /BoxClip {/CLW currentlinewidth def 2 {CLW add 4 1 roll} repeat 2 {CLW sub 4 1 roll} repeat initclip newpath 2 index exch 2 index exch dup 6 index exch moveto 3 {lineto} repeat closepath clip newpath} bd /Subregion {/A exch def /Uy exch def /Ux exch def /Ly exch def /Lx exch def Ux Lx sub A 0 get mul Lx add Uy Ly sub A 1 get mul Ly add Ux Lx sub A 2 get mul Lx add Uy Ly sub A 3 get mul Ly add} bd /SetFigure {Page aload pop Figure Subregion} bd /SetPlot {SetFigure Plot Subregion} bd /SetClip {ClipToPlot {SetPlot} {SetFigure} ifelse BoxClip} bd /SetPage {0 0 Width Height Page astore RastersPerPoint ScaleArray} bd /PageBegin {save /PageContext exch def /InPage true def} bd /PageEnd {PageContext restore /InPage false def} bd /Landscape false def /Region [21.48 111.72 590.28 680.52] def /RastersPerInch 300 def /PointSize 8.77778 def /Fonts [ /Helvetica 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1490 L 919 1500 L 913 1504 L 901 1511 L 885 1523 L 883 1525 L 865 1540 L 863 1541 L 847 1559 L 845 1560 L 832 1578 L 828 1583 L 820 1597 L 811 1616 L 810 1617 L 803 1634 L 795 1653 L 792 1659 L 787 1671 L 779 1690 L 774 1700 L 770 1709 L 762 1727 L 756 1740 L 753 1746 L 744 1764 L 737 1779 L 735 1783 L 726 1801 L 719 1815 L 717 1820 L 707 1839 L 701 1850 L E B 1593 2117 M 1588 2099 L 1583 2080 L 1578 2062 L 1575 2051 L 1572 2043 L 1566 2024 L 1560 2006 L 1557 1997 L 1553 1987 L 1546 1969 L 1538 1950 L 1538 1950 L 1531 1931 L 1523 1913 L 1520 1908 L 1514 1894 L 1505 1876 L 1502 1869 L 1497 1857 L 1488 1839 L 1484 1831 L 1478 1820 L 1469 1801 L 1466 1794 L 1460 1783 L 1451 1764 L 1447 1757 L 1442 1746 L 1433 1727 L 1429 1719 L 1424 1709 L 1416 1690 L 1411 1678 L 1408 1671 L 1399 1653 L 1393 1640 L 1389 1634 L 1379 1616 L 1375 1609 L 1367 1597 L 1356 1582 L 1354 1578 L 1338 1560 L 1338 1560 L 1320 1542 L 1320 1541 L 1302 1524 L 1300 1523 L 1284 1507 L 1281 1504 L 1265 1489 L 1261 1486 L 1247 1472 L 1241 1467 L 1229 1456 L 1219 1448 L 1211 1442 L 1194 1430 L 1192 1429 L 1174 1419 L 1159 1411 L 1156 1410 L 1138 1402 L 1120 1395 L 1111 1393 L 1101 1390 L 1083 1386 L 1065 1383 L 1047 1382 L 1029 1381 L 1010 1381 L 992 1383 L 974 1385 L 956 1388 L 938 1392 L 934 1393 L 919 1396 L 901 1401 L 883 1407 L 870 1411 L 865 1413 L 847 1420 L 828 1428 L 823 1430 L 810 1436 L 792 1445 L 786 1448 L 774 1457 L 758 1467 L 756 1470 L 740 1486 L 737 1490 L 730 1504 L 727 1523 L 728 1541 L 729 1560 L 731 1578 L 732 1597 L 731 1616 L 729 1634 L 725 1653 L 719 1671 L 719 1672 L 712 1690 L 704 1709 L 701 1715 L E B 1747 2117 M 1739 2109 L 1734 2099 L 1723 2080 L 1720 2076 L 1714 2062 L 1704 2043 L 1702 2040 L 1695 2024 L 1686 2006 L 1684 2002 L 1677 1987 L 1668 1969 L 1666 1965 L 1659 1950 L 1649 1931 L 1648 1928 L 1640 1913 L 1631 1894 L 1629 1892 L 1621 1876 L 1611 1858 L 1611 1857 L 1601 1839 L 1593 1824 L 1591 1820 L 1581 1801 L 1575 1790 L 1571 1783 L 1561 1764 L 1557 1757 L 1551 1746 L 1541 1727 L 1538 1723 L 1531 1709 L 1521 1690 L 1520 1688 L 1512 1671 L 1502 1653 L 1502 1652 L 1492 1634 L 1484 1621 L 1480 1616 L 1468 1597 L 1466 1593 L 1455 1578 L 1447 1569 L 1440 1560 L 1429 1549 L 1422 1541 L 1411 1531 L 1402 1523 L 1393 1514 L 1381 1504 L 1375 1499 L 1357 1486 L 1356 1485 L 1338 1471 L 1333 1467 L 1320 1457 L 1309 1448 L 1302 1442 L 1287 1430 L 1284 1427 L 1265 1411 L 1265 1411 L 1247 1396 L 1243 1393 L 1229 1382 L 1218 1374 L 1211 1369 L 1192 1358 L 1188 1356 L 1174 1348 L 1156 1340 L 1150 1337 L 1138 1331 L 1120 1324 L 1103 1318 L 1101 1318 L 1083 1313 L 1065 1310 L 1047 1308 L 1029 1307 L 1010 1307 L 992 1308 L 974 1310 L 956 1313 L 938 1316 L 928 1318 L 919 1320 L 901 1325 L 883 1330 L 865 1336 L 861 1337 L 847 1341 L 828 1347 L 810 1352 L 800 1356 L 792 1358 L 774 1364 L 756 1369 L 738 1374 L 737 1374 L 719 1379 L 701 1384 L E B 1757 1791 M 1743 1783 L 1739 1780 L 1720 1766 L 1719 1764 L 1702 1749 L 1699 1746 L 1684 1729 L 1682 1727 L 1666 1709 L 1666 1708 L 1651 1690 L 1648 1685 L 1637 1671 L 1629 1661 L 1624 1653 L 1611 1636 L 1610 1634 L 1596 1616 L 1593 1612 L 1582 1597 L 1575 1588 L 1567 1578 L 1557 1566 L 1551 1560 L 1538 1546 L 1534 1541 L 1520 1528 L 1515 1523 L 1502 1512 L 1493 1504 L 1484 1496 L 1470 1486 L 1466 1482 L 1447 1469 L 1445 1467 L 1429 1456 L 1417 1448 L 1411 1445 L 1393 1433 L 1387 1430 L 1375 1422 L 1357 1411 L 1356 1411 L 1338 1399 L 1330 1393 L 1320 1385 L 1306 1374 L 1302 1371 L 1284 1356 L 1284 1355 L 1265 1341 L 1260 1337 L 1247 1328 L 1233 1318 L 1229 1316 L 1211 1304 L 1204 1300 L 1192 1293 L 1174 1282 L 1172 1281 L 1156 1273 L 1138 1263 L 1136 1263 L 1120 1255 L 1101 1249 L 1087 1244 L 1083 1243 L 1065 1238 L 1047 1235 L 1029 1232 L 1010 1230 L 992 1228 L 974 1228 L 956 1228 L 938 1229 L 919 1231 L 901 1234 L 883 1238 L 865 1244 L 864 1244 L 847 1250 L 828 1256 L 811 1263 L 810 1263 L 792 1269 L 774 1275 L 755 1281 L 755 1281 L 737 1286 L 719 1290 L 701 1293 L E B 1757 1598 M 1755 1597 L 1739 1588 L 1725 1578 L 1720 1575 L 1702 1562 L 1699 1560 L 1684 1549 L 1675 1541 L 1666 1534 L 1652 1523 L 1648 1520 L 1629 1505 L 1628 1504 L 1611 1491 L 1604 1486 L 1593 1477 L 1579 1467 L 1575 1464 L 1557 1452 L 1551 1448 L 1538 1440 L 1521 1430 L 1520 1429 L 1502 1419 L 1488 1411 L 1484 1409 L 1466 1399 L 1454 1393 L 1447 1389 L 1429 1380 L 1419 1374 L 1411 1369 L 1393 1359 L 1387 1356 L 1375 1349 L 1356 1338 L 1354 1337 L 1338 1328 L 1323 1318 L 1320 1316 L 1302 1305 L 1294 1300 L 1284 1293 L 1266 1281 L 1265 1281 L 1247 1269 L 1237 1263 L 1229 1258 L 1211 1246 L 1208 1244 L 1192 1235 L 1178 1226 L 1174 1223 L 1156 1212 L 1145 1207 L 1138 1204 L 1120 1196 L 1101 1189 L 1100 1188 L 1083 1182 L 1065 1176 L 1047 1171 L 1044 1170 L 1029 1165 L 1010 1161 L 992 1156 L 974 1152 L 972 1151 L 956 1147 L 938 1143 L 919 1139 L 901 1135 L 892 1133 L 883 1130 L 865 1124 L 847 1117 L 840 1114 L 828 1105 L 818 1095 L 810 1089 L 800 1077 L 792 1069 L 784 1058 L 774 1044 L 771 1040 L 762 1021 L 756 1005 L 755 1003 L 750 984 L 747 965 L 745 947 L 745 928 L 747 910 L 747 891 L 747 873 L 745 854 L 744 835 L 742 817 L 739 798 L 737 783 L 737 780 L 734 761 L 731 743 L 727 724 L 724 705 L 720 687 L 719 682 L 716 668 L 713 650 L 709 631 L 706 612 L 702 594 L 701 585 L E B 749 297 M 746 315 L 743 334 L 741 352 L 739 371 L 738 390 L 738 408 L 738 427 L 739 445 L 740 464 L 742 482 L 744 501 L 746 520 L 749 538 L 752 557 L 756 575 L 756 575 L 759 594 L 763 612 L 767 631 L 770 650 L 774 665 L 774 668 L 778 687 L 782 705 L 786 724 L 790 743 L 792 751 L 794 761 L 798 780 L 801 798 L 804 817 L 808 835 L 810 850 L 811 854 L 814 873 L 816 891 L 818 910 L 819 928 L 823 947 L 828 961 L 830 965 L 841 984 L 847 991 L 856 1003 L 865 1011 L 877 1021 L 883 1026 L 901 1038 L 904 1040 L 919 1048 L 938 1058 L 939 1058 L 956 1067 L 974 1075 L 979 1077 L 992 1083 L 1010 1091 L 1020 1095 L 1029 1099 L 1047 1108 L 1060 1114 L 1065 1116 L 1083 1124 L 1101 1133 L 1101 1133 L 1120 1142 L 1138 1151 L 1139 1151 L 1156 1160 L 1171 1170 L 1174 1172 L 1192 1184 L 1200 1188 L 1211 1195 L 1229 1206 L 1230 1207 L 1247 1217 L 1262 1226 L 1265 1228 L 1284 1239 L 1293 1244 L 1302 1250 L 1320 1260 L 1325 1263 L 1338 1269 L 1356 1277 L 1366 1281 L 1375 1285 L 1393 1292 L 1411 1299 L 1414 1300 L 1429 1306 L 1447 1313 L 1461 1318 L 1466 1320 L 1484 1328 L 1502 1335 L 1507 1337 L 1520 1343 L 1538 1350 L 1550 1356 L 1557 1358 L 1575 1367 L 1590 1374 L 1593 1375 L 1611 1384 L 1628 1393 L 1629 1393 L 1648 1403 L 1663 1411 L 1666 1413 L 1684 1423 L 1696 1430 L 1702 1433 L 1720 1444 L 1729 1448 L 1739 1453 L 1757 1463 L E B 804 297 M 800 315 L 797 334 L 794 352 L 793 371 L 792 383 L 792 390 L 791 408 L 792 427 L 792 433 L 793 445 L 794 464 L 796 482 L 798 501 L 800 520 L 803 538 L 806 557 L 810 575 L 810 577 L 813 594 L 817 612 L 821 631 L 825 650 L 828 664 L 829 668 L 834 687 L 838 705 L 842 724 L 847 742 L 847 743 L 851 761 L 855 780 L 860 798 L 864 817 L 865 820 L 869 835 L 874 854 L 879 873 L 883 886 L 884 891 L 889 910 L 894 928 L 901 945 L 902 947 L 916 965 L 919 970 L 934 984 L 938 987 L 956 1001 L 958 1003 L 974 1013 L 989 1021 L 992 1023 L 1010 1032 L 1025 1040 L 1029 1041 L 1047 1050 L 1065 1058 L 1065 1058 L 1083 1067 L 1101 1076 L 1103 1077 L 1120 1086 L 1137 1095 L 1138 1096 L 1156 1108 L 1164 1114 L 1174 1121 L 1188 1133 L 1192 1136 L 1211 1149 L 1213 1151 L 1229 1161 L 1244 1170 L 1247 1172 L 1265 1181 L 1281 1188 L 1284 1190 L 1302 1198 L 1320 1207 L 1320 1207 L 1338 1215 L 1356 1222 L 1368 1226 L 1375 1228 L 1393 1233 L 1411 1238 L 1429 1243 L 1435 1244 L 1447 1247 L 1466 1251 L 1484 1256 L 1502 1260 L 1516 1263 L 1520 1264 L 1538 1268 L 1557 1272 L 1575 1276 L 1593 1281 L 1594 1281 L 1611 1286 L 1629 1291 L 1648 1296 L 1658 1300 L 1666 1302 L 1684 1309 L 1702 1317 L 1706 1318 L 1720 1325 L 1739 1334 L 1743 1337 L 1757 1344 L E B 861 297 M 856 315 L 853 334 L 850 352 L 848 371 L 847 389 L 847 390 L 846 408 L 846 427 L 847 439 L 847 445 L 848 464 L 850 482 L 852 501 L 854 520 L 857 538 L 860 557 L 864 575 L 865 582 L 867 594 L 871 612 L 875 631 L 879 650 L 883 667 L 883 668 L 888 687 L 892 705 L 897 724 L 901 740 L 902 743 L 907 761 L 912 780 L 917 798 L 919 806 L 923 817 L 929 835 L 937 854 L 938 856 L 945 873 L 953 891 L 956 897 L 961 910 L 970 928 L 974 934 L 983 947 L 992 956 L 1003 965 L 1010 971 L 1028 984 L 1029 985 L 1047 996 L 1057 1003 L 1065 1007 L 1083 1017 L 1092 1021 L 1101 1026 L 1120 1035 L 1128 1040 L 1138 1045 L 1156 1055 L 1161 1058 L 1174 1067 L 1186 1077 L 1192 1083 L 1206 1095 L 1211 1100 L 1227 1114 L 1229 1116 L 1247 1127 L 1257 1133 L 1265 1137 L 1284 1146 L 1296 1151 L 1302 1153 L 1320 1161 L 1338 1167 L 1348 1170 L 1356 1172 L 1375 1177 L 1393 1181 L 1411 1184 L 1429 1187 L 1441 1188 L 1447 1189 L 1466 1191 L 1484 1192 L 1502 1193 L 1520 1193 L 1538 1194 L 1557 1193 L 1575 1193 L 1593 1192 L 1611 1191 L 1629 1190 L 1648 1189 L 1658 1188 L 1666 1188 L 1684 1187 L 1702 1187 L 1720 1188 L 1735 1188 L 1739 1189 L 1757 1191 L E B 922 297 M 919 305 L 916 315 L 912 334 L 908 352 L 906 371 L 904 390 L 903 408 L 903 427 L 903 445 L 904 464 L 905 482 L 907 501 L 909 520 L 912 538 L 915 557 L 918 575 L 919 585 L 921 594 L 925 612 L 928 631 L 933 650 L 937 668 L 938 670 L 942 687 L 947 705 L 952 724 L 956 737 L 957 743 L 963 761 L 969 780 L 974 795 L 975 798 L 982 817 L 991 835 L 992 838 L 1001 854 L 1010 870 L 1012 873 L 1024 891 L 1029 899 L 1036 910 L 1047 925 L 1049 928 L 1065 944 L 1068 947 L 1083 959 L 1092 965 L 1101 972 L 1120 983 L 1121 984 L 1138 994 L 1152 1003 L 1156 1005 L 1174 1016 L 1181 1021 L 1192 1030 L 1204 1040 L 1211 1045 L 1226 1058 L 1229 1061 L 1247 1075 L 1250 1077 L 1265 1086 L 1281 1095 L 1284 1097 L 1302 1106 L 1320 1114 L 1320 1114 L 1338 1120 L 1356 1126 L 1375 1131 L 1384 1133 L 1393 1134 L 1411 1137 L 1429 1139 L 1447 1140 L 1466 1141 L 1484 1141 L 1502 1141 L 1520 1140 L 1538 1139 L 1557 1137 L 1575 1135 L 1593 1133 L 1594 1133 L 1611 1130 L 1629 1128 L 1648 1126 L 1666 1123 L 1684 1121 L 1702 1119 L 1720 1118 L 1739 1117 L 1757 1116 L E B 989 297 M 982 315 L 976 334 L 974 340 L 971 352 L 968 371 L 965 390 L 963 408 L 962 427 L 962 445 L 962 464 L 963 482 L 964 501 L 966 520 L 968 538 L 971 557 L 974 575 L 974 578 L 977 594 L 980 612 L 984 631 L 988 650 L 992 667 L 993 668 L 998 687 L 1003 705 L 1009 724 L 1010 730 L 1015 743 L 1021 761 L 1028 780 L 1029 781 L 1036 798 L 1045 817 L 1047 820 L 1056 835 L 1065 849 L 1069 854 L 1083 873 L 1083 873 L 1099 891 L 1101 894 L 1116 910 L 1120 914 L 1133 928 L 1138 932 L 1156 947 L 1156 947 L 1174 960 L 1182 965 L 1192 973 L 1207 984 L 1211 987 L 1229 1001 L 1230 1003 L 1247 1015 L 1256 1021 L 1265 1027 L 1284 1038 L 1287 1040 L 1302 1047 L 1320 1056 L 1325 1058 L 1338 1064 L 1356 1070 L 1375 1076 L 1379 1077 L 1393 1080 L 1411 1083 L 1429 1086 L 1447 1087 L 1466 1088 L 1484 1087 L 1502 1087 L 1520 1085 L 1538 1084 L 1557 1081 L 1575 1079 L 1589 1077 L 1593 1076 L 1611 1073 L 1629 1070 L 1648 1067 L 1666 1064 L 1684 1061 L 1702 1058 L 1702 1058 L 1720 1055 L 1739 1053 L 1757 1051 L E B 1064 297 M 1055 315 L 1047 334 L 1047 334 L 1041 352 L 1036 371 L 1032 390 L 1029 408 L 1029 409 L 1027 427 L 1025 445 L 1025 464 L 1025 482 L 1026 501 L 1027 520 L 1029 538 L 1029 539 L 1031 557 L 1033 575 L 1036 594 L 1039 612 L 1043 631 L 1047 650 L 1047 650 L 1052 668 L 1057 687 L 1063 705 L 1065 712 L 1069 724 L 1076 743 L 1083 759 L 1084 761 L 1092 780 L 1101 798 L 1102 798 L 1113 817 L 1120 825 L 1127 835 L 1138 848 L 1144 854 L 1156 867 L 1162 873 L 1174 884 L 1182 891 L 1192 900 L 1203 910 L 1211 916 L 1226 928 L 1229 931 L 1247 945 L 1250 947 L 1265 958 L 1276 965 L 1284 970 L 1302 980 L 1310 984 L 1320 989 L 1338 996 L 1356 1002 L 1357 1003 L 1375 1008 L 1393 1012 L 1411 1015 L 1429 1018 L 1447 1019 L 1466 1020 L 1484 1020 L 1502 1019 L 1520 1017 L 1538 1014 L 1557 1011 L 1575 1008 L 1593 1003 L 1596 1003 L 1611 998 L 1629 991 L 1648 984 L 1648 984 L 1666 974 L 1679 965 L 1684 962 L 1701 947 L 1702 945 L 1714 928 L 1720 913 L 1721 910 L 1725 891 L 1727 873 L 1728 854 L 1730 835 L 1732 817 L 1736 798 L 1739 788 L 1741 780 L 1743 761 L 1744 743 L 1744 724 L 1743 705 L 1743 687 L 1742 668 L 1742 650 L 1743 631 L 1744 612 L 1746 594 L 1750 575 L 1753 557 L 1757 540 L E B 1155 297 M 1142 315 L 1138 322 L 1131 334 L 1122 352 L 1120 358 L 1115 371 L 1109 390 L 1104 408 L 1101 419 L 1100 427 L 1097 445 L 1096 464 L 1095 482 L 1094 501 L 1095 520 L 1096 538 L 1097 557 L 1099 575 L 1101 593 L 1102 594 L 1105 612 L 1108 631 L 1113 650 L 1118 668 L 1120 674 L 1124 687 L 1130 705 L 1138 724 L 1138 724 L 1147 743 L 1156 761 L 1156 761 L 1167 780 L 1174 790 L 1180 798 L 1192 814 L 1195 817 L 1211 832 L 1214 835 L 1229 848 L 1235 854 L 1247 863 L 1259 873 L 1265 877 L 1284 889 L 1287 891 L 1302 899 L 1320 908 L 1324 910 L 1338 915 L 1356 920 L 1375 924 L 1393 927 L 1406 928 L 1411 929 L 1429 929 L 1447 928 L 1449 928 L 1466 927 L 1484 924 L 1502 919 L 1520 914 L 1531 910 L 1538 907 L 1557 898 L 1568 891 L 1575 886 L 1592 873 L 1593 872 L 1610 854 L 1611 852 L 1623 835 L 1629 825 L 1634 817 L 1642 798 L 1648 785 L 1650 780 L 1657 761 L 1663 743 L 1666 731 L 1668 724 L 1672 705 L 1676 687 L 1679 668 L 1682 650 L 1684 639 L 1685 631 L 1688 612 L 1692 594 L 1695 575 L 1699 557 L 1702 541 L 1703 538 L 1706 520 L 1710 501 L 1714 482 L 1717 464 L 1720 447 L 1721 445 L 1723 427 L 1726 408 L 1727 390 L 1727 371 L 1726 352 L 1723 334 L 1720 321 L 1719 315 L 1712 297 L E B 1290 297 M 1284 301 L 1266 315 L 1265 316 L 1247 333 L 1246 334 L 1231 352 L 1229 355 L 1218 371 L 1211 383 L 1207 390 L 1199 408 L 1192 424 L 1192 427 L 1187 445 L 1183 464 L 1180 482 L 1178 501 L 1177 520 L 1177 538 L 1178 557 L 1179 575 L 1182 594 L 1185 612 L 1189 631 L 1192 645 L 1194 650 L 1200 668 L 1208 687 L 1211 693 L 1217 705 L 1227 724 L 1229 727 L 1240 743 L 1247 752 L 1255 761 L 1265 772 L 1274 780 L 1284 787 L 1300 798 L 1302 799 L 1320 809 L 1338 817 L 1338 817 L 1356 823 L 1375 827 L 1393 829 L 1411 829 L 1429 827 L 1447 824 L 1466 818 L 1468 817 L 1484 809 L 1501 798 L 1502 798 L 1520 782 L 1522 780 L 1538 762 L 1539 761 L 1554 743 L 1557 739 L 1567 724 L 1575 712 L 1578 705 L 1588 687 L 1593 677 L 1597 668 L 1604 650 L 1611 631 L 1611 629 L 1616 612 L 1620 594 L 1625 575 L 1629 557 L 1629 554 L 1632 538 L 1635 520 L 1638 501 L 1640 482 L 1642 464 L 1643 445 L 1643 427 L 1642 408 L 1640 390 L 1636 371 L 1631 352 L 1629 349 L 1622 334 L 1611 316 L 1611 315 L 1595 297 L E B 1506 575 M 1511 557 L 1515 538 L 1516 520 L 1517 501 L 1514 482 L 1510 464 L 1502 445 L 1502 445 L 1487 427 L 1484 423 L 1466 411 L 1457 408 L 1447 405 L 1429 404 L 1411 405 L 1401 408 L 1393 411 L 1375 420 L 1364 427 L 1356 433 L 1344 445 L 1338 453 L 1331 464 L 1321 482 L 1320 485 L 1315 501 L 1311 520 L 1309 538 L 1310 557 L 1312 575 L 1317 594 L 1320 602 L 1325 612 L 1336 631 L 1338 634 L 1354 650 L 1356 652 L 1375 661 L 1393 665 L 1411 664 L 1429 659 L 1447 651 L 1449 650 L 1466 637 L 1472 631 L 1484 618 L 1488 612 L 1498 594 L 1502 585 L 1506 575 L E 1.4 Sx (EW) 1229 83 0.5 T 90 Sr 90 Sh (NS) 105 1207 0.5 T Z W %%EndDocument 262 565 a endTexFig 465 2142 a Fr(Figure)14 b(24:)k(Galaxy)12 b(data|con)o(tour)h(plot)h(of)f(lo) q(cal)g(regression)i(\014t.)991 2574 y(39)p eop %%Page: 38 17 bop 262 307 a Fr(underlying)15 b(pattern)i(is)f(substan)o(tial;)h(th)o(us)f (w)o(e)g(will)f(sp)q(ecify)i(a)f(lo)q(cally-quadratic)e(surface.)262 357 y(Since)9 b(man)o(y)f(p)q(oin)o(ts)h(app)q(ear)h(to)g(deviate)f(substan)o (tially)g(from)e(the)k(o)o(v)o(erall)d(pattern)i(compared)262 407 y(to)15 b(the)g(deviations)g(of)f(the)i(ma)r(jorit)o(y)d(of)i(p)q(oin)o (ts,)f(it)h(seems)h(pruden)o(t)g(to)f(sp)q(ecify)g(symmetric)262 457 y(errors.)k(Finally)m(,)12 b(it)h(mak)o(es)g(sense)j(to)d(preserv)o(e)j (the)f(spatial)e(metric)g(of)h(the)g(factors)h(and)f(not)262 506 y(normalize)e(the)i(v)n(ariation)e(in)i(their)g(measuremen)o(ts:)324 576 y Fi(struct)37 b(loess_str)o(uc)o(t)76 b(galaxy;)324 622 y(double)37 b(velocity[)o(])16 b(=)k Fh(f)p Fi(1769,)e(1749,)f(1749,)h(...)p Fh(g)p Fi(;)324 667 y(double)37 b(direction)o([])16 b(=)j Fh(f)p Fi(8.46279,)e(7.96498,)g(7.46717,)f(...)p Fh(g)p Fi(;)324 713 y(long)77 b(n)19 b(=)g(323,)f(p)h(=)h(2;)324 804 y(loess_set)o(up\()o(di)o (rec)o(ti)o(on,)c(velocity,)g(n,)j(p,)g(&galaxy\);)324 850 y(galaxy.mo)o(del)o(.s)o(pan)d(=)j(0.35;)324 896 y(galaxy.mo)o(del)o(.n)o (orm)o(al)o(ize)d(=)j(FALSE;)324 941 y(galaxy.mo)o(del)o(.f)o(ami)o(ly)d(=)j ("symmetric)o(";)324 987 y(loess\(&ga)o(lax)o(y\))o(;)324 1033 y(loess_sum)o(mar)o(y\()o(&ga)o(la)o(xy\))o(;)324 1124 y Fg(Num)o(b)q(er)13 b(of)g(Observ)n(ations:)h(323)324 1170 y(Equiv)n(alen)o(t)h(Num)o(b)q(er)f (of)e(P)o(arameters:)i(19.6)324 1215 y(Residual)h(Scale)f(Estimate:)g (12.1139)324 1289 y Fr(Let's)g(ev)n(aluate)g(the)g(surface)h(on)f(a)f(grid)h (and)f(then)i(mak)o(e)d(a)i(con)o(tour)g(plot:)324 1358 y Fi(struct)37 b(pred_stru)o(ct)95 b(galaxy_c)o(ont)o(ou)o(r;)324 1404 y(double)37 b(ew[59],)17 b(ns[99],)g(grid[116)o(82])o(;)324 1450 y(double)37 b(tmp;)324 1495 y(long)77 b(m)19 b(=)g(5841,)f(se_fit)f(=)i(FALSE;)324 1541 y(int)97 b(i,)19 b(j,)f(k;)324 1632 y(tmp)g(=)h(-29.0;)324 1678 y(for\(i)e(=)j(0;)f(i)g(<)g(59;)f(i++\))481 1724 y(ew[i])f(=)j(tmp++;) 324 1769 y(tmp)e(=)h(-49.0;)324 1815 y(for\(i)e(=)j(0;)f(i)g(<)g(99;)f(i++\)) 481 1861 y(ns[i])f(=)j(tmp++;)324 1906 y(for\(i)d(=)j(0;)f(i)g(<)g(99;)f (i++\))h Fh(f)481 1952 y Fi(k)g(=)g(i)g(*)h(59;)481 1998 y(for\(j)d(=)j(0;)e (j)i(<)f(59;)f(j++\))g Fh(f)638 2043 y Fi(grid[k)f(+)i(j])g(=)g(ew[j];)638 2089 y(grid[m)e(+)i(k)g(+)h(j])e(=)i(ns[i];)481 2135 y Fh(g)324 2180 y(g)324 2226 y Fi(predict\(g)o(rid)o(,)c(m,)j(&galaxy,)e(&galaxy_c)o(on) o(tou)o(r,)f(se_fit\);)262 2300 y Fr(The)h(result)g(is)g(sho)o(wn)g(in)f (Figure)h(24.)26 b(Recall)16 b(that)h(w)o(e)g(studied)g(the)h(\014ts)f(to)g Fi(ethanol)d Fr(and)262 2350 y Fi(air)h Fr(b)o(y)h(coplots,)h(but)g(in)g (this)f(application)g(it)g(mak)o(es)g(sense)i(to)f(use)g(a)g(con)o(tour)g (plot)f(since)262 2399 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{/A exch def /Uy exch def /Ux exch def /Ly exch def /Lx exch def Ux Lx sub A 0 get mul Lx add Uy Ly sub A 1 get mul Ly add Ux Lx sub A 2 get mul Lx add Uy Ly sub A 3 get mul Ly add} bd /SetFigure {Page aload pop Figure Subregion} bd /SetPlot {SetFigure Plot Subregion} bd /SetClip {ClipToPlot {SetPlot} {SetFigure} ifelse BoxClip} bd /SetPage {0 0 Width Height Page astore RastersPerPoint ScaleArray} bd /PageBegin {save /PageContext exch def /InPage true def} bd /PageEnd {PageContext restore /InPage false def} bd /Landscape false def /Region [21.48 111.72 590.28 680.52] def /RastersPerInch 300 def /PointSize 12.2889 def /Fonts [ /Helvetica /Courier /Times-Roman /Helvetica-Oblique /Helvetica-Bold /Helvetica-BoldOblique /Courier-Oblique /Courier-Bold /Courier-BoldOblique /Times-Italic /Times-Bold /Times-BoldItalic /Symbol /AvantGarde-Book /AvantGarde-BookOblique /AvantGarde-Demi /AvantGarde-DemiOblique /Bookman-Demi /Bookman-DemiItalic /Bookman-Light /Bookman-LightItalic /Helvetica-Narrow 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269 S 1354 280 1354 269 S 1398 280 1398 269 S 1442 280 1442 269 S 1485 280 1485 269 S 1529 280 1529 269 S 1573 280 1573 269 S 1617 280 1617 269 S 1310 280 1617 280 S 0 1 0 1 So 0.683714 0.826772 0.117963 0.261021 Sg 0 Sd B 1633 499 M 1639 502 L 1646 504 L 1652 507 L 1659 510 L 1665 512 L 1671 515 L 1678 517 L 1684 519 L 1691 522 L 1697 524 L 1703 526 L 1710 529 L 1716 531 L 1723 533 L 1729 535 L 1735 537 L 1742 539 L 1748 541 L 1755 543 L 1761 545 L 1768 546 L 1774 548 L 1780 550 L 1787 551 L 1793 553 L 1800 554 L 1806 556 L 1812 557 L 1819 559 L 1825 560 L 1832 561 L 1838 562 L 1844 563 L 1851 564 L 1857 565 L 1864 566 L 1870 566 L 1876 567 L 1883 568 L 1889 568 L 1896 568 L 1902 569 L 1908 569 L 1915 569 L 1921 569 L 1928 569 L 1934 569 L 1940 569 L 1947 569 L E B 1620 619 M 1620 280 L 1959 280 L 1959 619 L 1620 619 L E 90 Sr 0.111481 0.826772 0.117963 0.833254 So 0 1 0 1 Sg 90 Sh 1 Sd 1959 335 1970 335 S 1959 415 1970 415 S 1959 494 1970 494 S 1959 573 1970 573 S 1959 335 1959 573 S 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833 S 264 912 254 912 S 264 674 264 912 S 0 Sr 0 1 0 1 So 0.25454 0.397598 0.261021 0.404079 Sg 0 Sh 0 Sd B 616 740 M 622 742 L 629 743 L 635 744 L 641 746 L 648 747 L 654 748 L 661 750 L 667 751 L 673 752 L 680 753 L 686 755 L 693 756 L 699 757 L 706 758 L 712 759 L 718 761 L 725 762 L 731 763 L 738 764 L 744 765 L 750 766 L 757 767 L 763 768 L 770 769 L 776 770 L 782 771 L 789 772 L 795 773 L 802 774 L 808 775 L 814 776 L 821 777 L 827 778 L 834 779 L 840 779 L 846 780 L 853 781 L 859 782 L 866 783 L 872 784 L 878 784 L 885 785 L 891 786 L 898 786 L 904 787 L 911 788 L 917 788 L 923 789 L 930 789 L E B 603 958 M 603 619 L 942 619 L 942 958 L 603 958 L E 0.397598 0.540656 0.261021 0.404079 Sg B 955 765 M 961 767 L 968 769 L 974 770 L 980 772 L 987 773 L 993 775 L 1000 776 L 1006 778 L 1013 779 L 1019 781 L 1025 782 L 1032 784 L 1038 785 L 1045 786 L 1051 788 L 1057 789 L 1064 790 L 1070 791 L 1077 793 L 1083 794 L 1089 795 L 1096 796 L 1102 797 L 1109 798 L 1115 799 L 1121 800 L 1128 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1052 L 347 1053 L 354 1054 L 360 1055 L 366 1056 L 373 1057 L 379 1058 L 386 1059 L 392 1059 L 398 1060 L 405 1061 L 411 1062 L 418 1063 L 424 1064 L 431 1065 L 437 1066 L 443 1066 L 450 1067 L 456 1068 L 463 1069 L 469 1070 L 475 1071 L 482 1071 L 488 1072 L 495 1073 L 501 1074 L 507 1074 L 514 1075 L 520 1076 L 527 1076 L 533 1077 L 539 1077 L 546 1078 L 552 1079 L 559 1079 L 565 1079 L 571 1080 L 578 1080 L 584 1081 L 591 1081 L E B 264 1297 M 264 958 L 603 958 L 603 1297 L 264 1297 L E 90 Sr 0.111481 0.826772 0.117963 0.833254 So 0 1 0 1 Sg 90 Sh 1 Sd 264 1013 254 1013 S 264 1093 254 1093 S 264 1172 254 1172 S 264 1251 254 1251 S 264 1013 264 1251 S (2.5) 215 1013 0.5 T (3.5) 215 1172 0.5 T 0 Sr 0 1 0 1 So 0.25454 0.397598 0.404079 0.547138 Sg 0 Sh 0 Sd B 616 1059 M 622 1061 L 629 1062 L 635 1063 L 641 1065 L 648 1066 L 654 1067 L 661 1069 L 667 1070 L 673 1071 L 680 1072 L 686 1073 L 693 1075 L 699 1076 L 706 1077 L 712 1078 L 718 1079 L 725 1080 L 731 1081 L 738 1082 L 744 1083 L 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1269 1132 L E B 942 1297 M 942 958 L 1281 958 L 1281 1297 L 942 1297 L E 0.540656 0.683714 0.404079 0.547138 Sg B 1294 1118 M 1300 1120 L 1307 1122 L 1313 1124 L 1320 1126 L 1326 1128 L 1332 1130 L 1339 1132 L 1345 1134 L 1352 1136 L 1358 1137 L 1364 1139 L 1371 1141 L 1377 1143 L 1384 1144 L 1390 1146 L 1396 1147 L 1403 1149 L 1409 1150 L 1416 1152 L 1422 1153 L 1428 1154 L 1435 1155 L 1441 1156 L 1448 1158 L 1454 1159 L 1460 1160 L 1467 1160 L 1473 1161 L 1480 1162 L 1486 1163 L 1493 1163 L 1499 1164 L 1505 1165 L 1512 1165 L 1518 1166 L 1525 1166 L 1531 1167 L 1537 1167 L 1544 1167 L 1550 1167 L 1557 1168 L 1563 1168 L 1569 1168 L 1576 1168 L 1582 1168 L 1589 1168 L 1595 1168 L 1601 1168 L 1608 1167 L E B 1281 1297 M 1281 958 L 1620 958 L 1620 1297 L 1281 1297 L E 0.683714 0.826772 0.404079 0.547138 Sg B 1633 1155 M 1639 1157 L 1646 1160 L 1652 1163 L 1659 1165 L 1665 1168 L 1671 1170 L 1678 1172 L 1684 1175 L 1691 1177 L 1697 1179 L 1703 1182 L 1710 1184 L 1716 1186 L 1723 1188 L 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866 1415 L 872 1415 L 878 1416 L 885 1416 L 891 1416 L 898 1416 L 904 1417 L 911 1417 L 917 1417 L 923 1417 L 930 1417 L E B 603 1636 M 603 1297 L 942 1297 L 942 1636 L 603 1636 L E 0.397598 0.540656 0.547138 0.690196 Sg B 955 1399 M 961 1401 L 968 1403 L 974 1404 L 980 1405 L 987 1407 L 993 1408 L 1000 1410 L 1006 1411 L 1013 1412 L 1019 1414 L 1025 1415 L 1032 1416 L 1038 1417 L 1045 1419 L 1051 1420 L 1057 1421 L 1064 1422 L 1070 1423 L 1077 1424 L 1083 1425 L 1089 1426 L 1096 1427 L 1102 1428 L 1109 1429 L 1115 1430 L 1121 1430 L 1128 1431 L 1134 1432 L 1141 1433 L 1147 1433 L 1153 1434 L 1160 1434 L 1166 1435 L 1173 1435 L 1179 1436 L 1186 1436 L 1192 1436 L 1198 1437 L 1205 1437 L 1211 1438 L 1218 1438 L 1224 1438 L 1230 1438 L 1237 1439 L 1243 1439 L 1250 1439 L 1256 1439 L 1262 1439 L 1269 1439 L E B 942 1636 M 942 1297 L 1281 1297 L 1281 1636 L 942 1636 L E 0.540656 0.683714 0.547138 0.690196 Sg B 1294 1436 M 1300 1438 L 1307 1440 L 1313 1442 L 1320 1444 L 1326 1445 L 1332 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L 1832 1530 L 1838 1530 L 1844 1531 L 1851 1531 L 1857 1532 L 1864 1532 L 1870 1533 L 1876 1533 L 1883 1533 L 1889 1533 L 1896 1533 L 1902 1533 L 1908 1532 L 1915 1532 L 1921 1532 L 1928 1531 L 1934 1531 L 1940 1530 L 1947 1530 L E B 1620 1636 M 1620 1297 L 1959 1297 L 1959 1636 L 1620 1636 L E 90 Sr 0.111481 0.826772 0.117963 0.833254 So 0 1 0 1 Sg 90 Sh 1 Sd 1959 1352 1970 1352 S 1959 1432 1970 1432 S 1959 1511 1970 1511 S 1959 1590 1970 1590 S 1959 1352 1959 1590 S (2.5) 2009 1352 0.5 T (3.5) 2009 1511 0.5 T 0 Sr 0 1 0 1 So 0.111481 0.25454 0.690196 0.833254 Sg 0 Sh 0 Sd B 277 1696 M 283 1697 L 290 1699 L 296 1700 L 302 1702 L 309 1703 L 315 1704 L 322 1705 L 328 1707 L 334 1708 L 341 1709 L 347 1710 L 354 1711 L 360 1712 L 366 1714 L 373 1715 L 379 1716 L 386 1716 L 392 1717 L 398 1718 L 405 1719 L 411 1720 L 418 1721 L 424 1721 L 431 1722 L 437 1723 L 443 1723 L 450 1724 L 456 1725 L 463 1725 L 469 1726 L 475 1726 L 482 1726 L 488 1727 L 495 1727 L 501 1727 L 507 1728 L 514 1728 L 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1339 688 1339 S 264 1445 688 1445 S 370 1127 370 1551 S 476 1127 476 1551 S 582 1127 582 1551 S 1 Sw 1 Sc 281 1143 P 287 1303 P 288 1303 P 300 1237 P 302 1194 P 304 1260 P 316 1292 P 324 1249 P 330 1222 P 382 1332 P 406 1260 P 416 1255 P 436 1260 P 450 1255 P 539 1292 P 548 1296 P 557 1307 P 557 1260 P 579 1275 P 582 1307 P 600 1265 P 620 1249 P 640 1337 P 647 1284 P 658 1326 P 672 1265 P B 281 1258 M 289 1258 L 297 1259 L 305 1260 L 313 1260 L 321 1261 L 329 1261 L 337 1262 L 345 1262 L 353 1263 L 361 1264 L 369 1264 L 377 1265 L 385 1266 L 393 1266 L 401 1267 L 409 1267 L 417 1268 L 425 1269 L 433 1269 L 441 1270 L 449 1271 L 457 1272 L 465 1273 L 473 1273 L 481 1274 L 489 1275 L 497 1276 L 505 1277 L 513 1277 L 521 1278 L 529 1279 L 537 1280 L 545 1281 L 553 1282 L 561 1283 L 569 1283 L 577 1284 L 585 1285 L 592 1286 L 600 1287 L 608 1288 L 616 1289 L 624 1290 L 632 1291 L 640 1292 L 648 1293 L 656 1293 L 664 1294 L 672 1295 L E B 264 1551 M 264 1127 L 688 1127 L 688 1551 L 264 1551 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1299 1336 L 1306 1338 L 1313 1340 L 1320 1341 L 1327 1342 L 1334 1344 L 1341 1344 L 1348 1345 L 1355 1345 L 1362 1345 L 1369 1346 L 1376 1346 L 1383 1346 L 1391 1346 L 1398 1346 L 1405 1347 L 1412 1347 L 1419 1347 L 1426 1347 L 1433 1347 L 1440 1347 L 1447 1347 L 1454 1347 L 1461 1347 L 1468 1346 L 1475 1346 L 1482 1346 L 1489 1346 L 1496 1346 L E B 1112 1551 M 1112 1127 L 1536 1127 L 1536 1551 L 1112 1551 L E 1.5 Sw 0.1 Sc 0.64795 0.826772 0.475608 0.654431 Sg 1536 1233 1959 1233 S 1536 1339 1959 1339 S 1536 1445 1959 1445 S 1642 1127 1642 1551 S 1748 1127 1748 1551 S 1853 1127 1853 1551 S 1 Sw 1 Sc 1641 1380 P 1695 1323 P 1710 1343 P 1773 1363 P 1787 1424 P 1807 1402 P 1818 1444 P 1826 1332 P 1841 1374 P 1848 1394 P 1871 1320 P 1872 1340 P 1920 1353 P 1931 1351 P B 1641 1353 M 1647 1354 L 1653 1355 L 1659 1356 L 1665 1357 L 1671 1357 L 1677 1358 L 1683 1359 L 1689 1360 L 1694 1361 L 1700 1362 L 1706 1362 L 1712 1363 L 1718 1363 L 1724 1364 L 1730 1364 L 1736 1365 L 1742 1365 L 1748 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0 eq { CharWidth Cos div } { /H Text-y Sin div def /W CharWidth Cos div def H W lt {H} {W} ifelse } ifelse } ifelse 2 div /CharDist exch def CharDist 0 translate 0 0 moveto gsave RotDiff rotate CharWidth 2 div neg Text-y 2 div neg rmoveto Outline {false charpath stroke} {show} ifelse grestore CharDist 0 translate 0 0 moveto } forall } bd /Show {Outline {false charpath stroke} {show} ifelse} bd /BoxClip {/CLW currentlinewidth def 2 {CLW add 4 1 roll} repeat 2 {CLW sub 4 1 roll} repeat initclip newpath 2 index exch 2 index exch dup 6 index exch moveto 3 {lineto} repeat closepath clip newpath} bd /Subregion {/A exch def /Uy exch def /Ux exch def /Ly exch def /Lx exch def Ux Lx sub A 0 get mul Lx add Uy Ly sub A 1 get mul Ly add Ux Lx sub A 2 get mul Lx add Uy Ly sub A 3 get mul Ly add} bd /SetFigure {Page aload pop Figure Subregion} bd /SetPlot {SetFigure Plot Subregion} bd /SetClip {ClipToPlot {SetPlot} {SetFigure} ifelse BoxClip} bd /SetPage {0 0 Width Height Page astore RastersPerPoint ScaleArray} bd /PageBegin {save /PageContext exch def /InPage true def} bd /PageEnd {PageContext restore /InPage false def} bd /Landscape false def /Region [21.48 16.92 590.28 775.32] def /RastersPerInch 300 def /PointSize 12.2889 def /Fonts [ /Helvetica /Courier /Times-Roman /Helvetica-Oblique /Helvetica-Bold /Helvetica-BoldOblique /Courier-Oblique /Courier-Bold /Courier-BoldOblique /Times-Italic /Times-Bold /Times-BoldItalic /Symbol /AvantGarde-Book /AvantGarde-BookOblique /AvantGarde-Demi /AvantGarde-DemiOblique /Bookman-Demi /Bookman-DemiItalic /Bookman-Light /Bookman-LightItalic /Helvetica-Narrow /Helvetica-Narrow-Bold /Helvetica-Narrow-BoldOblique /Helvetica-Narrow-Oblique /NewCenturySchlbk-Roman /NewCenturySchlbk-Bold /NewCenturySchlbk-Italic /NewCenturySchlbk-BoldItalic /Palatino-Roman /Palatino-Bold /Palatino-Italic /Palatino-BoldItalic /ZapfChancery-MediumItalic /ZapfDingbats ] def /Colors [ 0 0.6 0.3 0.9 0.4 0.7 0.1 0.5 0.8 0.2 ] def I A 1 St 1 Sw 1 Sc 0 Sr 254 Sp 0.7 Sx 0.0309872 0.969013 0.0309872 0.969013 So 0.111481 0.320648 0.150099 0.306974 Sg 0 Sh 0 Sd 1 Sf B 297 555 M 306 561 L 314 567 L 323 575 L 332 582 L 341 590 L 350 599 L 358 608 L 367 618 L 376 628 L 385 639 L 393 650 L 402 662 L 411 675 L 420 689 L 429 703 L 437 717 L 446 735 L 455 754 L 464 771 L 473 787 L 481 803 L 490 817 L 499 831 L 508 842 L 516 849 L 525 853 L 534 855 L 543 853 L 552 847 L 560 836 L 569 822 L 578 808 L 587 796 L 596 782 L 604 767 L 613 748 L 622 727 L 631 709 L 639 693 L 648 677 L 657 665 L 666 654 L 675 644 L 683 636 L 692 630 L 701 625 L 710 622 L 719 620 L 727 620 L E B 280 955 M 280 490 L 745 490 L 745 955 L 280 955 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 280 563 265 563 S 280 646 265 646 S 280 730 265 730 S 280 813 265 813 S 280 896 265 896 S 280 563 280 896 S 0 Sr 0 Sh 337 490 337 475 S 460 490 460 475 S 584 490 584 475 S 708 490 708 475 S 337 490 708 490 S (0.6) 337 437 0.5 T (0.8) 460 437 0.5 T (1.0) 584 437 0.5 T (1.2) 708 437 0.5 T 0.0309872 0.969013 0.0309872 0.969013 So 0.320648 0.529815 0.150099 0.306974 Sg 0 Sd B 793 558 M 801 564 L 810 571 L 819 579 L 828 586 L 836 595 L 845 604 L 854 613 L 863 623 L 872 633 L 880 644 L 889 656 L 898 668 L 907 681 L 916 695 L 924 710 L 933 724 L 942 741 L 951 761 L 959 778 L 968 793 L 977 808 L 986 823 L 995 836 L 1003 847 L 1012 854 L 1021 858 L 1030 859 L 1039 858 L 1047 851 L 1056 839 L 1065 825 L 1074 811 L 1082 798 L 1091 784 L 1100 769 L 1109 750 L 1118 728 L 1126 710 L 1135 693 L 1144 678 L 1153 665 L 1162 654 L 1170 645 L 1179 637 L 1188 630 L 1197 625 L 1206 622 L 1214 620 L 1223 620 L E B 775 955 M 775 490 L 1240 490 L 1240 955 L 775 955 L E 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 1 Sd 833 490 833 475 S 956 490 956 475 S 1080 490 1080 475 S 1203 490 1203 475 S 833 490 1203 490 S 0.0309872 0.969013 0.0309872 0.969013 So 0.529815 0.738981 0.150099 0.306974 Sg 0 Sd B 1288 562 M 1297 568 L 1306 575 L 1315 583 L 1323 591 L 1332 599 L 1341 608 L 1350 618 L 1359 628 L 1367 639 L 1376 650 L 1385 661 L 1394 674 L 1402 687 L 1411 702 L 1420 716 L 1429 731 L 1438 748 L 1446 767 L 1455 784 L 1464 799 L 1473 814 L 1482 829 L 1490 841 L 1499 852 L 1508 859 L 1517 862 L 1525 863 L 1534 862 L 1543 855 L 1552 843 L 1561 829 L 1569 814 L 1578 801 L 1587 786 L 1596 771 L 1605 751 L 1613 729 L 1622 711 L 1631 694 L 1640 679 L 1649 666 L 1657 655 L 1666 645 L 1675 637 L 1684 630 L 1692 625 L 1701 622 L 1710 620 L 1719 619 L E B 1271 955 M 1271 490 L 1736 490 L 1736 955 L 1271 955 L E 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 1 Sd 1328 490 1328 475 S 1452 490 1452 475 S 1575 490 1575 475 S 1699 490 1699 475 S 1328 490 1699 490 S (0.6) 1328 437 0.5 T (0.8) 1452 437 0.5 T (1.0) 1575 437 0.5 T (1.2) 1699 437 0.5 T 0.0309872 0.969013 0.0309872 0.969013 So 0.738981 0.948148 0.150099 0.306974 Sg 0 Sd B 1784 565 M 1793 572 L 1802 579 L 1810 587 L 1819 595 L 1828 603 L 1837 613 L 1845 623 L 1854 633 L 1863 644 L 1872 655 L 1881 667 L 1889 680 L 1898 693 L 1907 708 L 1916 723 L 1925 737 L 1933 755 L 1942 774 L 1951 790 L 1960 806 L 1968 820 L 1977 834 L 1986 847 L 1995 857 L 2004 864 L 2012 867 L 2021 868 L 2030 866 L 2039 859 L 2048 847 L 2056 832 L 2065 817 L 2074 804 L 2083 788 L 2092 772 L 2100 753 L 2109 731 L 2118 712 L 2127 695 L 2135 679 L 2144 667 L 2153 655 L 2162 645 L 2171 637 L 2179 630 L 2188 625 L 2197 622 L 2206 619 L 2215 619 L E B 1767 955 M 1767 490 L 2232 490 L 2232 955 L 1767 955 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 2232 563 2247 563 S 2232 646 2247 646 S 2232 730 2247 730 S 2232 813 2247 813 S 2232 896 2247 896 S 2232 563 2232 896 S (0) 2284 563 0.5 T (1) 2284 646 0.5 T (2) 2284 730 0.5 T (3) 2284 813 0.5 T (4) 2284 896 0.5 T 0 Sr 0 Sh 1824 490 1824 475 S 1948 490 1948 475 S 2071 490 2071 475 S 2195 490 2195 475 S 1824 490 2195 490 S 0.0309872 0.969013 0.0309872 0.969013 So 0.111481 0.320648 0.306974 0.463849 Sg 0 Sd B 297 1064 M 306 1071 L 314 1078 L 323 1086 L 332 1095 L 341 1104 L 350 1113 L 358 1123 L 367 1134 L 376 1145 L 385 1156 L 393 1168 L 402 1181 L 411 1195 L 420 1210 L 429 1225 L 437 1240 L 446 1257 L 455 1276 L 464 1292 L 473 1307 L 481 1322 L 490 1335 L 499 1348 L 508 1358 L 516 1364 L 525 1367 L 534 1368 L 543 1366 L 552 1358 L 560 1346 L 569 1331 L 578 1316 L 587 1303 L 596 1286 L 604 1270 L 613 1250 L 622 1228 L 631 1209 L 639 1192 L 648 1176 L 657 1163 L 666 1151 L 675 1142 L 683 1133 L 692 1126 L 701 1121 L 710 1117 L 719 1115 L 727 1114 L E B 280 1450 M 280 985 L 745 985 L 745 1450 L 280 1450 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 280 1059 265 1059 S 280 1142 265 1142 S 280 1225 265 1225 S 280 1308 265 1308 S 280 1391 265 1391 S 280 1059 280 1391 S (0) 227 1059 0.5 T (1) 227 1142 0.5 T (2) 227 1225 0.5 T (3) 227 1308 0.5 T (4) 227 1391 0.5 T 0 Sr 0.0309872 0.969013 0.0309872 0.969013 So 0.320648 0.529815 0.306974 0.463849 Sg 0 Sh 0 Sd B 793 1068 M 801 1075 L 810 1082 L 819 1090 L 828 1099 L 836 1108 L 845 1118 L 854 1128 L 863 1139 L 872 1150 L 880 1162 L 889 1174 L 898 1187 L 907 1201 L 916 1216 L 924 1231 L 933 1246 L 942 1264 L 951 1282 L 959 1299 L 968 1313 L 977 1327 L 986 1341 L 995 1353 L 1003 1363 L 1012 1369 L 1021 1372 L 1030 1372 L 1039 1370 L 1047 1362 L 1056 1350 L 1065 1335 L 1074 1320 L 1082 1305 L 1091 1289 L 1100 1272 L 1109 1251 L 1118 1229 L 1126 1210 L 1135 1193 L 1144 1177 L 1153 1164 L 1162 1152 L 1170 1142 L 1179 1133 L 1188 1126 L 1197 1121 L 1206 1117 L 1214 1115 L 1223 1114 L E B 775 1450 M 775 985 L 1240 985 L 1240 1450 L 775 1450 L E 0.529815 0.738981 0.306974 0.463849 Sg B 1288 1071 M 1297 1078 L 1306 1086 L 1315 1094 L 1323 1103 L 1332 1113 L 1341 1122 L 1350 1133 L 1359 1144 L 1367 1155 L 1376 1167 L 1385 1180 L 1394 1193 L 1402 1207 L 1411 1222 L 1420 1238 L 1429 1253 L 1438 1270 L 1446 1289 L 1455 1305 L 1464 1319 L 1473 1333 L 1482 1346 L 1490 1359 L 1499 1368 L 1508 1374 L 1517 1376 L 1525 1377 L 1534 1374 L 1543 1366 L 1552 1353 L 1561 1339 L 1569 1323 L 1578 1308 L 1587 1291 L 1596 1274 L 1605 1253 L 1613 1230 L 1622 1211 L 1631 1194 L 1640 1178 L 1649 1164 L 1657 1152 L 1666 1142 L 1675 1134 L 1684 1126 L 1692 1121 L 1701 1117 L 1710 1114 L 1719 1113 L E B 1271 1450 M 1271 985 L 1736 985 L 1736 1450 L 1271 1450 L E 0.738981 0.948148 0.306974 0.463849 Sg B 1784 1074 M 1793 1082 L 1802 1090 L 1810 1098 L 1819 1107 L 1828 1117 L 1837 1127 L 1845 1138 L 1854 1149 L 1863 1160 L 1872 1173 L 1881 1185 L 1889 1199 L 1898 1213 L 1907 1229 L 1916 1244 L 1925 1259 L 1933 1277 L 1942 1296 L 1951 1311 L 1960 1325 L 1968 1339 L 1977 1352 L 1986 1364 L 1995 1373 L 2004 1379 L 2012 1381 L 2021 1381 L 2030 1378 L 2039 1370 L 2048 1357 L 2056 1342 L 2065 1326 L 2074 1311 L 2083 1293 L 2092 1275 L 2100 1254 L 2109 1231 L 2118 1212 L 2127 1194 L 2135 1178 L 2144 1165 L 2153 1153 L 2162 1143 L 2171 1134 L 2179 1127 L 2188 1121 L 2197 1117 L 2206 1114 L 2215 1113 L E B 1767 1450 M 1767 985 L 2232 985 L 2232 1450 L 1767 1450 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 2232 1059 2247 1059 S 2232 1142 2247 1142 S 2232 1225 2247 1225 S 2232 1308 2247 1308 S 2232 1391 2247 1391 S 2232 1059 2232 1391 S 0 Sr 0.0309872 0.969013 0.0309872 0.969013 So 0.111481 0.320648 0.463849 0.620724 Sg 0 Sh 0 Sd B 297 1574 M 306 1581 L 314 1589 L 323 1598 L 332 1607 L 341 1617 L 350 1627 L 358 1638 L 367 1650 L 376 1661 L 385 1674 L 393 1687 L 402 1700 L 411 1715 L 420 1731 L 429 1746 L 437 1762 L 446 1779 L 455 1798 L 464 1813 L 473 1827 L 481 1840 L 490 1853 L 499 1865 L 508 1874 L 516 1879 L 525 1881 L 534 1881 L 543 1878 L 552 1869 L 560 1857 L 569 1842 L 578 1825 L 587 1809 L 596 1791 L 604 1773 L 613 1751 L 622 1728 L 631 1709 L 639 1691 L 648 1675 L 657 1661 L 666 1649 L 675 1639 L 683 1630 L 692 1622 L 701 1617 L 710 1612 L 719 1610 L 727 1608 L E B 280 1946 M 280 1481 L 745 1481 L 745 1946 L 280 1946 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 280 1555 265 1555 S 280 1638 265 1638 S 280 1721 265 1721 S 280 1804 265 1804 S 280 1887 265 1887 S 280 1555 280 1887 S 0 Sr 0.0309872 0.969013 0.0309872 0.969013 So 0.320648 0.529815 0.463849 0.620724 Sg 0 Sh 0 Sd B 793 1577 M 801 1585 L 810 1593 L 819 1602 L 828 1612 L 836 1622 L 845 1632 L 854 1643 L 863 1655 L 872 1667 L 880 1679 L 889 1692 L 898 1706 L 907 1721 L 916 1737 L 924 1753 L 933 1768 L 942 1786 L 951 1804 L 959 1819 L 968 1833 L 977 1846 L 986 1859 L 995 1870 L 1003 1879 L 1012 1884 L 1021 1886 L 1030 1886 L 1039 1882 L 1047 1873 L 1056 1860 L 1065 1845 L 1074 1829 L 1082 1812 L 1091 1794 L 1100 1775 L 1109 1752 L 1118 1729 L 1126 1710 L 1135 1692 L 1144 1676 L 1153 1662 L 1162 1650 L 1170 1639 L 1179 1630 L 1188 1623 L 1197 1617 L 1206 1612 L 1214 1609 L 1223 1608 L E B 775 1946 M 775 1481 L 1240 1481 L 1240 1946 L 775 1946 L E 0.529815 0.738981 0.463849 0.620724 Sg B 1288 1581 M 1297 1589 L 1306 1597 L 1315 1606 L 1323 1616 L 1332 1626 L 1341 1637 L 1350 1648 L 1359 1659 L 1367 1672 L 1376 1685 L 1385 1698 L 1394 1712 L 1402 1727 L 1411 1743 L 1420 1759 L 1429 1775 L 1438 1793 L 1446 1811 L 1455 1826 L 1464 1839 L 1473 1851 L 1482 1864 L 1490 1876 L 1499 1884 L 1508 1889 L 1517 1891 L 1525 1890 L 1534 1886 L 1543 1877 L 1552 1864 L 1561 1849 L 1569 1832 L 1578 1815 L 1587 1796 L 1596 1777 L 1605 1754 L 1613 1730 L 1622 1711 L 1631 1693 L 1640 1676 L 1649 1663 L 1657 1650 L 1666 1640 L 1675 1630 L 1684 1623 L 1692 1617 L 1701 1612 L 1710 1609 L 1719 1608 L E B 1271 1946 M 1271 1481 L 1736 1481 L 1736 1946 L 1271 1946 L E 0.738981 0.948148 0.463849 0.620724 Sg B 1784 1584 M 1793 1592 L 1802 1601 L 1810 1610 L 1819 1620 L 1828 1630 L 1837 1641 L 1845 1653 L 1854 1664 L 1863 1677 L 1872 1690 L 1881 1703 L 1889 1718 L 1898 1733 L 1907 1749 L 1916 1766 L 1925 1782 L 1933 1799 L 1942 1817 L 1951 1832 L 1960 1845 L 1968 1857 L 1977 1870 L 1986 1881 L 1995 1890 L 2004 1894 L 2012 1895 L 2021 1895 L 2030 1890 L 2039 1881 L 2048 1868 L 2056 1852 L 2065 1835 L 2074 1818 L 2083 1798 L 2092 1778 L 2100 1755 L 2109 1731 L 2118 1712 L 2127 1694 L 2135 1677 L 2144 1663 L 2153 1651 L 2162 1640 L 2171 1631 L 2179 1623 L 2188 1617 L 2197 1612 L 2206 1609 L 2215 1607 L E B 1767 1946 M 1767 1481 L 2232 1481 L 2232 1946 L 1767 1946 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 2232 1555 2247 1555 S 2232 1638 2247 1638 S 2232 1721 2247 1721 S 2232 1804 2247 1804 S 2232 1887 2247 1887 S 2232 1555 2232 1887 S (0) 2284 1555 0.5 T (1) 2284 1638 0.5 T (2) 2284 1721 0.5 T (3) 2284 1804 0.5 T (4) 2284 1887 0.5 T 0 Sr 0.0309872 0.969013 0.0309872 0.969013 So 0.111481 0.320648 0.620724 0.777599 Sg 0 Sh 0 Sd B 297 2083 M 306 2092 L 314 2101 L 323 2110 L 332 2120 L 341 2131 L 350 2142 L 358 2153 L 367 2165 L 376 2178 L 385 2191 L 393 2205 L 402 2219 L 411 2235 L 420 2251 L 429 2268 L 437 2284 L 446 2302 L 455 2320 L 464 2334 L 473 2347 L 481 2359 L 490 2371 L 499 2382 L 508 2390 L 516 2395 L 525 2396 L 534 2395 L 543 2390 L 552 2380 L 560 2367 L 569 2352 L 578 2334 L 587 2316 L 596 2296 L 604 2276 L 613 2252 L 622 2228 L 631 2208 L 639 2190 L 648 2174 L 657 2160 L 666 2147 L 675 2136 L 683 2127 L 692 2119 L 701 2112 L 710 2108 L 719 2104 L 727 2103 L E B 280 2442 M 280 1977 L 745 1977 L 745 2442 L 280 2442 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 280 2051 265 2051 S 280 2134 265 2134 S 280 2217 265 2217 S 280 2300 265 2300 S 280 2383 265 2383 S 280 2051 280 2383 S (0) 227 2051 0.5 T (1) 227 2134 0.5 T (2) 227 2217 0.5 T (3) 227 2300 0.5 T (4) 227 2383 0.5 T 0 Sr 0 Sh 337 2442 337 2457 S 460 2442 460 2457 S 584 2442 584 2457 S 708 2442 708 2457 S 337 2442 708 2442 S 0.0309872 0.969013 0.0309872 0.969013 So 0.320648 0.529815 0.620724 0.777599 Sg 0 Sd B 793 2087 M 801 2095 L 810 2104 L 819 2114 L 828 2124 L 836 2135 L 845 2146 L 854 2158 L 863 2170 L 872 2183 L 880 2197 L 889 2210 L 898 2225 L 907 2241 L 916 2258 L 924 2274 L 933 2291 L 942 2308 L 951 2326 L 959 2340 L 968 2353 L 977 2364 L 986 2376 L 995 2387 L 1003 2396 L 1012 2400 L 1021 2400 L 1030 2399 L 1039 2394 L 1047 2384 L 1056 2371 L 1065 2355 L 1074 2337 L 1082 2319 L 1091 2299 L 1100 2278 L 1109 2254 L 1118 2229 L 1126 2209 L 1135 2191 L 1144 2175 L 1153 2160 L 1162 2148 L 1170 2136 L 1179 2127 L 1188 2119 L 1197 2112 L 1206 2107 L 1214 2104 L 1223 2102 L E B 775 2442 M 775 1977 L 1240 1977 L 1240 2442 L 775 2442 L E 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 1 Sd 833 2442 833 2457 S 956 2442 956 2457 S 1080 2442 1080 2457 S 1203 2442 1203 2457 S 833 2442 1203 2442 S (0.6) 833 2494 0.5 T (0.8) 956 2494 0.5 T (1.0) 1080 2494 0.5 T (1.2) 1203 2494 0.5 T 0.0309872 0.969013 0.0309872 0.969013 So 0.529815 0.738981 0.620724 0.777599 Sg 0 Sd B 1288 2090 M 1297 2099 L 1306 2108 L 1315 2118 L 1323 2128 L 1332 2139 L 1341 2151 L 1350 2163 L 1359 2175 L 1367 2188 L 1376 2202 L 1385 2216 L 1394 2231 L 1402 2247 L 1411 2264 L 1420 2281 L 1429 2297 L 1438 2315 L 1446 2333 L 1455 2346 L 1464 2359 L 1473 2370 L 1482 2382 L 1490 2393 L 1499 2401 L 1508 2404 L 1517 2405 L 1525 2403 L 1534 2398 L 1543 2388 L 1552 2375 L 1561 2358 L 1569 2341 L 1578 2322 L 1587 2301 L 1596 2280 L 1605 2255 L 1613 2230 L 1622 2210 L 1631 2192 L 1640 2175 L 1649 2161 L 1657 2148 L 1666 2137 L 1675 2127 L 1684 2119 L 1692 2112 L 1701 2107 L 1710 2104 L 1719 2102 L E B 1271 2442 M 1271 1977 L 1736 1977 L 1736 2442 L 1271 2442 L E 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 1 Sd 1328 2442 1328 2457 S 1452 2442 1452 2457 S 1575 2442 1575 2457 S 1699 2442 1699 2457 S 1328 2442 1699 2442 S 0.0309872 0.969013 0.0309872 0.969013 So 0.738981 0.948148 0.620724 0.777599 Sg 0 Sd B 1784 2093 M 1793 2102 L 1802 2112 L 1810 2122 L 1819 2133 L 1828 2144 L 1837 2155 L 1845 2168 L 1854 2180 L 1863 2194 L 1872 2207 L 1881 2222 L 1889 2237 L 1898 2253 L 1907 2270 L 1916 2287 L 1925 2304 L 1933 2321 L 1942 2339 L 1951 2353 L 1960 2365 L 1968 2376 L 1977 2388 L 1986 2398 L 1995 2406 L 2004 2409 L 2012 2410 L 2021 2408 L 2030 2402 L 2039 2392 L 2048 2378 L 2056 2362 L 2065 2344 L 2074 2325 L 2083 2303 L 2092 2282 L 2100 2257 L 2109 2232 L 2118 2211 L 2127 2193 L 2135 2176 L 2144 2162 L 2153 2149 L 2162 2137 L 2171 2127 L 2179 2119 L 2188 2112 L 2197 2107 L 2206 2104 L 2215 2102 L E B 1767 2442 M 1767 1977 L 2232 1977 L 2232 2442 L 1767 2442 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 2232 2051 2247 2051 S 2232 2134 2247 2134 S 2232 2217 2247 2217 S 2232 2300 2247 2300 S 2232 2383 2247 2383 S 2232 2051 2232 2383 S 0 Sr 0 Sh 1824 2442 1824 2457 S 1948 2442 1948 2457 S 2071 2442 2071 2457 S 2195 2442 2195 2457 S 1824 2442 2195 2442 S (0.6) 1824 2494 0.5 T (0.8) 1948 2494 0.5 T (1.0) 2071 2494 0.5 T (1.2) 2195 2494 0.5 T 0 1 0.268472 0.731528 So 0.111481 0.948148 0.777599 0.904345 Sg 0 Sd B 264 2750 M 264 2565 L 2247 2565 L 2247 2750 L 264 2750 L E 1 Sd 425 2565 425 2553 S 775 2565 775 2553 S 1125 2565 1125 2553 S 1474 2565 1474 2553 S 1824 2565 1824 2553 S 2174 2565 2174 2553 S 425 2565 2174 2565 S 425 2750 425 2762 S 775 2750 775 2762 S 1125 2750 1125 2762 S 1474 2750 1474 2762 S 1824 2750 1824 2762 S 2174 2750 2174 2762 S 425 2750 2174 2750 S (8) 425 2802 0.5 T (10) 775 2802 0.5 T (12) 1125 2802 0.5 T (14) 1474 2802 0.5 T (16) 1824 2802 0.5 T (18) 2174 2802 0.5 T 4 Sw 0 Sd 338 2578 338 2582 S 460 2588 460 2592 S 582 2599 582 2602 S 705 2609 705 2612 S 827 2619 827 2622 S 950 2629 950 2632 S 1072 2639 1072 2642 S 1194 2649 1194 2652 S 1317 2659 1317 2663 S 1439 2669 1439 2673 S 1562 2679 1562 2683 S 1684 2689 1684 2693 S 1806 2700 1806 2703 S 1929 2710 1929 2713 S 2051 2720 2051 2723 S 2174 2730 2174 2733 S 338 2578 338 2582 S 460 2588 460 2592 S 582 2599 582 2602 S 705 2609 705 2612 S 827 2619 827 2622 S 950 2629 950 2632 S 1072 2639 1072 2642 S 1194 2649 1194 2652 S 1317 2659 1317 2663 S 1439 2669 1439 2673 S 1562 2679 1562 2683 S 1684 2689 1684 2693 S 1806 2700 1806 2703 S 1929 2710 1929 2713 S 2051 2720 2051 2723 S 2174 2730 2174 2733 S 338 2578 338 2578 S 460 2588 460 2588 S 582 2599 582 2599 S 705 2609 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0.306974 0.463849 Sg B 1784 1323 M 1793 1325 L 1802 1327 L 1810 1328 L 1819 1330 L 1828 1331 L 1837 1333 L 1845 1335 L 1854 1336 L 1863 1338 L 1872 1340 L 1881 1341 L 1889 1343 L 1898 1344 L 1907 1346 L 1916 1348 L 1925 1349 L 1933 1351 L 1942 1353 L 1951 1354 L 1960 1356 L 1968 1357 L 1977 1359 L 1986 1361 L 1995 1362 L 2004 1364 L 2012 1366 L 2021 1367 L 2030 1369 L 2039 1371 L 2048 1372 L 2056 1374 L 2065 1375 L 2074 1377 L 2083 1379 L 2092 1380 L 2100 1382 L 2109 1384 L 2118 1385 L 2127 1387 L 2135 1389 L 2144 1390 L 2153 1392 L 2162 1393 L 2171 1395 L 2179 1397 L 2188 1398 L 2197 1400 L 2206 1402 L 2215 1403 L E B 1767 1450 M 1767 985 L 2232 985 L 2232 1450 L 1767 1450 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 2232 1059 2247 1059 S 2232 1141 2247 1141 S 2232 1224 2247 1224 S 2232 1307 2247 1307 S 2232 1389 2247 1389 S 2232 1059 2232 1389 S 0 Sr 0.0309872 0.969013 0.0309872 0.969013 So 0.111481 0.320648 0.463849 0.620724 Sg 0 Sh 0 Sd B 297 1843 M 306 1844 L 314 1846 L 323 1847 L 332 1849 L 341 1850 L 350 1851 L 358 1853 L 367 1854 L 376 1856 L 385 1857 L 393 1858 L 402 1860 L 411 1861 L 420 1863 L 429 1864 L 437 1865 L 446 1867 L 455 1868 L 464 1870 L 473 1871 L 481 1872 L 490 1874 L 499 1875 L 508 1877 L 516 1878 L 525 1879 L 534 1881 L 543 1882 L 552 1884 L 560 1885 L 569 1886 L 578 1888 L 587 1889 L 596 1891 L 604 1892 L 613 1893 L 622 1895 L 631 1896 L 639 1898 L 648 1899 L 657 1900 L 666 1902 L 675 1903 L 683 1905 L 692 1906 L 701 1907 L 710 1909 L 719 1910 L 727 1912 L E B 280 1946 M 280 1481 L 745 1481 L 745 1946 L 280 1946 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 280 1555 265 1555 S 280 1637 265 1637 S 280 1720 265 1720 S 280 1803 265 1803 S 280 1885 265 1885 S 280 1555 280 1885 S 0 Sr 0.0309872 0.969013 0.0309872 0.969013 So 0.320648 0.529815 0.463849 0.620724 Sg 0 Sh 0 Sd B 793 1832 M 801 1834 L 810 1835 L 819 1836 L 828 1837 L 836 1838 L 845 1839 L 854 1841 L 863 1842 L 872 1843 L 880 1844 L 889 1845 L 898 1846 L 907 1848 L 916 1849 L 924 1850 L 933 1851 L 942 1852 L 951 1853 L 959 1854 L 968 1856 L 977 1857 L 986 1858 L 995 1859 L 1003 1860 L 1012 1861 L 1021 1862 L 1030 1864 L 1039 1865 L 1047 1866 L 1056 1867 L 1065 1868 L 1074 1869 L 1082 1871 L 1091 1872 L 1100 1873 L 1109 1874 L 1118 1875 L 1126 1876 L 1135 1877 L 1144 1879 L 1153 1880 L 1162 1881 L 1170 1882 L 1179 1883 L 1188 1884 L 1197 1886 L 1206 1887 L 1214 1888 L 1223 1889 L E B 775 1946 M 775 1481 L 1240 1481 L 1240 1946 L 775 1946 L E 0.529815 0.738981 0.463849 0.620724 Sg B 1288 1789 M 1297 1790 L 1306 1791 L 1315 1792 L 1323 1793 L 1332 1794 L 1341 1795 L 1350 1796 L 1359 1797 L 1367 1797 L 1376 1798 L 1385 1799 L 1394 1800 L 1402 1801 L 1411 1802 L 1420 1803 L 1429 1804 L 1438 1805 L 1446 1806 L 1455 1807 L 1464 1807 L 1473 1808 L 1482 1809 L 1490 1810 L 1499 1811 L 1508 1812 L 1517 1813 L 1525 1814 L 1534 1815 L 1543 1816 L 1552 1817 L 1561 1818 L 1569 1818 L 1578 1819 L 1587 1820 L 1596 1821 L 1605 1822 L 1613 1823 L 1622 1824 L 1631 1825 L 1640 1826 L 1649 1827 L 1657 1827 L 1666 1828 L 1675 1829 L 1684 1830 L 1692 1831 L 1701 1832 L 1710 1833 L 1719 1834 L E B 1271 1946 M 1271 1481 L 1736 1481 L 1736 1946 L 1271 1946 L E 0.738981 0.948148 0.463849 0.620724 Sg B 1784 1740 M 1793 1740 L 1802 1741 L 1810 1741 L 1819 1742 L 1828 1742 L 1837 1742 L 1845 1743 L 1854 1743 L 1863 1744 L 1872 1744 L 1881 1745 L 1889 1745 L 1898 1746 L 1907 1746 L 1916 1747 L 1925 1747 L 1933 1747 L 1942 1748 L 1951 1748 L 1960 1749 L 1968 1749 L 1977 1750 L 1986 1750 L 1995 1750 L 2004 1751 L 2012 1751 L 2021 1752 L 2030 1752 L 2039 1753 L 2048 1753 L 2056 1753 L 2065 1754 L 2074 1754 L 2083 1755 L 2092 1755 L 2100 1756 L 2109 1756 L 2118 1756 L 2127 1757 L 2135 1757 L 2144 1758 L 2153 1758 L 2162 1759 L 2171 1759 L 2179 1760 L 2188 1760 L 2197 1761 L 2206 1761 L 2215 1762 L E B 1767 1946 M 1767 1481 L 2232 1481 L 2232 1946 L 1767 1946 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 2232 1555 2247 1555 S 2232 1637 2247 1637 S 2232 1720 2247 1720 S 2232 1803 2247 1803 S 2232 1885 2247 1885 S 2232 1555 2232 1885 S (0) 2284 1555 0.5 T (1) 2284 1637 0.5 T (2) 2284 1720 0.5 T (3) 2284 1803 0.5 T (4) 2284 1885 0.5 T 0 Sr 0.0309872 0.969013 0.0309872 0.969013 So 0.111481 0.320648 0.620724 0.777599 Sg 0 Sh 0 Sd B 297 2176 M 306 2176 L 314 2176 L 323 2176 L 332 2177 L 341 2177 L 350 2177 L 358 2177 L 367 2178 L 376 2178 L 385 2178 L 393 2178 L 402 2179 L 411 2179 L 420 2179 L 429 2179 L 437 2180 L 446 2180 L 455 2180 L 464 2180 L 473 2181 L 481 2181 L 490 2181 L 499 2182 L 508 2182 L 516 2182 L 525 2182 L 534 2183 L 543 2183 L 552 2183 L 560 2183 L 569 2184 L 578 2184 L 587 2184 L 596 2184 L 604 2185 L 613 2185 L 622 2185 L 631 2186 L 639 2186 L 648 2186 L 657 2186 L 666 2187 L 675 2187 L 683 2187 L 692 2187 L 701 2188 L 710 2188 L 719 2188 L 727 2188 L E B 280 2442 M 280 1977 L 745 1977 L 745 2442 L 280 2442 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 280 2050 265 2050 S 280 2133 265 2133 S 280 2216 265 2216 S 280 2298 265 2298 S 280 2381 265 2381 S 280 2050 280 2381 S (0) 227 2050 0.5 T (1) 227 2133 0.5 T (2) 227 2216 0.5 T (3) 227 2298 0.5 T (4) 227 2381 0.5 T 0 Sr 0 Sh 317 2442 317 2457 S 399 2442 399 2457 S 481 2442 481 2457 S 563 2442 563 2457 S 645 2442 645 2457 S 727 2442 727 2457 S 317 2442 727 2442 S 0.0309872 0.969013 0.0309872 0.969013 So 0.320648 0.529815 0.620724 0.777599 Sg 0 Sd B 793 2136 M 801 2136 L 810 2136 L 819 2136 L 828 2136 L 836 2136 L 845 2136 L 854 2136 L 863 2137 L 872 2137 L 880 2137 L 889 2137 L 898 2137 L 907 2137 L 916 2137 L 924 2138 L 933 2138 L 942 2138 L 951 2138 L 959 2138 L 968 2138 L 977 2138 L 986 2139 L 995 2139 L 1003 2139 L 1012 2139 L 1021 2139 L 1030 2139 L 1039 2139 L 1047 2140 L 1056 2140 L 1065 2140 L 1074 2140 L 1082 2140 L 1091 2140 L 1100 2140 L 1109 2141 L 1118 2141 L 1126 2141 L 1135 2141 L 1144 2141 L 1153 2141 L 1162 2141 L 1170 2142 L 1179 2142 L 1188 2142 L 1197 2142 L 1206 2142 L 1214 2142 L 1223 2142 L E B 775 2442 M 775 1977 L 1240 1977 L 1240 2442 L 775 2442 L E 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 1 Sd 813 2442 813 2457 S 895 2442 895 2457 S 977 2442 977 2457 S 1059 2442 1059 2457 S 1141 2442 1141 2457 S 1223 2442 1223 2457 S 813 2442 1223 2442 S (8) 813 2494 0.5 T (10) 895 2494 0.5 T (12) 977 2494 0.5 T (14) 1059 2494 0.5 T (16) 1141 2494 0.5 T (18) 1223 2494 0.5 T 0.0309872 0.969013 0.0309872 0.969013 So 0.529815 0.738981 0.620724 0.777599 Sg 0 Sd B 1288 2113 M 1297 2113 L 1306 2113 L 1315 2113 L 1323 2113 L 1332 2113 L 1341 2113 L 1350 2113 L 1359 2113 L 1367 2113 L 1376 2113 L 1385 2113 L 1394 2113 L 1402 2113 L 1411 2113 L 1420 2113 L 1429 2113 L 1438 2113 L 1446 2113 L 1455 2113 L 1464 2113 L 1473 2113 L 1482 2113 L 1490 2113 L 1499 2113 L 1508 2113 L 1517 2113 L 1525 2113 L 1534 2113 L 1543 2113 L 1552 2113 L 1561 2113 L 1569 2113 L 1578 2113 L 1587 2113 L 1596 2113 L 1605 2113 L 1613 2113 L 1622 2113 L 1631 2113 L 1640 2113 L 1649 2113 L 1657 2113 L 1666 2113 L 1675 2113 L 1684 2113 L 1692 2113 L 1701 2113 L 1710 2113 L 1719 2113 L E B 1271 2442 M 1271 1977 L 1736 1977 L 1736 2442 L 1271 2442 L E 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 1 Sd 1309 2442 1309 2457 S 1391 2442 1391 2457 S 1473 2442 1473 2457 S 1555 2442 1555 2457 S 1637 2442 1637 2457 S 1719 2442 1719 2457 S 1309 2442 1719 2442 S 0.0309872 0.969013 0.0309872 0.969013 So 0.738981 0.948148 0.620724 0.777599 Sg 0 Sd B 1784 2107 M 1793 2107 L 1802 2106 L 1810 2106 L 1819 2106 L 1828 2106 L 1837 2106 L 1845 2106 L 1854 2106 L 1863 2106 L 1872 2105 L 1881 2105 L 1889 2105 L 1898 2105 L 1907 2105 L 1916 2105 L 1925 2105 L 1933 2105 L 1942 2105 L 1951 2104 L 1960 2104 L 1968 2104 L 1977 2104 L 1986 2104 L 1995 2104 L 2004 2104 L 2012 2104 L 2021 2104 L 2030 2103 L 2039 2103 L 2048 2103 L 2056 2103 L 2065 2103 L 2074 2103 L 2083 2103 L 2092 2103 L 2100 2103 L 2109 2102 L 2118 2102 L 2127 2102 L 2135 2102 L 2144 2102 L 2153 2102 L 2162 2102 L 2171 2102 L 2179 2101 L 2188 2101 L 2197 2101 L 2206 2101 L 2215 2101 L E B 1767 2442 M 1767 1977 L 2232 1977 L 2232 2442 L 1767 2442 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 2232 2050 2247 2050 S 2232 2133 2247 2133 S 2232 2216 2247 2216 S 2232 2298 2247 2298 S 2232 2381 2247 2381 S 2232 2050 2232 2381 S 0 Sr 0 Sh 1804 2442 1804 2457 S 1886 2442 1886 2457 S 1968 2442 1968 2457 S 2051 2442 2051 2457 S 2133 2442 2133 2457 S 2215 2442 2215 2457 S 1804 2442 2215 2442 S (8) 1804 2494 0.5 T (10) 1886 2494 0.5 T (12) 1968 2494 0.5 T (14) 2051 2494 0.5 T (16) 2133 2494 0.5 T (18) 2215 2494 0.5 T 0 1 0.268472 0.731528 So 0.111481 0.948148 0.777599 0.904345 Sg 0 Sd B 264 2750 M 264 2565 L 2247 2565 L 2247 2750 L 264 2750 L E 1 Sd 509 2565 509 2553 S 1036 2565 1036 2553 S 1563 2565 1563 2553 S 2089 2565 2089 2553 S 509 2565 2089 2565 S 509 2750 509 2762 S 1036 2750 1036 2762 S 1563 2750 1563 2762 S 2089 2750 2089 2762 S 509 2750 2089 2750 S (0.6) 509 2802 0.5 T (0.8) 1036 2802 0.5 T (1.0) 1563 2802 0.5 T (1.2) 2089 2802 0.5 T 4 Sw 0 Sd 338 2578 338 2582 S 460 2588 460 2592 S 582 2599 582 2602 S 705 2609 705 2612 S 827 2619 827 2622 S 950 2629 950 2632 S 1072 2639 1072 2642 S 1194 2649 1194 2652 S 1317 2659 1317 2663 S 1439 2669 1439 2673 S 1562 2679 1562 2683 S 1684 2689 1684 2693 S 1806 2700 1806 2703 S 1929 2710 1929 2713 S 2051 2720 2051 2723 S 2174 2730 2174 2733 S 338 2578 338 2582 S 460 2588 460 2592 S 582 2599 582 2602 S 705 2609 705 2612 S 827 2619 827 2622 S 950 2629 950 2632 S 1072 2639 1072 2642 S 1194 2649 1194 2652 S 1317 2659 1317 2663 S 1439 2669 1439 2673 S 1562 2679 1562 2683 S 1684 2689 1684 2693 S 1806 2700 1806 2703 S 1929 2710 1929 2713 S 2051 2720 2051 2723 S 2174 2730 2174 2733 S 338 2578 338 2578 S 460 2588 460 2588 S 582 2599 582 2599 S 705 2609 705 2609 S 827 2619 827 2619 S 950 2629 950 2629 S 1072 2639 1072 2639 S 1194 2649 1194 2649 S 1317 2659 1317 2659 S 1439 2669 1439 2669 S 1562 2679 1562 2679 S 1684 2689 1684 2689 S 1806 2700 1806 2700 S 1929 2710 1929 2710 S 2051 2720 2051 2720 S 2174 2730 2174 2730 S 338 2582 338 2582 S 460 2592 460 2592 S 582 2602 582 2602 S 705 2612 705 2612 S 827 2622 827 2622 S 950 2632 950 2632 S 1072 2642 1072 2642 S 1194 2652 1194 2652 S 1317 2663 1317 2663 S 1439 2673 1439 2673 S 1562 2683 1562 2683 S 1684 2693 1684 2693 S 1806 2703 1806 2703 S 1929 2713 1929 2713 S 2051 2723 2051 2723 S 2174 2733 2174 2733 S 2 St 1 Sw 264 2615 2247 2615 S 264 2656 2247 2656 S 264 2696 2247 2696 S 1 St 1.2 Sx 0.111481 0.948148 0.150099 0.904345 So 0 1 0 1 Sg 1 Sd (C) 1256 345 0.5 T 90 Sr 90 Sh (NOx) 135 1466 0.5 T 0 Sr 0 Sh (Given : E) 1256 2895 0.5 T 0.7 Sx 0.0309872 0.969013 0.0309872 0.969013 So 0.111481 0.320648 0.150099 0.306974 Sg 0 Sd 297 507 297 602 S 369 523 369 603 S 440 538 440 605 S 512 552 512 608 S 584 564 584 613 S 656 573 656 621 S 727 579 727 632 S 0.320648 0.529815 0.150099 0.306974 Sg 793 545 793 607 S 864 561 864 612 S 936 577 936 616 S 1008 591 1008 622 S 1080 603 1080 630 S 1151 612 1151 642 S 1223 618 1223 656 S 0.529815 0.738981 0.150099 0.306974 Sg 1288 583 1288 623 S 1360 599 1360 631 S 1432 615 1432 639 S 1504 629 1504 648 S 1575 640 1575 661 S 1647 649 1647 676 S 1719 656 1719 691 S 0.738981 0.948148 0.150099 0.306974 Sg 1784 622 1784 650 S 1856 638 1856 661 S 1927 653 1927 673 S 1999 666 1999 686 S 2071 678 2071 701 S 2143 689 2143 717 S 2215 699 2215 734 S 0.0309872 0.969013 0.0309872 0.969013 So 0.111481 0.320648 0.306974 0.463849 Sg 297 1160 297 1182 S 369 1176 369 1196 S 440 1192 440 1210 S 512 1207 512 1226 S 584 1220 584 1243 S 656 1233 656 1260 S 727 1245 727 1277 S 0.320648 0.529815 0.306974 0.463849 Sg 793 1206 793 1229 S 864 1224 864 1244 S 936 1241 936 1260 S 1008 1257 1008 1277 S 1080 1272 1080 1295 S 1151 1287 1151 1313 S 1223 1301 1223 1332 S 0.529815 0.738981 0.306974 0.463849 Sg 1288 1264 1288 1287 S 1360 1281 1360 1301 S 1432 1296 1432 1316 S 1504 1310 1504 1332 S 1575 1324 1575 1350 S 1647 1336 1647 1367 S 1719 1349 1719 1385 S 0.738981 0.948148 0.306974 0.463849 Sg 1784 1311 1784 1335 S 1856 1326 1856 1347 S 1927 1340 1927 1360 S 1999 1353 1999 1373 S 2071 1365 2071 1388 S 2143 1376 2143 1404 S 2215 1387 2215 1420 S 0.0309872 0.969013 0.0309872 0.969013 So 0.111481 0.320648 0.463849 0.620724 Sg 297 1830 297 1856 S 369 1843 369 1866 S 440 1855 440 1877 S 512 1866 512 1889 S 584 1876 584 1902 S 656 1885 656 1915 S 727 1894 727 1929 S 0.320648 0.529815 0.463849 0.620724 Sg 793 1820 793 1845 S 864 1831 864 1853 S 936 1841 936 1862 S 1008 1850 1008 1872 S 1080 1857 1080 1883 S 1151 1864 1151 1895 S 1223 1871 1223 1907 S 0.529815 0.738981 0.463849 0.620724 Sg 1288 1775 1288 1803 S 1360 1785 1360 1808 S 1432 1794 1432 1814 S 1504 1802 1504 1821 S 1575 1808 1575 1830 S 1647 1813 1647 1839 S 1719 1818 1719 1849 S 0.738981 0.948148 0.463849 0.620724 Sg 1784 1726 1784 1753 S 1856 1732 1856 1755 S 1927 1737 1927 1757 S 1999 1741 1999 1760 S 2071 1744 2071 1765 S 2143 1745 2143 1770 S 2215 1747 2215 1776 S 0.0309872 0.969013 0.0309872 0.969013 So 0.111481 0.320648 0.620724 0.777599 Sg 297 2163 297 2188 S 369 2166 369 2189 S 440 2170 440 2190 S 512 2172 512 2192 S 584 2173 584 2195 S 656 2174 656 2199 S 727 2174 727 2203 S 0.320648 0.529815 0.620724 0.777599 Sg 793 2123 793 2148 S 864 2125 864 2148 S 936 2128 936 2148 S 1008 2129 1008 2149 S 1080 2130 1080 2150 S 1151 2130 1151 2153 S 1223 2129 1223 2156 S 0.529815 0.738981 0.620724 0.777599 Sg 1288 2098 1288 2127 S 1360 2101 1360 2125 S 1432 2103 1432 2123 S 1504 2104 1504 2122 S 1575 2104 1575 2122 S 1647 2102 1647 2124 S 1719 2100 1719 2127 S 0.738981 0.948148 0.620724 0.777599 Sg 1784 2083 1784 2130 S 1856 2086 1856 2126 S 1927 2088 1927 2122 S 1999 2088 1999 2119 S 2071 2088 2071 2118 S 2143 2086 2143 2118 S 2215 2082 2215 2120 S Z W %%EndDocument 262 285 a endTexFig 262 2372 a Fr(Figure)9 b(18:)16 b(Ethanol)9 b(data|coplot)f(of)h (conditionally)f(parametric)h(lo)q(cal-regression)h(\014t)g(with)262 2421 y(p)q(oin)o(t)o(wise)j(99\045)g(con\014dence)j(in)o(terv)n(als.)991 2574 y(30)p eop %%Page: 29 26 bop 262 307 a Fr(the)15 b(coplot)g(of)f(the)i(data)e(in)h(Figure)g(11,)f(NO) 990 313 y Fl(x)1024 307 y Fr(app)q(ears)i(to)f(b)q(e)h(a)e(v)o(ery)i(smo)q (oth)d(function)i(of)262 357 y Fp(C)s Fr(;)i(in)f(fact,)h(the)g(coplot)f (suggests)i(that)f(giv)o(en)f Fp(E)r Fr(,)h(the)g(dep)q(endence)i(is)e (actually)f(linear)g(in)262 407 y Fp(C)s Fr(.)21 b(Second,)15 b(the)h(undulations)f(in)f(Figure)h(16)g(are)g(small)e(compared)i(with)f(the) i(sizes)g(of)f(the)262 457 y(con\014dence)g(in)o(terv)n(als.)324 506 y(As)f(w)o(e)h(sa)o(w)f(from)e(the)j(diagnostic)f(c)o(hec)o(king,)g(if)f (w)o(e)h(increase)i Fp(\013)e Fr(and)g(thereb)o(y)h(get)f(more)262 556 y(smo)q(othness)d(as)h(a)g(function)f(of)g Fp(C)s Fr(,)h(w)o(e)g(in)o (tro)q(duce)g(lac)o(k)f(of)g(\014t.)18 b(Instead,)12 b(w)o(e)g(will)f(cut)h (bac)o(k)g(on)262 606 y(the)h(v)n(ariation)e(of)g(the)j(\014t)e(as)h(a)f (function)g(of)g Fp(C)j Fr(b)o(y)e(dropping)f Fp(C)1271 591 y Fl(2)1302 606 y Fr(from)e(the)j(\014tting)g(v)n(ariables;)262 656 y(this)h(lea)o(v)o(es)g(us)h(with)f(a)g(constan)o(t,)g Fp(E)r Fr(,)g Fp(C)s Fr(,)f Fp(E)r(C)s Fr(,)h(and)g Fp(E)1148 641 y Fl(2)1167 656 y Fr(.)19 b(In)14 b(addition,)f(w)o(e)h(will)f(sp)q (ecify)i(the)262 706 y(surface)f(to)g(b)q(e)g(conditionally)d(parametric)i (in)g Fp(C)s Fr(;)g(this)h(will)e(result)i(in)g(a)f(\014t)h(that)f(is)h (linear)f(in)262 756 y Fp(C)j Fr(giv)o(en)d Fp(E)r Fr(:)324 827 y Fi(struct)37 b(loess_str)o(uc)o(t)76 b(ethanol_)o(cp;)324 918 y(loess_set)o(up\()o(C_)o(E,)16 b(NOx,)i(n,)h(p,)g(ðanol_)o(cp\))o(;) 324 964 y(ethanol_c)o(p.m)o(od)o(el.)o(sp)o(an)d(=)k(0.25;)324 1009 y(ethanol_c)o(p.m)o(od)o(el.)o(pa)o(ram)o(etr)o(ic)o([0])c(=)j(TRUE;)324 1055 y(ethanol_c)o(p.m)o(od)o(el.)o(dr)o(op_)o(squ)o(ar)o(e[0)o(])d(=)k (TRUE;)324 1101 y(loess\(&et)o(han)o(ol)o(_cp)o(\);)262 1176 y Fr(Let's)14 b(compare)f(the)h(old)g(\014t)g(and)f(the)i(new:)324 1247 y 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2157 L 854 2169 L 863 2182 L 872 2195 L 880 2208 L 889 2221 L 898 2237 L 907 2253 L 916 2271 L 924 2289 L 933 2309 L 942 2328 L 951 2344 L 959 2356 L 968 2367 L 977 2377 L 986 2387 L 995 2396 L 1003 2401 L 1012 2406 L 1021 2408 L 1030 2408 L 1039 2403 L 1047 2393 L 1056 2378 L 1065 2362 L 1074 2347 L 1082 2331 L 1091 2310 L 1100 2288 L 1109 2264 L 1118 2242 L 1126 2223 L 1135 2207 L 1144 2191 L 1153 2177 L 1162 2164 L 1170 2153 L 1179 2143 L 1188 2134 L 1197 2127 L 1206 2122 L 1214 2118 L 1223 2116 L E B 775 2442 M 775 1977 L 1240 1977 L 1240 2442 L 775 2442 L E 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 1 Sd 833 2442 833 2457 S 956 2442 956 2457 S 1080 2442 1080 2457 S 1203 2442 1203 2457 S 833 2442 1203 2442 S (0.6) 833 2494 0.5 T (0.8) 956 2494 0.5 T (1.0) 1080 2494 0.5 T (1.2) 1203 2494 0.5 T 0.0309872 0.969013 0.0309872 0.969013 So 0.529815 0.738981 0.620724 0.777599 Sg 0 Sd B 1288 2101 M 1297 2111 L 1306 2122 L 1315 2133 L 1323 2145 L 1332 2156 L 1341 2168 L 1350 2181 L 1359 2194 L 1367 2207 L 1376 2220 L 1385 2234 L 1394 2249 L 1402 2267 L 1411 2285 L 1420 2303 L 1429 2321 L 1438 2338 L 1446 2352 L 1455 2362 L 1464 2371 L 1473 2380 L 1482 2388 L 1490 2396 L 1499 2402 L 1508 2407 L 1517 2409 L 1525 2408 L 1534 2404 L 1543 2394 L 1552 2380 L 1561 2365 L 1569 2351 L 1578 2335 L 1587 2315 L 1596 2292 L 1605 2269 L 1613 2246 L 1622 2227 L 1631 2210 L 1640 2194 L 1649 2179 L 1657 2166 L 1666 2154 L 1675 2144 L 1684 2135 L 1692 2128 L 1701 2122 L 1710 2118 L 1719 2117 L E B 1271 2442 M 1271 1977 L 1736 1977 L 1736 2442 L 1271 2442 L E 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 1 Sd 1328 2442 1328 2457 S 1452 2442 1452 2457 S 1575 2442 1575 2457 S 1699 2442 1699 2457 S 1328 2442 1699 2442 S 0.0309872 0.969013 0.0309872 0.969013 So 0.738981 0.948148 0.620724 0.777599 Sg 0 Sd B 1784 2113 M 1793 2124 L 1802 2135 L 1810 2146 L 1819 2157 L 1828 2169 L 1837 2181 L 1845 2194 L 1854 2207 L 1863 2220 L 1872 2233 L 1881 2247 L 1889 2262 L 1898 2279 L 1907 2296 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264 2565 L 2247 2565 L 2247 2750 L 264 2750 L E 1 Sd 425 2565 425 2553 S 775 2565 775 2553 S 1125 2565 1125 2553 S 1474 2565 1474 2553 S 1824 2565 1824 2553 S 2174 2565 2174 2553 S 425 2565 2174 2565 S 425 2750 425 2762 S 775 2750 775 2762 S 1125 2750 1125 2762 S 1474 2750 1474 2762 S 1824 2750 1824 2762 S 2174 2750 2174 2762 S 425 2750 2174 2750 S (8) 425 2802 0.5 T (10) 775 2802 0.5 T (12) 1125 2802 0.5 T (14) 1474 2802 0.5 T (16) 1824 2802 0.5 T (18) 2174 2802 0.5 T 4 Sw 0 Sd 338 2578 338 2582 S 460 2588 460 2592 S 582 2599 582 2602 S 705 2609 705 2612 S 827 2619 827 2622 S 950 2629 950 2632 S 1072 2639 1072 2642 S 1194 2649 1194 2652 S 1317 2659 1317 2663 S 1439 2669 1439 2673 S 1562 2679 1562 2683 S 1684 2689 1684 2693 S 1806 2700 1806 2703 S 1929 2710 1929 2713 S 2051 2720 2051 2723 S 2174 2730 2174 2733 S 338 2578 338 2582 S 460 2588 460 2592 S 582 2599 582 2602 S 705 2609 705 2612 S 827 2619 827 2622 S 950 2629 950 2632 S 1072 2639 1072 2642 S 1194 2649 1194 2652 S 1317 2659 1317 2663 S 1439 2669 1439 2673 S 1562 2679 1562 2683 S 1684 2689 1684 2693 S 1806 2700 1806 2703 S 1929 2710 1929 2713 S 2051 2720 2051 2723 S 2174 2730 2174 2733 S 338 2578 338 2578 S 460 2588 460 2588 S 582 2599 582 2599 S 705 2609 705 2609 S 827 2619 827 2619 S 950 2629 950 2629 S 1072 2639 1072 2639 S 1194 2649 1194 2649 S 1317 2659 1317 2659 S 1439 2669 1439 2669 S 1562 2679 1562 2679 S 1684 2689 1684 2689 S 1806 2700 1806 2700 S 1929 2710 1929 2710 S 2051 2720 2051 2720 S 2174 2730 2174 2730 S 338 2582 338 2582 S 460 2592 460 2592 S 582 2602 582 2602 S 705 2612 705 2612 S 827 2622 827 2622 S 950 2632 950 2632 S 1072 2642 1072 2642 S 1194 2652 1194 2652 S 1317 2663 1317 2663 S 1439 2673 1439 2673 S 1562 2683 1562 2683 S 1684 2693 1684 2693 S 1806 2703 1806 2703 S 1929 2713 1929 2713 S 2051 2723 2051 2723 S 2174 2733 2174 2733 S 2 St 1 Sw 264 2615 2247 2615 S 264 2656 2247 2656 S 264 2696 2247 2696 S 1 St 1.2 Sx 0.111481 0.948148 0.150099 0.904345 So 0 1 0 1 Sg 1 Sd (E) 1256 345 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1335 S 656 1168 656 1200 S 727 1098 727 1152 S 0.320648 0.529815 0.306974 0.463849 Sg 793 1046 793 1204 S 864 1138 864 1181 S 936 1281 936 1334 S 1008 1364 1008 1407 S 1080 1307 1080 1339 S 1151 1166 1151 1204 S 1223 1095 1223 1152 S 0.529815 0.738981 0.306974 0.463849 Sg 1288 1050 1288 1176 S 1360 1143 1360 1181 S 1432 1284 1432 1330 S 1504 1370 1504 1409 S 1575 1306 1575 1342 S 1647 1163 1647 1207 S 1719 1092 1719 1154 S 0.738981 0.948148 0.306974 0.463849 Sg 1784 1053 1784 1152 S 1856 1148 1856 1181 S 1927 1284 1927 1324 S 1999 1375 1999 1411 S 2071 1308 2071 1343 S 2143 1164 2143 1206 S 2215 1092 2215 1153 S 0.0309872 0.969013 0.0309872 0.969013 So 0.111481 0.320648 0.463849 0.620724 Sg 297 1549 297 1628 S 369 1647 369 1677 S 440 1779 440 1815 S 512 1874 512 1911 S 584 1807 584 1838 S 656 1663 656 1697 S 727 1589 727 1646 S 0.320648 0.529815 0.463849 0.620724 Sg 793 1547 793 1617 S 864 1650 864 1679 S 936 1776 936 1813 S 1008 1875 1008 1916 S 1080 1808 1080 1840 S 1151 1665 1151 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1490 648 L 1499 649 L 1508 649 L 1517 650 L 1525 651 L 1534 651 L 1543 652 L 1552 653 L 1561 654 L 1569 655 L 1578 656 L 1587 657 L 1596 658 L 1605 659 L 1613 661 L 1622 663 L 1631 665 L 1640 667 L 1649 670 L 1657 673 L 1666 676 L 1675 679 L 1684 683 L 1692 686 L 1701 690 L 1710 694 L 1719 698 L E B 1271 955 M 1271 490 L 1736 490 L 1736 955 L 1271 955 L E 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 1 Sd 1309 490 1309 475 S 1391 490 1391 475 S 1473 490 1473 475 S 1555 490 1555 475 S 1637 490 1637 475 S 1719 490 1719 475 S 1309 490 1719 490 S (8) 1309 437 0.5 T (10) 1391 437 0.5 T (12) 1473 437 0.5 T (14) 1555 437 0.5 T (16) 1637 437 0.5 T (18) 1719 437 0.5 T 0.0309872 0.969013 0.0309872 0.969013 So 0.738981 0.948148 0.150099 0.306974 Sg 0 Sd B 1784 646 M 1793 649 L 1802 651 L 1810 654 L 1819 657 L 1828 659 L 1837 662 L 1845 665 L 1854 668 L 1863 670 L 1872 673 L 1881 675 L 1889 676 L 1898 678 L 1907 679 L 1916 681 L 1925 682 L 1933 683 L 1942 684 L 1951 684 L 1960 685 L 1968 686 L 1977 686 L 1986 687 L 1995 688 L 2004 688 L 2012 689 L 2021 689 L 2030 690 L 2039 690 L 2048 691 L 2056 692 L 2065 693 L 2074 694 L 2083 695 L 2092 697 L 2100 698 L 2109 700 L 2118 702 L 2127 705 L 2135 708 L 2144 711 L 2153 714 L 2162 717 L 2171 721 L 2179 724 L 2188 728 L 2197 732 L 2206 736 L 2215 740 L E B 1767 955 M 1767 490 L 2232 490 L 2232 955 L 1767 955 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 2232 495 2247 495 S 2232 577 2247 577 S 2232 659 2247 659 S 2232 740 2247 740 S 2232 822 2247 822 S 2232 904 2247 904 S 2232 495 2232 904 S (-1) 2284 495 0.5 T (0) 2284 577 0.5 T (1) 2284 659 0.5 T (2) 2284 740 0.5 T (3) 2284 822 0.5 T (4) 2284 904 0.5 T 0 Sr 0 Sh 1804 490 1804 475 S 1886 490 1886 475 S 1968 490 1968 475 S 2051 490 2051 475 S 2133 490 2133 475 S 2215 490 2215 475 S 1804 490 2215 490 S 0.0309872 0.969013 0.0309872 0.969013 So 0.111481 0.320648 0.306974 0.463849 Sg 0 Sd B 297 1177 M 306 1181 L 314 1186 L 323 1191 L 332 1196 L 341 1202 L 350 1207 L 358 1211 L 367 1215 L 376 1218 L 385 1220 L 393 1223 L 402 1225 L 411 1226 L 420 1228 L 429 1229 L 437 1230 L 446 1231 L 455 1231 L 464 1231 L 473 1232 L 481 1232 L 490 1232 L 499 1232 L 508 1232 L 516 1232 L 525 1232 L 534 1232 L 543 1232 L 552 1232 L 560 1232 L 569 1233 L 578 1234 L 587 1235 L 596 1236 L 604 1237 L 613 1239 L 622 1241 L 631 1244 L 639 1247 L 648 1250 L 657 1254 L 666 1258 L 675 1262 L 683 1266 L 692 1270 L 701 1274 L 710 1278 L 719 1281 L 727 1285 L E B 280 1450 M 280 985 L 745 985 L 745 1450 L 280 1450 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 280 991 265 991 S 280 1073 265 1073 S 280 1154 265 1154 S 280 1236 265 1236 S 280 1318 265 1318 S 280 1399 265 1399 S 280 991 280 1399 S (-1) 227 991 0.5 T (0) 227 1073 0.5 T (1) 227 1154 0.5 T (2) 227 1236 0.5 T (3) 227 1318 0.5 T (4) 227 1399 0.5 T 0 Sr 0.0309872 0.969013 0.0309872 0.969013 So 0.320648 0.529815 0.306974 0.463849 Sg 0 Sh 0 Sd B 793 1221 M 801 1228 L 810 1237 L 819 1246 L 828 1256 L 836 1266 L 845 1274 L 854 1280 L 863 1285 L 872 1289 L 880 1293 L 889 1296 L 898 1298 L 907 1300 L 916 1301 L 924 1302 L 933 1303 L 942 1303 L 951 1303 L 959 1303 L 968 1302 L 977 1302 L 986 1301 L 995 1300 L 1003 1299 L 1012 1298 L 1021 1297 L 1030 1296 L 1039 1296 L 1047 1295 L 1056 1295 L 1065 1295 L 1074 1295 L 1082 1295 L 1091 1296 L 1100 1297 L 1109 1299 L 1118 1301 L 1126 1304 L 1135 1307 L 1144 1311 L 1153 1314 L 1162 1318 L 1170 1322 L 1179 1325 L 1188 1329 L 1197 1332 L 1206 1335 L 1214 1337 L 1223 1339 L E B 775 1450 M 775 985 L 1240 985 L 1240 1450 L 775 1450 L E 0.529815 0.738981 0.306974 0.463849 Sg B 1288 1273 M 1297 1279 L 1306 1285 L 1315 1293 L 1323 1301 L 1332 1309 L 1341 1316 L 1350 1322 L 1359 1328 L 1367 1332 L 1376 1336 L 1385 1340 L 1394 1343 L 1402 1345 L 1411 1347 L 1420 1349 L 1429 1350 L 1438 1351 L 1446 1352 L 1455 1353 L 1464 1353 L 1473 1353 L 1482 1353 L 1490 1353 L 1499 1352 L 1508 1352 L 1517 1352 L 1525 1351 L 1534 1351 L 1543 1351 L 1552 1351 L 1561 1351 L 1569 1351 L 1578 1352 L 1587 1353 L 1596 1354 L 1605 1356 L 1613 1357 L 1622 1359 L 1631 1360 L 1640 1362 L 1649 1364 L 1657 1365 L 1666 1367 L 1675 1368 L 1684 1370 L 1692 1371 L 1701 1372 L 1710 1373 L 1719 1374 L E B 1271 1450 M 1271 985 L 1736 985 L 1736 1450 L 1271 1450 L E 0.738981 0.948148 0.306974 0.463849 Sg B 1784 1329 M 1793 1332 L 1802 1336 L 1810 1339 L 1819 1343 L 1828 1346 L 1837 1350 L 1845 1354 L 1854 1357 L 1863 1361 L 1872 1364 L 1881 1367 L 1889 1369 L 1898 1371 L 1907 1373 L 1916 1375 L 1925 1377 L 1933 1378 L 1942 1380 L 1951 1381 L 1960 1382 L 1968 1383 L 1977 1383 L 1986 1384 L 1995 1385 L 2004 1386 L 2012 1386 L 2021 1387 L 2030 1387 L 2039 1388 L 2048 1389 L 2056 1389 L 2065 1390 L 2074 1391 L 2083 1392 L 2092 1393 L 2100 1395 L 2109 1395 L 2118 1396 L 2127 1397 L 2135 1397 L 2144 1398 L 2153 1398 L 2162 1398 L 2171 1398 L 2179 1398 L 2188 1398 L 2197 1399 L 2206 1399 L 2215 1399 L E B 1767 1450 M 1767 985 L 2232 985 L 2232 1450 L 1767 1450 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 2232 991 2247 991 S 2232 1073 2247 1073 S 2232 1154 2247 1154 S 2232 1236 2247 1236 S 2232 1318 2247 1318 S 2232 1399 2247 1399 S 2232 991 2232 1399 S 0 Sr 0.0309872 0.969013 0.0309872 0.969013 So 0.111481 0.320648 0.463849 0.620724 Sg 0 Sh 0 Sd B 297 1854 M 306 1855 L 314 1856 L 323 1858 L 332 1858 L 341 1860 L 350 1861 L 358 1862 L 367 1864 L 376 1866 L 385 1867 L 393 1869 L 402 1870 L 411 1871 L 420 1872 L 429 1874 L 437 1875 L 446 1876 L 455 1877 L 464 1878 L 473 1879 L 481 1880 L 490 1881 L 499 1883 L 508 1884 L 516 1885 L 525 1887 L 534 1888 L 543 1889 L 552 1891 L 560 1892 L 569 1894 L 578 1896 L 587 1897 L 596 1899 L 604 1900 L 613 1902 L 622 1903 L 631 1904 L 639 1905 L 648 1906 L 657 1906 L 666 1907 L 675 1907 L 683 1907 L 692 1908 L 701 1908 L 710 1908 L 719 1908 L 727 1908 L E B 280 1946 M 280 1481 L 745 1481 L 745 1946 L 280 1946 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 280 1487 265 1487 S 280 1569 265 1569 S 280 1650 265 1650 S 280 1732 265 1732 S 280 1813 265 1813 S 280 1895 265 1895 S 280 1487 280 1895 S 0 Sr 0.0309872 0.969013 0.0309872 0.969013 So 0.320648 0.529815 0.463849 0.620724 Sg 0 Sh 0 Sd B 793 1848 M 801 1849 L 810 1849 L 819 1850 L 828 1850 L 836 1851 L 845 1852 L 854 1853 L 863 1854 L 872 1854 L 880 1855 L 889 1855 L 898 1856 L 907 1856 L 916 1857 L 924 1857 L 933 1857 L 942 1858 L 951 1858 L 959 1859 L 968 1860 L 977 1861 L 986 1862 L 995 1863 L 1003 1864 L 1012 1865 L 1021 1866 L 1030 1867 L 1039 1868 L 1047 1870 L 1056 1871 L 1065 1872 L 1074 1874 L 1082 1875 L 1091 1877 L 1100 1878 L 1109 1880 L 1118 1881 L 1126 1882 L 1135 1884 L 1144 1885 L 1153 1885 L 1162 1886 L 1170 1887 L 1179 1887 L 1188 1888 L 1197 1888 L 1206 1888 L 1214 1889 L 1223 1889 L E B 775 1946 M 775 1481 L 1240 1481 L 1240 1946 L 775 1946 L E 0.529815 0.738981 0.463849 0.620724 Sg B 1288 1807 M 1297 1807 L 1306 1808 L 1315 1808 L 1323 1808 L 1332 1808 L 1341 1809 L 1350 1809 L 1359 1810 L 1367 1811 L 1376 1811 L 1385 1812 L 1394 1812 L 1402 1813 L 1411 1813 L 1420 1814 L 1429 1814 L 1438 1815 L 1446 1815 L 1455 1815 L 1464 1816 L 1473 1816 L 1482 1817 L 1490 1817 L 1499 1817 L 1508 1818 L 1517 1818 L 1525 1818 L 1534 1819 L 1543 1819 L 1552 1820 L 1561 1820 L 1569 1821 L 1578 1822 L 1587 1823 L 1596 1824 L 1605 1826 L 1613 1827 L 1622 1829 L 1631 1830 L 1640 1832 L 1649 1834 L 1657 1836 L 1666 1837 L 1675 1839 L 1684 1840 L 1692 1841 L 1701 1842 L 1710 1843 L 1719 1843 L E B 1271 1946 M 1271 1481 L 1736 1481 L 1736 1946 L 1271 1946 L E 0.738981 0.948148 0.463849 0.620724 Sg B 1784 1759 M 1793 1759 L 1802 1759 L 1810 1759 L 1819 1760 L 1828 1760 L 1837 1760 L 1845 1760 L 1854 1760 L 1863 1761 L 1872 1761 L 1881 1761 L 1889 1761 L 1898 1761 L 1907 1762 L 1916 1762 L 1925 1762 L 1933 1762 L 1942 1762 L 1951 1762 L 1960 1763 L 1968 1763 L 1977 1763 L 1986 1763 L 1995 1762 L 2004 1762 L 2012 1761 L 2021 1760 L 2030 1759 L 2039 1759 L 2048 1758 L 2056 1758 L 2065 1757 L 2074 1757 L 2083 1757 L 2092 1758 L 2100 1758 L 2109 1759 L 2118 1760 L 2127 1761 L 2135 1763 L 2144 1764 L 2153 1766 L 2162 1767 L 2171 1769 L 2179 1770 L 2188 1771 L 2197 1772 L 2206 1773 L 2215 1774 L E B 1767 1946 M 1767 1481 L 2232 1481 L 2232 1946 L 1767 1946 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 2232 1487 2247 1487 S 2232 1569 2247 1569 S 2232 1650 2247 1650 S 2232 1732 2247 1732 S 2232 1813 2247 1813 S 2232 1895 2247 1895 S 2232 1487 2232 1895 S (-1) 2284 1487 0.5 T (0) 2284 1569 0.5 T (1) 2284 1650 0.5 T (2) 2284 1732 0.5 T (3) 2284 1813 0.5 T (4) 2284 1895 0.5 T 0 Sr 0.0309872 0.969013 0.0309872 0.969013 So 0.111481 0.320648 0.620724 0.777599 Sg 0 Sh 0 Sd B 297 2195 M 306 2196 L 314 2197 L 323 2197 L 332 2198 L 341 2198 L 350 2199 L 358 2199 L 367 2199 L 376 2199 L 385 2199 L 393 2199 L 402 2199 L 411 2198 L 420 2198 L 429 2198 L 437 2198 L 446 2198 L 455 2198 L 464 2198 L 473 2198 L 481 2198 L 490 2198 L 499 2198 L 508 2198 L 516 2197 L 525 2197 L 534 2197 L 543 2196 L 552 2196 L 560 2196 L 569 2195 L 578 2195 L 587 2195 L 596 2195 L 604 2195 L 613 2196 L 622 2196 L 631 2197 L 639 2198 L 648 2199 L 657 2199 L 666 2200 L 675 2201 L 683 2202 L 692 2203 L 701 2204 L 710 2205 L 719 2206 L 727 2206 L E B 280 2442 M 280 1977 L 745 1977 L 745 2442 L 280 2442 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 280 1983 265 1983 S 280 2064 265 2064 S 280 2146 265 2146 S 280 2228 265 2228 S 280 2309 265 2309 S 280 2391 265 2391 S 280 1983 280 2391 S (-1) 227 1983 0.5 T (0) 227 2064 0.5 T (1) 227 2146 0.5 T (2) 227 2228 0.5 T (3) 227 2309 0.5 T (4) 227 2391 0.5 T 0 Sr 0 Sh 317 2442 317 2457 S 399 2442 399 2457 S 481 2442 481 2457 S 563 2442 563 2457 S 645 2442 645 2457 S 727 2442 727 2457 S 317 2442 727 2442 S 0.0309872 0.969013 0.0309872 0.969013 So 0.320648 0.529815 0.620724 0.777599 Sg 0 Sd B 793 2147 M 801 2148 L 810 2148 L 819 2148 L 828 2149 L 836 2149 L 845 2149 L 854 2150 L 863 2150 L 872 2150 L 880 2151 L 889 2151 L 898 2152 L 907 2152 L 916 2153 L 924 2153 L 933 2153 L 942 2154 L 951 2154 L 959 2154 L 968 2154 L 977 2154 L 986 2154 L 995 2154 L 1003 2154 L 1012 2154 L 1021 2154 L 1030 2154 L 1039 2154 L 1047 2153 L 1056 2153 L 1065 2153 L 1074 2153 L 1082 2153 L 1091 2153 L 1100 2154 L 1109 2154 L 1118 2154 L 1126 2155 L 1135 2155 L 1144 2155 L 1153 2156 L 1162 2156 L 1170 2157 L 1179 2157 L 1188 2158 L 1197 2158 L 1206 2159 L 1214 2159 L 1223 2160 L E B 775 2442 M 775 1977 L 1240 1977 L 1240 2442 L 775 2442 L E 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 1 Sd 813 2442 813 2457 S 895 2442 895 2457 S 977 2442 977 2457 S 1059 2442 1059 2457 S 1141 2442 1141 2457 S 1223 2442 1223 2457 S 813 2442 1223 2442 S (8) 813 2494 0.5 T (10) 895 2494 0.5 T (12) 977 2494 0.5 T (14) 1059 2494 0.5 T (16) 1141 2494 0.5 T (18) 1223 2494 0.5 T 0.0309872 0.969013 0.0309872 0.969013 So 0.529815 0.738981 0.620724 0.777599 Sg 0 Sd B 1288 2127 M 1297 2127 L 1306 2127 L 1315 2126 L 1323 2126 L 1332 2126 L 1341 2126 L 1350 2126 L 1359 2126 L 1367 2126 L 1376 2126 L 1385 2126 L 1394 2126 L 1402 2126 L 1411 2126 L 1420 2126 L 1429 2126 L 1438 2127 L 1446 2127 L 1455 2127 L 1464 2127 L 1473 2127 L 1482 2127 L 1490 2127 L 1499 2126 L 1508 2126 L 1517 2126 L 1525 2126 L 1534 2126 L 1543 2126 L 1552 2125 L 1561 2125 L 1569 2125 L 1578 2125 L 1587 2125 L 1596 2125 L 1605 2126 L 1613 2126 L 1622 2126 L 1631 2126 L 1640 2126 L 1649 2127 L 1657 2127 L 1666 2127 L 1675 2127 L 1684 2128 L 1692 2128 L 1701 2128 L 1710 2128 L 1719 2128 L E B 1271 2442 M 1271 1977 L 1736 1977 L 1736 2442 L 1271 2442 L E 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 1 Sd 1309 2442 1309 2457 S 1391 2442 1391 2457 S 1473 2442 1473 2457 S 1555 2442 1555 2457 S 1637 2442 1637 2457 S 1719 2442 1719 2457 S 1309 2442 1719 2442 S 0.0309872 0.969013 0.0309872 0.969013 So 0.738981 0.948148 0.620724 0.777599 Sg 0 Sd B 1784 2124 M 1793 2123 L 1802 2122 L 1810 2122 L 1819 2121 L 1828 2120 L 1837 2120 L 1845 2119 L 1854 2118 L 1863 2118 L 1872 2117 L 1881 2116 L 1889 2116 L 1898 2115 L 1907 2115 L 1916 2114 L 1925 2114 L 1933 2113 L 1942 2113 L 1951 2113 L 1960 2112 L 1968 2112 L 1977 2112 L 1986 2112 L 1995 2112 L 2004 2112 L 2012 2112 L 2021 2112 L 2030 2112 L 2039 2112 L 2048 2112 L 2056 2112 L 2065 2112 L 2074 2112 L 2083 2112 L 2092 2112 L 2100 2112 L 2109 2112 L 2118 2113 L 2127 2113 L 2135 2113 L 2144 2113 L 2153 2114 L 2162 2114 L 2171 2114 L 2179 2115 L 2188 2115 L 2197 2115 L 2206 2115 L 2215 2116 L E B 1767 2442 M 1767 1977 L 2232 1977 L 2232 2442 L 1767 2442 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 2232 1983 2247 1983 S 2232 2064 2247 2064 S 2232 2146 2247 2146 S 2232 2228 2247 2228 S 2232 2309 2247 2309 S 2232 2391 2247 2391 S 2232 1983 2232 2391 S 0 Sr 0 Sh 1804 2442 1804 2457 S 1886 2442 1886 2457 S 1968 2442 1968 2457 S 2051 2442 2051 2457 S 2133 2442 2133 2457 S 2215 2442 2215 2457 S 1804 2442 2215 2442 S (8) 1804 2494 0.5 T (10) 1886 2494 0.5 T (12) 1968 2494 0.5 T (14) 2051 2494 0.5 T (16) 2133 2494 0.5 T (18) 2215 2494 0.5 T 0 1 0.268472 0.731528 So 0.111481 0.948148 0.777599 0.904345 Sg 0 Sd B 264 2750 M 264 2565 L 2247 2565 L 2247 2750 L 264 2750 L E 1 Sd 509 2565 509 2553 S 1036 2565 1036 2553 S 1563 2565 1563 2553 S 2089 2565 2089 2553 S 509 2565 2089 2565 S 509 2750 509 2762 S 1036 2750 1036 2762 S 1563 2750 1563 2762 S 2089 2750 2089 2762 S 509 2750 2089 2750 S (0.6) 509 2802 0.5 T (0.8) 1036 2802 0.5 T (1.0) 1563 2802 0.5 T (1.2) 2089 2802 0.5 T 4 Sw 0 Sd 338 2578 338 2582 S 460 2588 460 2592 S 582 2599 582 2602 S 705 2609 705 2612 S 827 2619 827 2622 S 950 2629 950 2632 S 1072 2639 1072 2642 S 1194 2649 1194 2652 S 1317 2659 1317 2663 S 1439 2669 1439 2673 S 1562 2679 1562 2683 S 1684 2689 1684 2693 S 1806 2700 1806 2703 S 1929 2710 1929 2713 S 2051 2720 2051 2723 S 2174 2730 2174 2733 S 338 2578 338 2582 S 460 2588 460 2592 S 582 2599 582 2602 S 705 2609 705 2612 S 827 2619 827 2622 S 950 2629 950 2632 S 1072 2639 1072 2642 S 1194 2649 1194 2652 S 1317 2659 1317 2663 S 1439 2669 1439 2673 S 1562 2679 1562 2683 S 1684 2689 1684 2693 S 1806 2700 1806 2703 S 1929 2710 1929 2713 S 2051 2720 2051 2723 S 2174 2730 2174 2733 S 338 2578 338 2578 S 460 2588 460 2588 S 582 2599 582 2599 S 705 2609 705 2609 S 827 2619 827 2619 S 950 2629 950 2629 S 1072 2639 1072 2639 S 1194 2649 1194 2649 S 1317 2659 1317 2659 S 1439 2669 1439 2669 S 1562 2679 1562 2679 S 1684 2689 1684 2689 S 1806 2700 1806 2700 S 1929 2710 1929 2710 S 2051 2720 2051 2720 S 2174 2730 2174 2730 S 338 2582 338 2582 S 460 2592 460 2592 S 582 2602 582 2602 S 705 2612 705 2612 S 827 2622 827 2622 S 950 2632 950 2632 S 1072 2642 1072 2642 S 1194 2652 1194 2652 S 1317 2663 1317 2663 S 1439 2673 1439 2673 S 1562 2683 1562 2683 S 1684 2693 1684 2693 S 1806 2703 1806 2703 S 1929 2713 1929 2713 S 2051 2723 2051 2723 S 2174 2733 2174 2733 S 2 St 1 Sw 264 2615 2247 2615 S 264 2656 2247 2656 S 264 2696 2247 2696 S 1 St 1.2 Sx 0.111481 0.948148 0.150099 0.904345 So 0 1 0 1 Sg 1 Sd (C) 1256 345 0.5 T 90 Sr 90 Sh (NOx) 135 1466 0.5 T 0 Sr 0 Sh (Given : E) 1256 2895 0.5 T 0.7 Sx 0.0309872 0.969013 0.0309872 0.969013 So 0.111481 0.320648 0.150099 0.306974 Sg 0 Sd 297 507 297 713 S 369 535 369 770 S 440 550 440 705 S 512 557 512 644 S 584 554 584 619 S 656 571 656 625 S 727 593 727 656 S 0.320648 0.529815 0.150099 0.306974 Sg 793 549 793 670 S 864 578 864 682 S 936 587 936 660 S 1008 596 1008 642 S 1080 602 1080 639 S 1151 617 1151 649 S 1223 637 1223 682 S 0.529815 0.738981 0.150099 0.306974 Sg 1288 589 1288 655 S 1360 614 1360 661 S 1432 622 1432 667 S 1504 633 1504 665 S 1575 640 1575 670 S 1647 655 1647 684 S 1719 677 1719 720 S 0.738981 0.948148 0.150099 0.306974 Sg 1784 625 1784 667 S 1856 648 1856 688 S 1927 661 1927 703 S 1999 672 1999 703 S 2071 678 2071 710 S 2143 694 2143 727 S 2215 719 2215 762 S 0.0309872 0.969013 0.0309872 0.969013 So 0.111481 0.320648 0.306974 0.463849 Sg 297 1161 297 1192 S 369 1194 369 1236 S 440 1209 440 1251 S 512 1215 512 1248 S 584 1217 584 1252 S 656 1237 656 1270 S 727 1265 727 1305 S 0.320648 0.529815 0.306974 0.463849 Sg 793 1207 793 1235 S 864 1259 864 1312 S 936 1277 936 1329 S 1008 1280 1008 1317 S 1080 1276 1080 1313 S 1151 1298 1151 1329 S 1223 1319 1223 1358 S 0.529815 0.738981 0.306974 0.463849 Sg 1288 1258 1288 1288 S 1360 1303 1360 1354 S 1432 1326 1432 1375 S 1504 1331 1504 1373 S 1575 1329 1575 1375 S 1647 1345 1647 1381 S 1719 1353 1719 1394 S 0.738981 0.948148 0.306974 0.463849 Sg 1784 1313 1784 1344 S 1856 1337 1856 1379 S 1927 1355 1927 1399 S 1999 1366 1999 1405 S 2071 1368 2071 1414 S 2143 1380 2143 1415 S 2215 1381 2215 1418 S 0.0309872 0.969013 0.0309872 0.969013 So 0.111481 0.320648 0.463849 0.620724 Sg 297 1836 297 1871 S 369 1841 369 1888 S 440 1857 440 1893 S 512 1867 512 1902 S 584 1875 584 1918 S 656 1887 656 1925 S 727 1887 727 1929 S 0.320648 0.529815 0.463849 0.620724 Sg 793 1831 793 1865 S 864 1831 864 1876 S 936 1840 936 1875 S 1008 1846 1008 1883 S 1080 1853 1080 1896 S 1151 1866 1151 1904 S 1223 1867 1223 1910 S 0.529815 0.738981 0.463849 0.620724 Sg 1288 1791 1288 1824 S 1360 1798 1360 1822 S 1432 1798 1432 1830 S 1504 1801 1504 1833 S 1575 1803 1575 1841 S 1647 1818 1647 1849 S 1719 1823 1719 1863 S 0.738981 0.948148 0.463849 0.620724 Sg 1784 1742 1784 1776 S 1856 1749 1856 1772 S 1927 1746 1927 1778 S 1999 1745 1999 1778 S 2071 1739 2071 1775 S 2143 1749 2143 1779 S 2215 1756 2215 1791 S 0.0309872 0.969013 0.0309872 0.969013 So 0.111481 0.320648 0.620724 0.777599 Sg 297 2178 297 2213 S 369 2186 369 2211 S 440 2179 440 2216 S 512 2179 512 2216 S 584 2178 584 2213 S 656 2184 656 2215 S 727 2188 727 2225 S 0.320648 0.529815 0.620724 0.777599 Sg 793 2128 793 2167 S 864 2130 864 2170 S 936 2135 936 2172 S 1008 2135 1008 2173 S 1080 2138 1080 2169 S 1151 2142 1151 2169 S 1223 2142 1223 2177 S 0.529815 0.738981 0.620724 0.777599 Sg 1288 2107 1288 2147 S 1360 2106 1360 2145 S 1432 2109 1432 2144 S 1504 2108 1504 2144 S 1575 2108 1575 2142 S 1647 2111 1647 2142 S 1719 2113 1719 2144 S 0.738981 0.948148 0.620724 0.777599 Sg 1784 2089 1784 2159 S 1856 2091 1856 2145 S 1927 2086 1927 2142 S 1999 2083 1999 2141 S 2071 2082 2071 2141 S 2143 2089 2143 2138 S 2215 2094 2215 2137 S Z W %%EndDocument 262 289 a endTexFig 262 2376 a Fr(Figure)20 b(16:)30 b(Ethanol)20 b(data|coplot)f(of)h(the)h(lo)q (cal)e(regression)j(\014t)e(with)g(p)q(oin)o(t)o(wise)g(99\045)262 2425 y(con\014dence)15 b(in)o(terv)n(als.)991 2574 y(27)p eop %%Page: 26 29 bop 262 565 a 23681433 23444613 1381416 7301775 38877020 44797378 startTexFig 262 565 a %%BeginDocument: eth.coresE.p 100 dict begin /bd {bind def} def /I {Coord SetPage 1 setlinecap 1 setlinejoin LineTypes {RastersPerPoint ScaleArray} forall /Helvetica findfont PointSize RastersPerPoint mul Cex mul scalefont setfont} bd /A {PageBegin} bd /B {newpath} bd /C {currentpoint stroke moveto} bd /E {stroke} bd /M {moveto} bd /L {lineto} bd /S {moveto lineto stroke} bd /F {closepath 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P 720 737 P 720 707 P 720 601 P 720 513 P 886 644 P 886 539 P 886 757 P B 303 540 M 315 543 L 327 546 L 339 549 L 351 552 L 362 555 L 374 558 L 386 560 L 398 563 L 410 566 L 422 568 L 434 571 L 446 574 L 458 577 L 470 579 L 482 582 L 493 585 L 505 587 L 517 590 L 529 592 L 541 594 L 553 597 L 565 599 L 577 601 L 589 603 L 601 605 L 613 607 L 624 610 L 636 612 L 648 614 L 660 616 L 672 618 L 684 619 L 696 621 L 708 622 L 720 624 L 732 625 L 744 626 L 755 627 L 767 628 L 779 629 L 791 630 L 803 632 L 815 633 L 827 634 L 839 635 L 851 636 L 863 637 L 875 639 L 886 640 L E B 280 1120 M 280 490 L 910 490 L 910 1120 L 280 1120 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 280 614 260 614 S 280 773 260 773 S 280 933 260 933 S 280 1092 260 1092 S 280 614 280 1092 S (1) 223 614 0.5 T (2) 223 773 0.5 T (3) 223 933 0.5 T (4) 223 1092 0.5 T 0 Sr 0 Sh 331 490 331 470 S 442 490 442 470 S 553 490 553 470 S 664 490 664 470 S 775 490 775 470 S 886 490 886 470 S 331 490 886 490 S (8) 331 433 0.5 T (10) 442 433 0.5 T (12) 553 433 0.5 T (14) 664 433 0.5 T (16) 775 433 0.5 T (18) 886 433 0.5 T 1.5 Sw 0.1 Sc 0.0232404 0.97676 0.0232404 0.97676 So 0.39037 0.669259 0.150099 0.359266 Sg 0 Sd 941 647 1571 647 S 941 805 1571 805 S 941 962 1571 962 S 1098 490 1098 1120 S 1256 490 1256 1120 S 1413 490 1413 1120 S 1 Sw 1 Sc 964 602 P 964 677 P 964 712 P 1047 808 P 1047 680 P 1047 636 P 1214 820 P 1214 708 P 1381 672 P 1381 737 P 1381 707 P 1381 698 P 1547 757 P B 964 664 M 976 666 L 988 667 L 1000 668 L 1012 670 L 1023 671 L 1035 672 L 1047 674 L 1059 675 L 1071 676 L 1083 677 L 1095 678 L 1107 680 L 1119 681 L 1131 682 L 1143 683 L 1154 684 L 1166 686 L 1178 687 L 1190 688 L 1202 689 L 1214 690 L 1226 692 L 1238 693 L 1250 695 L 1262 696 L 1274 698 L 1285 700 L 1297 701 L 1309 703 L 1321 705 L 1333 706 L 1345 708 L 1357 710 L 1369 712 L 1381 713 L 1393 715 L 1405 717 L 1416 719 L 1428 721 L 1440 723 L 1452 725 L 1464 727 L 1476 729 L 1488 731 L 1500 733 L 1512 735 L 1524 737 L 1536 739 L 1547 741 L E B 941 1120 M 941 490 L 1571 490 L 1571 1120 L 941 1120 L E 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 1 Sd 992 490 992 470 S 1103 490 1103 470 S 1214 490 1214 470 S 1325 490 1325 470 S 1436 490 1436 470 S 1547 490 1547 470 S 992 490 1547 490 S 1.5 Sw 0.1 Sc 0.0232404 0.97676 0.0232404 0.97676 So 0.669259 0.948148 0.150099 0.359266 Sg 0 Sd 1602 647 2232 647 S 1602 805 2232 805 S 1602 962 2232 962 S 1759 490 1759 1120 S 1917 490 1917 1120 S 2074 490 2074 1120 S 1 Sw 1 Sc 1625 752 P 1625 715 P 1625 730 P 1625 848 P 1625 805 P 1625 712 P 1625 783 P 1708 956 P 1708 808 P 1875 820 P 2208 990 P 2208 1041 P B 1625 768 M 1637 771 L 1649 775 L 1661 779 L 1672 783 L 1684 786 L 1696 790 L 1708 794 L 1720 798 L 1732 803 L 1744 807 L 1756 811 L 1768 815 L 1780 820 L 1792 824 L 1803 829 L 1815 833 L 1827 838 L 1839 842 L 1851 847 L 1863 852 L 1875 857 L 1887 862 L 1899 866 L 1911 871 L 1923 877 L 1934 882 L 1946 887 L 1958 892 L 1970 897 L 1982 903 L 1994 908 L 2006 913 L 2018 919 L 2030 924 L 2042 930 L 2054 936 L 2065 941 L 2077 947 L 2089 953 L 2101 959 L 2113 965 L 2125 971 L 2137 977 L 2149 983 L 2161 989 L 2173 995 L 2185 1001 L 2196 1008 L 2208 1014 L E B 1602 1120 M 1602 490 L 2232 490 L 2232 1120 L 1602 1120 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 2232 614 2252 614 S 2232 773 2252 773 S 2232 933 2252 933 S 2232 1092 2252 1092 S 2232 614 2232 1092 S 0 Sr 0 Sh 1653 490 1653 470 S 1764 490 1764 470 S 1875 490 1875 470 S 1986 490 1986 470 S 2097 490 2097 470 S 2208 490 2208 470 S 1653 490 2208 490 S (8) 1653 433 0.5 T (10) 1764 433 0.5 T (12) 1875 433 0.5 T (14) 1986 433 0.5 T (16) 2097 433 0.5 T (18) 2208 433 0.5 T 1.5 Sw 0.1 Sc 0.0232404 0.97676 0.0232404 0.97676 So 0.111481 0.39037 0.359266 0.568433 Sg 0 Sd 280 1308 910 1308 S 280 1466 910 1466 S 280 1623 910 1623 S 437 1151 437 1781 S 595 1151 595 1781 S 752 1151 752 1781 S 1 Sw 1 Sc 303 1626 P 303 1509 P 303 1466 P 303 1698 P 303 1671 P 386 1617 P 386 1684 P 386 1661 P 386 1676 P 553 1676 P 720 1742 P 720 1655 P 886 1715 P B 303 1642 M 315 1643 L 327 1645 L 339 1647 L 351 1649 L 362 1651 L 374 1652 L 386 1654 L 398 1656 L 410 1658 L 422 1659 L 434 1661 L 446 1663 L 458 1665 L 470 1666 L 482 1668 L 493 1670 L 505 1671 L 517 1673 L 529 1675 L 541 1676 L 553 1678 L 565 1679 L 577 1681 L 589 1682 L 601 1684 L 613 1685 L 624 1686 L 636 1688 L 648 1689 L 660 1690 L 672 1692 L 684 1693 L 696 1694 L 708 1696 L 720 1697 L 732 1698 L 744 1700 L 755 1701 L 767 1703 L 779 1704 L 791 1705 L 803 1707 L 815 1708 L 827 1709 L 839 1711 L 851 1712 L 863 1713 L 875 1715 L 886 1716 L E B 280 1781 M 280 1151 L 910 1151 L 910 1781 L 280 1781 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 280 1274 260 1274 S 280 1434 260 1434 S 280 1594 260 1594 S 280 1753 260 1753 S 280 1274 280 1753 S 1.5 Sw 0.1 Sc 0 Sr 0.0232404 0.97676 0.0232404 0.97676 So 0.39037 0.669259 0.359266 0.568433 Sg 0 Sh 0 Sd 941 1308 1571 1308 S 941 1466 1571 1466 S 941 1623 1571 1623 S 1098 1151 1098 1781 S 1256 1151 1256 1781 S 1413 1151 1413 1781 S 1 Sw 1 Sc 964 1679 P 964 1698 P 964 1588 P 964 1671 P 1047 1613 P 1047 1684 P 1214 1712 P 1214 1700 P 1214 1640 P 1381 1758 P 1381 1693 P 1547 1745 P 1547 1710 P B 964 1663 M 976 1664 L 988 1665 L 1000 1666 L 1012 1667 L 1023 1669 L 1035 1670 L 1047 1671 L 1059 1672 L 1071 1673 L 1083 1675 L 1095 1676 L 1107 1677 L 1119 1678 L 1131 1680 L 1143 1681 L 1154 1682 L 1166 1684 L 1178 1686 L 1190 1687 L 1202 1689 L 1214 1691 L 1226 1692 L 1238 1694 L 1250 1696 L 1262 1697 L 1274 1699 L 1285 1700 L 1297 1702 L 1309 1703 L 1321 1705 L 1333 1706 L 1345 1708 L 1357 1709 L 1369 1711 L 1381 1712 L 1393 1714 L 1405 1715 L 1416 1717 L 1428 1718 L 1440 1720 L 1452 1721 L 1464 1723 L 1476 1724 L 1488 1725 L 1500 1727 L 1512 1728 L 1524 1730 L 1536 1731 L 1547 1733 L E B 941 1781 M 941 1151 L 1571 1151 L 1571 1781 L 941 1781 L E 1.5 Sw 0.1 Sc 0.0232404 0.97676 0.0232404 0.97676 So 0.669259 0.948148 0.359266 0.568433 Sg 1602 1308 2232 1308 S 1602 1466 2232 1466 S 1602 1623 2232 1623 S 1759 1151 1759 1781 S 1917 1151 1917 1781 S 2074 1151 2074 1781 S 1 Sw 1 Sc 1625 1569 P 1625 1567 P 1625 1459 P 1625 1588 P 1708 1613 P 1708 1527 P 1875 1575 P 1875 1491 P 1875 1640 P 2042 1552 P 2042 1448 P 2208 1525 P 2208 1710 P B 1625 1558 M 1637 1558 L 1649 1558 L 1661 1557 L 1672 1557 L 1684 1557 L 1696 1557 L 1708 1557 L 1720 1557 L 1732 1557 L 1744 1557 L 1756 1556 L 1768 1556 L 1780 1556 L 1792 1555 L 1803 1555 L 1815 1554 L 1827 1553 L 1839 1553 L 1851 1552 L 1863 1551 L 1875 1549 L 1887 1548 L 1899 1548 L 1911 1548 L 1923 1548 L 1934 1548 L 1946 1549 L 1958 1550 L 1970 1551 L 1982 1552 L 1994 1553 L 2006 1554 L 2018 1555 L 2030 1556 L 2042 1557 L 2054 1557 L 2065 1558 L 2077 1559 L 2089 1560 L 2101 1561 L 2113 1562 L 2125 1563 L 2137 1564 L 2149 1565 L 2161 1567 L 2173 1568 L 2185 1569 L 2196 1570 L 2208 1571 L E B 1602 1781 M 1602 1151 L 2232 1151 L 2232 1781 L 1602 1781 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 2232 1274 2252 1274 S 2232 1434 2252 1434 S 2232 1594 2252 1594 S 2232 1753 2252 1753 S 2232 1274 2232 1753 S (1) 2289 1274 0.5 T (2) 2289 1434 0.5 T (3) 2289 1594 0.5 T (4) 2289 1753 0.5 T 1.5 Sw 0.1 Sc 0 Sr 0.0232404 0.97676 0.0232404 0.97676 So 0.111481 0.39037 0.568433 0.777599 Sg 0 Sh 0 Sd 280 1969 910 1969 S 280 2127 910 2127 S 280 2284 910 2284 S 437 1812 437 2442 S 595 1812 595 2442 S 752 1812 752 2442 S 1 Sw 1 Sc 303 2120 P 386 1963 P 386 2069 P 386 2050 P 553 2015 P 553 2152 P 553 2064 P 720 2089 P 720 1967 P 886 1998 P 886 2087 P 886 2186 P B 303 2066 M 315 2065 L 327 2065 L 339 2064 L 351 2064 L 362 2063 L 374 2063 L 386 2062 L 398 2062 L 410 2061 L 422 2060 L 434 2060 L 446 2059 L 458 2058 L 470 2057 L 482 2056 L 493 2056 L 505 2055 L 517 2055 L 529 2054 L 541 2054 L 553 2054 L 565 2054 L 577 2054 L 589 2055 L 601 2055 L 613 2056 L 624 2057 L 636 2058 L 648 2059 L 660 2061 L 672 2062 L 684 2063 L 696 2064 L 708 2064 L 720 2065 L 732 2066 L 744 2066 L 755 2067 L 767 2068 L 779 2069 L 791 2069 L 803 2070 L 815 2071 L 827 2072 L 839 2072 L 851 2073 L 863 2074 L 875 2075 L 886 2076 L E B 280 2442 M 280 1812 L 910 1812 L 910 2442 L 280 2442 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 280 1935 260 1935 S 280 2095 260 2095 S 280 2255 260 2255 S 280 2414 260 2414 S 280 1935 280 2414 S (1) 223 1935 0.5 T (2) 223 2095 0.5 T (3) 223 2255 0.5 T (4) 223 2414 0.5 T 0 Sr 0 Sh 331 2442 331 2462 S 442 2442 442 2462 S 553 2442 553 2462 S 664 2442 664 2462 S 775 2442 775 2462 S 886 2442 886 2462 S 331 2442 886 2442 S 1.5 Sw 0.1 Sc 0.0232404 0.97676 0.0232404 0.97676 So 0.39037 0.669259 0.568433 0.777599 Sg 0 Sd 941 1969 1571 1969 S 941 2127 1571 2127 S 941 2284 1571 2284 S 1098 1812 1098 2442 S 1256 1812 1256 2442 S 1413 1812 1413 2442 S 1 Sw 1 Sc 964 1938 P 964 1939 P 964 1897 P 1047 1963 P 1047 1903 P 1214 1897 P 1214 1935 P 1381 1932 P 1381 1914 P 1381 1967 P 1381 1930 P 1547 1905 P 1547 1998 P B 964 1926 M 976 1926 L 988 1926 L 1000 1926 L 1012 1926 L 1023 1926 L 1035 1926 L 1047 1926 L 1059 1926 L 1071 1926 L 1083 1926 L 1095 1926 L 1107 1927 L 1119 1927 L 1131 1927 L 1143 1927 L 1154 1927 L 1166 1927 L 1178 1927 L 1190 1927 L 1202 1928 L 1214 1928 L 1226 1928 L 1238 1928 L 1250 1929 L 1262 1929 L 1274 1929 L 1285 1930 L 1297 1930 L 1309 1931 L 1321 1932 L 1333 1932 L 1345 1933 L 1357 1934 L 1369 1934 L 1381 1935 L 1393 1936 L 1405 1937 L 1416 1938 L 1428 1939 L 1440 1940 L 1452 1942 L 1464 1943 L 1476 1944 L 1488 1945 L 1500 1946 L 1512 1947 L 1524 1948 L 1536 1949 L 1547 1950 L E B 941 2442 M 941 1812 L 1571 1812 L 1571 2442 L 941 2442 L E 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 1 Sd 992 2442 992 2462 S 1103 2442 1103 2462 S 1214 2442 1214 2462 S 1325 2442 1325 2462 S 1436 2442 1436 2462 S 1547 2442 1547 2462 S 992 2442 1547 2442 S (8) 992 2499 0.5 T (10) 1103 2499 0.5 T (12) 1214 2499 0.5 T (14) 1325 2499 0.5 T (16) 1436 2499 0.5 T (18) 1547 2499 0.5 T 1.5 Sw 0.1 Sc 0.0232404 0.97676 0.0232404 0.97676 So 0.669259 0.948148 0.568433 0.777599 Sg 0 Sd 1602 1969 2232 1969 S 1602 2127 2232 2127 S 1602 2284 2232 2284 S 1759 1812 1759 2442 S 1917 1812 1917 2442 S 2074 1812 2074 2442 S 1 Sw 1 Sc 1625 1896 P 1708 1878 P 1708 1892 P 1708 1903 P 1875 1897 P 1875 1873 P 2042 1862 P 2042 1930 P 2208 1842 P 2208 1905 P 2208 1929 P 2208 1883 P 2208 1869 P B 1625 1893 M 1637 1893 L 1649 1893 L 1661 1892 L 1672 1892 L 1684 1892 L 1696 1892 L 1708 1891 L 1720 1891 L 1732 1891 L 1744 1891 L 1756 1890 L 1768 1890 L 1780 1890 L 1792 1890 L 1803 1890 L 1815 1889 L 1827 1889 L 1839 1889 L 1851 1889 L 1863 1889 L 1875 1889 L 1887 1889 L 1899 1889 L 1911 1888 L 1923 1888 L 1934 1888 L 1946 1888 L 1958 1888 L 1970 1888 L 1982 1888 L 1994 1888 L 2006 1888 L 2018 1888 L 2030 1887 L 2042 1887 L 2054 1887 L 2065 1887 L 2077 1887 L 2089 1887 L 2101 1887 L 2113 1887 L 2125 1887 L 2137 1887 L 2149 1887 L 2161 1887 L 2173 1887 L 2185 1887 L 2196 1887 L 2208 1887 L E B 1602 2442 M 1602 1812 L 2232 1812 L 2232 2442 L 1602 2442 L E 90 Sr 0.111481 0.948148 0.150099 0.777599 So 0 1 0 1 Sg 90 Sh 1 Sd 2232 1935 2252 1935 S 2232 2095 2252 2095 S 2232 2255 2252 2255 S 2232 2414 2252 2414 S 2232 1935 2232 2414 S 0 Sr 0 Sh 1653 2442 1653 2462 S 1764 2442 1764 2462 S 1875 2442 1875 2462 S 1986 2442 1986 2462 S 2097 2442 2097 2462 S 2208 2442 2208 2462 S 1653 2442 2208 2442 S 0 1 0.268472 0.731528 So 0.111481 0.948148 0.777599 0.904345 Sg 0 Sd B 264 2750 M 264 2565 L 2247 2565 L 2247 2750 L 264 2750 L E 1 Sd 509 2565 509 2555 S 1036 2565 1036 2555 S 1563 2565 1563 2555 S 2089 2565 2089 2555 S 509 2565 2089 2565 S 509 2750 509 2759 S 1036 2750 1036 2759 S 1563 2750 1563 2759 S 2089 2750 2089 2759 S 509 2750 2089 2750 S (0.6) 509 2807 0.5 T (0.8) 1036 2807 0.5 T (1.0) 1563 2807 0.5 T (1.2) 2089 2807 0.5 T 0 Sd 338 2583 338 2589 S 654 2600 654 2606 S 859 2617 859 2623 S 1057 2635 1057 2640 S 1278 2652 1278 2657 S 1536 2669 1536 2675 S 1673 2686 1673 2692 S 1865 2703 1865 2709 S 2024 2720 2024 2726 S 735 2583 735 2589 S 933 2600 933 2606 S 1065 2617 1065 2623 S 1296 2635 1296 2640 S 1568 2652 1568 2657 S 1681 2669 1681 2675 S 1892 2686 1892 2692 S 2060 2703 2060 2709 S 2174 2720 2174 2726 S 338 2583 735 2583 S 654 2600 933 2600 S 859 2617 1065 2617 S 1057 2635 1296 2635 S 1278 2652 1568 2652 S 1536 2669 1681 2669 S 1673 2686 1892 2686 S 1865 2703 2060 2703 S 2024 2720 2174 2720 S 338 2589 735 2589 S 654 2606 933 2606 S 859 2623 1065 2623 S 1057 2640 1296 2640 S 1278 2657 1568 2657 S 1536 2675 1681 2675 S 1673 2692 1892 2692 S 1865 2709 2060 2709 S 2024 2726 2174 2726 S 2 St 264 2629 2247 2629 S 264 2680 2247 2680 S 1 St 1.2 Sx 0.111481 0.948148 0.150099 0.904345 So 0 1 0 1 Sg 1 Sd (C) 1256 345 0.5 T 90 Sr 90 Sh (NOx) 135 1466 0.5 T 0 Sr 0 Sh (Given : E) 1256 2895 0.5 T Z W %%EndDocument 262 285 a endTexFig 262 2372 a Fr(Figure)10 b(11:)15 b(Ethanol)10 b(data|coplot)f(of)g(NO)961 2378 y Fl(x)991 2372 y Fr(against)g Fp(C)k Fr(giv)o(en)c Fp(E)j Fr(with)e(scatterplot)h(smo)q(oth-)262 2421 y(ings.)991 2574 y(21)p eop %%Page: 20 35 bop 262 307 a Fr(the)16 b(matrix,)d(a)j(scatterplot)g(of)f(NO)842 313 y Fl(x)877 307 y Fr(against)g Fp(E)r Fr(,)h(sho)o(ws)g(a)f(strong)h (nonlinear)f(dep)q(endence)262 357 y(with)h(a)h(p)q(eak)g(b)q(et)o(w)o(een)i (0.8)d(and)g(1.0.)27 b(This)17 b(mak)o(es)f(it)g(immediately)e(clear)j(that)g (w)o(e)g(need)262 407 y(to)c(use)i(lo)q(cally)d(quadratic)i(\014tting.)k(The) c(\(2,3\))f(panel)h(of)f(the)i(scatterplot)f(matrix)e(sho)o(ws)j(no)262 457 y(apparen)o(t)f(dep)q(endence)i(of)d(NO)769 463 y Fl(x)802 457 y Fr(on)h Fp(C)s Fr(;)e(ho)o(w)o(ev)o(er,)i(w)o(e)g(should)g(not)g(at)f (this)h(p)q(oin)o(t)f(dra)o(w)h(an)o(y)262 506 y(\014rm)d(conclusion)h(since) h(it)f(is)h(p)q(ossible)f(that)h(a)f(dep)q(endence)j(is)d(b)q(eing)h(mask)o (ed)e(b)o(y)h(the)h(strong)262 556 y(e\013ect)j(of)d Fp(E)r Fr(.)20 b(The)15 b(\(1,2\))f(panel,)f(whic)o(h)i(graphs)f(the)h (con\014guration)f(of)g(p)q(oin)o(ts)g(in)g(the)h(space)262 606 y(of)h(the)h(factors,)h(sho)o(ws)f(that)g(the)g(v)n(alues)g(of)f(the)i(t) o(w)o(o)e(v)n(ariables)g(are)i(nearly)e(uncorrelated)262 656 y(and)d(that)h Fp(C)j Fr(tak)o(es)d(on)g(one)g(of)f(\014v)o(e)h(v)n(alues.) 324 706 y(Coplots)i(are)h(an)f(essen)o(tial)h(to)q(ol)f(in)h(\014tting)f(lo)q (cal)g(regression)h(mo)q(dels.)25 b(Figure)17 b(11)f(is)h(a)262 756 y(coplot)10 b(of)h(the)h(ethanol)e(data.)17 b(The)12 b(dep)q(endence)i (panels)d(are)h(the)f(3)t Fk(\002)t Fr(3)g(arra)o(y)m(,)f(and)h(the)h(giv)o (en)262 805 y(panel)g(is)g(at)h(the)g(top.)18 b(On)13 b(eac)o(h)g(dep)q (endence)i(panel,)d(NO)1187 811 y Fl(x)1219 805 y Fr(is)g(graphed)h(against)f Fp(C)j Fr(for)e(those)262 855 y(observ)n(ations)i(whose)h(v)n(alues)f(of)g Fp(E)i Fr(lie)e(in)g(an)g(in)o(terv)n(al;)g(on)g(the)h(panel,)f(w)o(e)g(are)h (seeing)g(ho)o(w)262 905 y(NO)325 911 y Fl(x)357 905 y Fr(dep)q(ends)f(on)e Fp(C)j Fr(for)c Fp(E)j 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b(errors)h(are)g(computed)e(should)h(b)q(e)h(mo)q(dest)f (compared)f(to)h(those)h(at)f(whic)o(h)g(w)o(e)h(do)262 1895 y(ev)n(aluations;)f(this)f(is)g(not)h(a)f(limitati)o(on)d(for)j(the)h (practice)h(of)e(lo)q(cal)f(regression)j(mo)q(deling)262 1945 y(since)15 b(it)g(mak)o(es)e(statistical)i(and)g(graphical)f(sense)i(to)f (compute)f(in)o(terv)n(als)h(at)f(a)h(limited)e(set)262 1995 y(of)g(p)q(oin)o(ts.)324 2044 y(In)h(our)g(\014rst)h(\014t)f(to)g(the)h (made-up)e(data)h(w)o(e)g(to)q(ok)g Fi(span)e Fr(to)i(b)q(e)h(1/2.)j(Can)c(w) o(e)g(increase)i(it)262 2094 y(and)d(still)h(get)g(a)g(go)q(o)q(d)g(\014t?)k (The)d(b)q(est)g(w)o(a)o(y)f(to)g(c)o(hec)o(k)h(is)f(to)g(use)h(graphical)e (diagnostics,)g(but)262 2144 y(the)h(analysis)f(of)g(v)n(ariance)h(can)g (also)f(pro)o(vide)h(some)f(guidance:)324 2221 y Fi(struct)37 b(loess_str)o(uc)o(t)76 b(madeup2;)324 2267 y(struct)37 b(anova_str)o(uc)o(t) 76 b(madeup_a)o(nov)o(a;)324 2358 y(loess_set)o(up\()o(on)o(e_t)o(wo)o(,)17 b(response,)f(n,)j(p,)f(&madeup2\);)324 2403 y(madeup2.m)o(ode)o(l.)o(spa)o (n)e(=)k(0.75;)324 2449 y(loess\(&ma)o(deu)o(p2)o(\);)991 2574 y Fr(10)p eop %%Page: 9 46 bop 262 307 a Fr(options)14 b(to)g(default)g(v)n(alues.)19 b(The)c(analyst)f(assigns)h(to)f(v)n(arious)g(\014elds)h(of)f(the)h Fi(loess)p 1634 307 12 2 v 12 w(struct)262 357 y Fr(ob)r(ject)h(to)g(o)o(v)o (erride)g(the)h(defaults)f(as)g(desired,)h(then)f(calls)g Fi(loess\(\))d Fr(to)j(p)q(erform)f(the)i(main)262 407 y(calculation.)f(Un)o(til)c(no)o(w)g (w)o(e)h(ha)o(v)o(e)f(b)q(een)i(\014tting)e(Gaussian)h(mo)q(dels)e(b)q (ecause)j(the)g(argumen)o(t)262 457 y(that)g(con)o(trols)h(this,)g Fi(madeup)p 725 457 V 12 w(new.mode)o(l.f)o(ami)o(ly)o Fr(,)d(defaults)j(to)f Fi("gaussian")o Fr(.)k(No)o(w)c(let)h(us)g(\014t)262 506 y(a)e(mo)q(del)f (with)i(the)h(error)f(distribution)g(sp)q(eci\014ed)h(to)f(b)q(e)g (symmetric:)324 585 y Fi(madeup_ne)o(w.m)o(od)o(el.)o(fa)o(mil)o(y)j(=)i ("symmetri)o(c")o(;)324 631 y(loess\(&ma)o(deu)o(p_)o(new)o(\);)324 677 y(loess_sum)o(mar)o(y\()o(&ma)o(de)o(up_)o(new)o(\);)324 768 y Fg(Num)o(b)q(er)13 b(of)g(Observ)n(ations:)h(100)324 814 y(Equiv)n(alen)o(t)h(Num)o(b)q(er)f(of)e(P)o(arameters:)i(6.9)324 859 y(Residual)h(Scale)f(Estimate:)g(1.0868)262 942 y Fr(Also,)e(w)o(e)i(ha)o (v)o(e)f(b)q(een)h(using)f(the)h(standard)f(normalization)e(to)i(normalize)e (the)j(scales)g(of)f(the)262 992 y(t)o(w)o(o)h(factors;)g(this)h(is)f(con)o (trolled)h(b)o(y)f(the)h(argumen)o(t)e Fi(madeup)p 1244 992 V 12 w(new.model.)o(no)o(rma)o(liz)o(e)p Fr(,)e(whose)262 1042 y(v)n(alue)i(in)g(the)i(ab)q(o)o(v)o(e)e(mo)q(dels)g(has)h(b)q(een)h Fi(1)p Fr(.)j(Let's)c(no)o(w)f(remo)o(v)o(e)g(the)i(normalization:)324 1121 y Fi(madeup_ne)o(w.m)o(od)o(el.)o(no)o(rma)o(liz)o(e)h(=)k(FALSE;)262 1204 y Fr(W)m(e)13 b(do)h(not)f(need)i(to)f(see)h(the)g(output)f(this)g (time.)324 1254 y(The)e(function)f Fi(predict\(\))d Fr(can)k(b)q(e)g(used)h 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324 307 a Fi(#include)16 b()324 353 y(#include)g("loess.h")324 444 y(struct)37 b(loess_str)o(uc)o(t)76 b(madeup;)324 490 y(long)h(n)19 b(=)g(100,)f(p)h(=)h(2;)324 535 y(double)37 b(one_two[])16 b(=)j Fh(f)p Fi(-0.957581,)d(-2.80955,)g(-0.696511,)g(...)p Fh(g)p Fi(;)324 581 y(double)37 b(response[)o(])16 b(=)k Fh(f)p Fi(14.4536,)c(6.62283,)h(13.6714,)f(...)p Fh(g)p Fi(;)324 672 y(main\(\))h Fh(f)481 718 y Fi(loess_set)o(up)o(\(on)o(e_t)o(wo)o(,)g (response)o(,)g(n,)i(p,)f(&madeup\);)481 764 y(madeup.mo)o(de)o(l.s)o(pan)e (=)j(0.5;)481 809 y(loess\(&ma)o(de)o(up\))o(;)481 855 y(loess_sum)o(ma)o (ry\()o(&ma)o(de)o(up\))o(;)324 901 y Fh(g)262 975 y Fr(Compiling)o(,)11 b(linking)h(with)h(the)i(lo)q(ess)f(library)m(,)f(and)g(executing)i(giv)o(es) f(us)g(the)g(output:)324 1090 y Fg(Num)o(b)q(er)f(of)g(Observ)n(ations:)h (100)324 1136 y(Equiv)n(alen)o(t)h(Num)o(b)q(er)f(of)e(P)o(arameters:)i(14.9) 324 1181 y(Residual)h(Standard)g(Error:)e(0.9693)262 1255 y Fr(The)18 b Fq(e)n(quivalent)i(numb)n(er)f(of)g(p)n(ar)n(ameters)p Fr(,)f Fp(\026)p Fr(,)i(measures)e(the)i(amoun)o(t)c(of)i(smo)q(othing,)f(as) 262 1305 y(de\014ned)11 b(in)g(Section)g(4.1,)e(and)i(is)g(analogous)e(to)i (the)g(n)o(um)o(b)q(er)f(of)g(parameters)h(in)f(a)g(parametric)262 1355 y(\014t.)18 b(Also)13 b(sho)o(wn)h(is)g(an)g(estimate)f(of)g Fp(\033)q Fr(,)h(the)g(standard)h(error)f(of)g(the)g(residuals.)324 1405 y(Notice)e(that)g Fi(one)p 602 1405 12 2 v 13 w(two[])p Fr(,)e(the)j(v)o(ector)f(of)g(the)g(t)o(w)o(o)g(predictors)h(is)f(of)f (length)h Fi(\(n)19 b(*)g(p\))p Fr(.)e(One)262 1455 y(can)f(think)f(of)h(it)f (as)i(a)e(concatenated)j(v)o(ector)f(of)e(all)g(the)h(predictor)h(v)o (ectors,)g(in)f(whic)o(h)g(the)262 1504 y Fp(j)r Fr(-th)f(co)q(ordinate)f(of) g(the)i Fp(i)p Fr(-th)e(p)q(oin)o(t)h(is)f(in)g Fi(one)p 1018 1504 V 13 w(two[i+n*j])o Fr(,)d(where)16 b(0)d Fk(\024)g Fp(j)i(<)e(p)p Fr(,)h(0)e Fk(\024)h Fp(i)g(<)g(n)p Fr(.)262 1554 y(W)m(e)j(will)g(adhere)i 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y(loess_sum)o(mar)o(y\()o(&ma)o(de)o(up_)o(new)o(\);)324 2234 y Fg(Num)o(b)q(er)13 b(of)g(Observ)n(ations:)h(100)324 2280 y(Equiv)n(alen)o(t)h(Num)o(b)q(er)f(of)e(P)o(arameters:)i(6.9)324 2325 y(Residual)h(Standard)g(Error:)e(1.4804)262 2399 y Fr(The)e(purp)q(ose)h (of)f(splitting)f(the)h(in)o(v)o(o)q(cation)f(in)o(to)g(t)o(w)o(o)h(function) g(calls)f(is)h(no)o(w)g(clear.)17 b(The)12 b(role)262 2449 y(of)c Fi(loess)p 406 2449 V 12 w(setup\(\))f Fr(is)i(to)g(lo)q(ok)g(at)g (the)h(input)f(data)g(and)g(set)h(a)f(host)h(of)e(in)o(ternal)h(parameters)h (and)1001 2574 y(8)p eop %%Page: 7 48 bop 324 307 a Fr(The)14 b(lo)q(ess)h(robust)g(estimate)f(b)q(egins)g(with)g (the)h(Gaussian-error)f(estimate,)h(^)-22 b Fp(g)q Fr(\()p Fp(x)p Fr(\).)19 b(Then)262 357 y(the)14 b(residuals)882 407 y(^)-24 b Fp(")898 413 y Fo(i)924 407 y Fr(=)12 b Fp(y)988 413 y Fo(i)1011 407 y Fk(\000)f Fr(^)-22 b Fp(g)q Fr(\()p Fp(x)1114 413 y Fo(i)1128 407 y Fr(\))262 482 y(are)14 b(computed.)j(Let)614 595 y Fp(B)r 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Fr(\),)g(replaced)g(b)o(y)f Fp(r)1153 1130 y Fo(i)1167 1124 y Fp(w)1197 1130 y Fo(i)1210 1124 y Fr(\()p Fp(x)p Fr(\);)j(th)o(us,)e(p)q (oin)o(ts)f(\()p Fp(x)1579 1130 y Fo(i)1593 1124 y Fp(;)7 b(y)1632 1130 y Fo(i)1645 1124 y Fr(\))20 b(with)262 1174 y(large)15 b(residuals)h(receiv)o(e)h(reduced)h(w)o(eigh)o(t.)23 b(Then)16 b(new)h(residuals)f(are)g(computed)f(and)h(the)262 1224 y(pro)q(cedure)d(is)f (rep)q(eated.)19 b(The)13 b(\014nal)e(robust)i(estimate)e(is)h(the)g(result)h (of)e(up)q(dating)h(the)g(initial)262 1274 y(estimate)h(sev)o(eral)h(times.) 262 1390 y Fm(Errors)k(with)g(Unequal)g(Scales)262 1467 y Fr(Supp)q(ose)f(w)o (e)f(sp)q(ecify)h(that)f Fp(a)744 1473 y Fo(i)758 1467 y Fp(")777 1473 y Fo(i)807 1467 y Fr(ha)o(v)o(e)g(constan)o(t)h(v)n(ariance)f Fp(\033)1265 1452 y Fl(2)1284 1467 y Fr(.)25 b(Then,)17 b(for)e(the)i (Gaussian-)262 1517 y(error)d(estimate,)e(the)i(neigh)o(b)q(orho)q(o)q(d)f(w) o(eigh)o(t,)g Fp(w)1044 1523 y Fo(i)1058 1517 y Fr(\()p Fp(x)p Fr(\),)g(is)g(replaced)h(b)o(y)f Fp(a)1422 1523 y Fo(i)1436 1517 y Fp(w)1466 1523 y Fo(i)1480 1517 y Fr(\()p Fp(x)p Fr(\),)g(and)g(for)g (the)262 1566 y(robust)h(estimate,)f(the)h(w)o(eigh)o(t)g Fp(r)791 1572 y Fo(i)804 1566 y Fp(w)834 1572 y Fo(i)848 1566 y Fr(\()p Fp(x)p Fr(\))g(is)f(replaced)i(b)o(y)f Fp(a)1203 1572 y Fo(i)1217 1566 y Fp(r)1236 1572 y Fo(i)1249 1566 y Fp(w)1279 1572 y Fo(i)1293 1566 y Fr(\()p Fp(x)p Fr(\).)262 1704 y Fn(2)69 b(C)22 b(F)-6 b(unctions)262 1795 y Fr(This)11 b(section)h(describ)q(es)h(the)f(C)g (functions)f(for)g(lo)q(cal)g(regression)i(mo)q(deling.)i(In)c(eac)o(h)h (subsec-)262 1844 y(tion)i(w)o(e)h(analyze)g(a)f(dataset,)i(illustrating)d (ho)o(w)i(the)g(C)g(functions)g(are)g(used)h(to)f(\014t)g(mo)q(dels.)262 1894 y(W)m(e)9 b(also)g(use)i(graphics)f(to)g(explore)h(the)f(data)g(and)g (carry)g(out)g(graphical)f(diagnostics)h(to)g(c)o(hec)o(k)262 1944 y(the)15 b(sp)q(eci\014cations)i(of)d(the)i(\014tted)g(mo)q(dels.)k(Our) c(goal)e(is)h(to)g(sho)o(w)g(ho)o(w)g(the)h(data)f(are)g(ana-)262 1994 y(lyzed)c(in)f(practice)i(using)f(the)h(C)f(routines)g(and)g(graphics,)g (and)g(ho)o(w)g(eac)o(h)g(dataset)h(presen)o(ts)h(a)262 2044 y(di\013eren)o(t)g(c)o(hallenge.)k(W)m(e)12 b(b)q(egin,)g(ho)o(w)o(ev)o(er,)h (b)o(y)f(rapidly)f(running)h(through)g(the)h(C)f(functions)262 2093 y(for)f(\014tting)h(and)g(inference)h(to)f(giv)o(e)g(an)f(o)o(v)o (erview;)h(the)h(reader)g(need)g(not)f(understand)i(details)262 2143 y(at)f(this)h(p)q(oin)o(t.)324 2193 y(The)k(basic)f(mo)q(deling)e (function)i(is)g Fi(loess\(\))p Fr(.)26 b(Let's)17 b(apply)g(it)g(to)g(some)g (madeup)f(data)262 2243 y(consisting)d(of)g(100)g(observ)n(ations)h(of)f (three)i(v)n(ariables,)e(one)h(resp)q(onse)i(and)d(t)o(w)o(o)h(factors.)k(W)m (e)262 2293 y(will)c(\014t)j(a)f(Gaussian)g(mo)q(del)f(with)h(the)h(smo)q (othing)d(parameter,)j Fp(\013)p Fr(,)f(equal)g(to)g(0.5)g(and)g(the)262 2343 y(degree,)e Fp(\025)p Fr(,)g(of)f(the)i(lo)q(cally-\014tted)e(p)q (olynomial)d(equal)k(to)g(1:)1001 2574 y(7)p eop %%Page: 6 49 bop 324 307 a Fr(If)20 b(w)o(e)g(ha)o(v)o(e)g(sp)q(eci\014ed)h(the)g(surface) g(to)f(b)q(e)h(lo)q(cally)e(w)o(ell)g(appro)o(ximated)f(b)o(y)i(a)g(linear) 262 357 y(p)q(olynomial)o(|that)7 b(is,)k(if)f Fp(\025)h Fr(is)g(1|then)f(a)h (linear)f(p)q(olynomial)d(is)k(\014tted)g(to)g Fp(y)1472 363 y Fo(i)1497 357 y Fr(using)f(w)o(eigh)o(ted)262 407 y(least)h(squares)i(with) e(the)h(w)o(eigh)o(ts)g Fp(w)838 413 y Fo(i)851 407 y Fr(\()p Fp(x)p Fr(\);)g(the)h(v)n(alue)d(of)h(this)h(\014tted)g(p)q(olynomial)d(at)i Fp(x)g Fr(is)i(^)-22 b Fp(g)q Fr(\()p Fp(x)p Fr(\).)262 457 y(If)14 b Fp(\025)g Fr(is)h(2,)f(a)g(quadratic)h(is)f(\014tted.)21 b(Note)15 b(that)f(as)h Fp(\013)d Fk(!)h(1)p Fr(,)i(^)-23 b Fp(g)r Fr(\()p Fp(x)p Fr(\))14 b(tends)i(to)e(a)g(linear)g(surface)262 506 y(for)f(lo)q(cally)g(linear)g(\014tting)g(or)h(a)g(quadratic)g(surface)h (for)e(lo)q(cally)g(quadratic)g(\014tting.)262 623 y Fm(Iden)n(tically)21 b(Distributed,)h(Gaussian)i(Errors:)33 b(Tw)n(o)24 b(or)f(More)g(Nu-)262 681 y(meric)16 b(F)-5 b(actors)262 757 y Fr(W)m(e)16 b(con)o(tin)o(ue)h(to)f (supp)q(ose)i(the)g(errors)g(are)f(iden)o(tically)e(distributed)j(and)e (Gaussian.)26 b(The)262 807 y(one)19 b(additional)e(issue)j(that)f(needs)i (to)e(b)q(e)g(addressed)i(for)e Fp(p)g Fr(factors)h(with)e Fp(p)j(>)e Fr(1)g(is)g(the)262 857 y(notion)12 b(of)g(distance)h(in)g(the)g (space)h(of)e(the)h(factors.)18 b(Supp)q(ose)c Fp(x)f Fr(is)f(a)h(v)n(alue)f (in)g(the)i(space.)k(T)m(o)262 907 y(de\014ne)f(neigh)o(b)q(orho)q(o)q(d)f(w) o(eigh)o(ts)g(w)o(e)h(need)g(to)f(de\014ne)i(the)f(distance,)g(\001)1421 913 y Fo(i)1434 907 y Fr(\()p Fp(x)p Fr(\),)g(from)d Fp(x)i Fr(to)g Fp(x)1736 913 y Fo(i)1750 907 y Fr(,)262 957 y(the)h Fp(i)p Fr(th)f(observ)n(ation)g(of)g(the)h(factors.)26 b(W)m(e)16 b(will)f(use)i(Euclidean)g(distance,)g(but)g(the)g Fp(x)1688 963 y Fo(i)1718 957 y Fr(do)262 1006 y(not)e(ha)o(v)o(e)h(to)g(b)q(e)h(the)f (ra)o(w)g(measuremen)o(ts.)24 b(T)o(ypically)m(,)14 b(it)i(mak)o(es)f(sense)i (to)f(tak)o(e)g Fp(x)1636 1012 y Fo(i)1666 1006 y Fr(to)g(b)q(e)262 1056 y(the)g(ra)o(w)g(measuremen)o(ts)f(normalized)f(in)i(some)f(w)o(a)o(y)m (.)23 b(W)m(e)15 b(will)g(normalize)f(the)i(factors)h(b)o(y)262 1106 y(dividing)c(them)i(b)o(y)g(their)h(10\045)e(trimmed)f(sample)h (standard)i(deviation,)f(and)g(call)f(this)i(the)262 1156 y Fq(standar)n(d)f(normalization)p Fr(.)i(There)e(are,)f(ho)o(w)o(ev)o(er,)f (situations)h(where)h(w)o(e)f(migh)o(t)d(c)o(ho)q(ose)k(not)262 1206 y(to)e(normalize|for)f(example,)g(if)h(the)h(factors)h(represen)o(t)h(p) q(osition)d(in)g(space.)324 1256 y(Armed)k(with)h(the)g(\001)674 1262 y Fo(i)688 1256 y Fr(\()p Fp(x)p Fr(\),)g(the)h(lo)q(ess)f(\014tting)g (metho)q(d)f(for)h Fp(p)g(>)g Fr(1)g(is)f(just)i(an)e(ob)o(vious)262 1305 y(generalization)d(of)h(the)h(one-factor)f(metho)q(d.)21 b(F)m(or)15 b Fp(\013)e(<)i Fr(1,)f(neigh)o(b)q(orho)q(o)q(d)h(w)o(eigh)o (ts,)g Fp(w)1680 1311 y Fo(i)1694 1305 y Fr(\()p Fp(x)p Fr(\),)262 1355 y(are)i(de\014ned)i(using)e(the)h(same)f(form)o(ulas)e(used)j(for)f(one) h(factor;)h(th)o(us,)f(if)f Fp(\025)g Fr(=)h(1,)g(w)o(e)f(\014t)h(a)262 1405 y(linear)e(p)q(olynomial)d(in)k(the)g(factors)h(using)e(w)o(eigh)o(ted)h (least)g(squares,)i(or,)e(if)f Fp(\025)h Fr(=)f(2,)h(w)o(e)g(\014t)262 1455 y(a)g(quadratic.)29 b(F)m(or)18 b Fp(\013)g(>)g Fr(1,)g(the)g Fp(w)843 1461 y Fo(i)857 1455 y Fr(\()p Fp(x)p Fr(\))f(are)h(de\014ned)h(b)o (y)f(the)g(same)f(form)o(ula)e(except)k(that)262 1505 y(\001)297 1512 y Fl(\()p Fo(q)q Fl(\))340 1505 y Fr(\()p Fp(x)p Fr(\))14 b(is)g(replaced)h(b)o(y)e(\001)708 1512 y Fl(\()p Fo(n)p Fl(\))757 1505 y Fr(\()p Fp(x)p Fr(\))p Fp(\013)840 1490 y Fl(1)p Fo(=p)892 1505 y Fr(.)262 1621 y Fm(Dropping)24 b(Squares)h(and)h(Conditionally)e(P)n (arametric)f(Fitting)h(for)262 1679 y(Tw)n(o)19 b(or)g(More)f(F)-5 b(actors)262 1756 y Fr(Supp)q(ose)15 b Fp(\025)f Fr(has)g(b)q(een)h(sp)q (eci\014ed)h(to)e(b)q(e)g(2.)19 b(Supp)q(ose,)14 b(in)g(addition,)f(that)h(w) o(e)g(ha)o(v)o(e)g(sp)q(eci\014ed)262 1805 y(the)i(squares)g(of)f(certain)i (factors)f(to)f(b)q(e)h(dropp)q(ed.)24 b(Then)16 b(those)h(monom)o(ial)o(s)c (are)j(not)g(used)262 1855 y(in)d(the)h(lo)q(cal)f(\014tting.)324 1905 y(Supp)q(ose)18 b(a)g(prop)q(er)g(subset)h(of)f(the)g(factors)g(has)g(b) q(een)g(sp)q(eci\014ed)i(to)d(b)q(e)h(conditionally)262 1955 y(parametric.)k(Then)16 b(w)o(e)g(simply)e(ignore)h(these)i(factors)f(in)g (computing)e(the)i(Euclidean)g(dis-)262 2005 y(tances)g(that)e(are)i(used)f (in)g(the)g(de\014nition)g(of)f(the)h(neigh)o(b)q(orho)q(o)q(d)g(w)o(eigh)o (ts,)g Fp(w)1527 2011 y Fo(i)1540 2005 y Fr(\()p Fp(x)p Fr(\).)21 b(It)15 b(is)g(an)262 2054 y(easy)f(exercise)i(to)d(sho)o(w)h(that)g(this)g (results)h(in)e(a)h(conditionally)e(parametric)h(\014t.)262 2171 y Fm(Symme)o(tri)o(c)j(Errors)i(and)h(Robust)g(Fitting)262 2247 y Fr(Supp)q(ose)h(the)g Fp(")526 2253 y Fo(i)559 2247 y Fr(ha)o(v)o(e)f(b)q(een)i(sp)q(eci\014ed)g(to)e(ha)o(v)o(e)g(a)g(symmetric) f(distribution.)33 b(Then)20 b(w)o(e)262 2297 y(mo)q(dify)14 b(the)k(lo)q(ess)g(\014tting)e(pro)q(cedures)k(to)d(pro)q(duce)h(a)f(robust)h (estimate;)f(the)h(estimate)f(is)262 2347 y(not)e(adv)o(ersely)h(a\013ected)h (if)d(the)i(errors)h(ha)o(v)o(e)e(a)g(long-tailed)f(distribution,)h(but)h(it) f(has)g(high)262 2397 y(e\016ciency)f(in)g(the)g(Gaussian)f(case.)1001 2574 y(6)p eop %%Page: 5 50 bop 262 307 a Fm(Summary)16 b(of)i(the)h(Choices)262 384 y Fr(Th)o(us,)e(the)h(\014tting)e(of)h(lo)q(cal)f(regression)i(mo)q(dels)e(in)o (v)o(olv)o(es)g(making)f(the)i(follo)o(wing)e(c)o(hoices)262 434 y(ab)q(out)e(the)i(sp)q(eci\014cation)f(of)g(prop)q(erties)h(of)e(the)i (errors)g(and)f(the)g(regression)h(surface:)324 516 y Fk(\017)20 b Fr(Gaussian)14 b(or)f(symmetric)g(distribution;)324 598 y Fk(\017)20 b Fr(constan)o(t)15 b(v)n(ariance)e(or)h(a)g(priori)f(w)o(eigh)o (ts;)324 681 y Fk(\017)20 b Fr(lo)q(cally)13 b(linear)g(or)h(lo)q(cally)e (quadratic)i(in)g(the)g(factors;)324 763 y Fk(\017)20 b Fr(neigh)o(b)q(orho)q (o)q(d)14 b(size;)324 846 y Fk(\017)20 b Fr(normalization)11 b(of)j(the)g(scales;)324 928 y Fk(\017)20 b Fr(dropping)14 b(squares;)324 1011 y Fk(\017)20 b Fr(conditionally)12 b(parametric)h (subset.)262 1127 y Fm(1.2)55 b(Lo)r(ess:)24 b(Fitting)17 b(Lo)r(cal)h (Regression)g(Mo)r(dels)262 1203 y Fr(The)c(metho)q(d)f(w)o(e)h(will)e(use)j (to)e(\014t)h(lo)q(cal)f(regression)i(mo)q(dels)e(is)g(called)h Fq(lo)n(ess)p Fr(,)f(whic)o(h)g(is)h(short)262 1253 y(for)i Fq(lo)n(c)n(al)h(r)n(e)n(gr)n(ession)p Fr(,)f(and)h(w)o(as)f(c)o(hosen)i(as)f (the)g(name)f(since)i(a)e(lo)q(ess)h(is)g(a)g(dep)q(osit)g(of)f(\014ne)262 1303 y(cla)o(y)c(or)g(silt)g(along)g(a)g(riv)o(er)h(v)n(alley)m(,)e(and)h(th) o(us)h(is)g(a)f(surface)i(of)e(sorts.)18 b(The)13 b(w)o(ord)g(comes)f(from) 262 1353 y(the)i(German)f Fq(l\177)-21 b(oss)p Fr(,)13 b(and)g(is)h (pronounced)h Fq(l\026)-21 b(o)960 1344 y(\023)962 1353 y(is)p Fr(.)262 1469 y Fm(Iden)n(tically)11 b(Distributed,)h(Gaussian)i(Errors:)21 b(One)13 b(Numeric)e(F)-5 b(actor)262 1545 y Fr(Let's)18 b(b)q(egin)g(with)f (the)i(classical)f(case)g(of)g(Gaussian)f(errors)i(with)f(constan)o(t)g(v)n (ariance)g Fp(\033)1731 1530 y Fl(2)1750 1545 y Fr(.)262 1595 y(Supp)q(ose)13 b(there)g(is)f(just)g(one)g(factor.)18 b(Let)12 b Fp(x)g Fr(b)q(e)h(an)o(y)e(v)n(alue)h(along)f(the)h(scale)h(of)e (measuremen)o(t)262 1645 y(of)g(the)i(v)n(ariable.)k(The)c(lo)q(ess)f (\014tting)g(pro)q(cedure)j(is)d(a)g(n)o(umerical)f(algorithm)f(that)i (prescrib)q(es)262 1695 y(ho)o(w)i(^)-22 b Fp(g)q Fr(\()p Fp(x)p Fr(\),)14 b(the)g(estimate)f(of)h Fp(g)h Fr(at)f(a)f(sp)q(eci\014c)j(v)n (alue)d(of)g Fp(x)p Fr(,)g(is)h(computed.)324 1745 y(Let)i(\001)435 1751 y Fo(i)448 1745 y Fr(\()p Fp(x)p Fr(\))e(=)g Fk(j)p Fp(x)9 b Fk(\000)i Fp(x)676 1751 y Fo(i)689 1745 y Fk(j)p Fr(,)k(let)g(\001)824 1752 y Fl(\()p Fo(i)p Fl(\))863 1745 y Fr(\()p Fp(x)p Fr(\))g(b)q(e)h(the)g (v)n(alues)f(of)g(these)h(distances)h(ordered)f(from)262 1795 y(smallest)c(to)i(largest,)f(and)h(let)643 1907 y Fp(T)6 b Fr(\()p Fp(u)p Fr(;)h Fp(t)p Fr(\))k(=)818 1849 y Fj(\032)856 1886 y Fr(\(1)e Fk(\000)g Fr(\()p Fp(u=t)p Fr(\))1035 1871 y Fl(3)1054 1886 y Fr(\))1070 1871 y Fl(3)1089 1886 y Fp(;)41 b Fr(for)13 b(0)e Fk(\024)h Fp(u)f(<)h(t)856 1936 y Fr(0)265 b(for)13 b Fp(u)e Fk(\025)h Fp(t)262 2020 y Fr(b)q(e)i(the)h Fq(tricub)n(e)f(weight)g(function)p Fr(.)324 2070 y(The)e(smo)q(othness)f(of) g(the)h(lo)q(ess)f(\014t)h(dep)q(ends)h(on)e(the)h(sp)q(eci\014cation)g(of)f (the)h(neigh)o(b)q(orho)q(o)q(d)262 2120 y(parameter,)i Fp(\013)f(>)g Fr(0.)21 b(As)16 b Fp(\013)e Fr(increases,)k(^)-22 b Fp(g)16 b Fr(b)q(ecomes)f(smo)q(other.)20 b(Supp)q(ose)c Fp(\013)d Fk(\024)h Fr(1.)21 b(Let)15 b Fp(q)h Fr(b)q(e)262 2169 y(equal)d(to)h Fp(\013n)f Fr(truncated)i(to)f(an)g(in)o(teger.)k(W)m(e)c(de\014ne)h(a)e(w)o (eigh)o(t)h(for)f(\()p Fp(x)1399 2175 y Fo(i)1413 2169 y Fp(;)7 b(y)1452 2175 y 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put dup stringwidth pop /CharWidth exch def Cos 0 eq { Text-y Sin div } { Sin 0 eq { CharWidth Cos div } { /H Text-y Sin div def /W CharWidth Cos div def H W lt {H} {W} ifelse } ifelse } ifelse 2 div /CharDist exch def CharDist 0 translate 0 0 moveto gsave RotDiff rotate CharWidth 2 div neg Text-y 2 div neg rmoveto Outline {false charpath stroke} {show} ifelse grestore CharDist 0 translate 0 0 moveto } forall } bd /Show {Outline {false charpath stroke} {show} ifelse} bd /BoxClip {/CLW currentlinewidth def 2 {CLW add 4 1 roll} repeat 2 {CLW sub 4 1 roll} repeat initclip newpath 2 index exch 2 index exch dup 6 index exch moveto 3 {lineto} repeat closepath clip newpath} bd /Subregion {/A exch def /Uy exch def /Ux exch def /Ly exch def /Lx exch def Ux Lx sub A 0 get mul Lx add Uy Ly sub A 1 get mul Ly add Ux Lx sub A 2 get mul Lx add Uy Ly sub A 3 get mul Ly add} bd /SetFigure {Page aload pop Figure Subregion} bd /SetPlot {SetFigure Plot Subregion} bd /SetClip {ClipToPlot {SetPlot} {SetFigure} ifelse BoxClip} bd /SetPage {0 0 Width Height Page astore RastersPerPoint ScaleArray} bd /PageBegin {save /PageContext exch def /InPage true def} bd /PageEnd {PageContext restore /InPage false def} bd /Landscape false def /Region [21.48 111.72 590.28 680.52] def /RastersPerInch 300 def /PointSize 8.77778 def /Fonts [ /Helvetica /Courier /Times-Roman /Helvetica-Oblique /Helvetica-Bold /Helvetica-BoldOblique /Courier-Oblique /Courier-Bold /Courier-BoldOblique /Times-Italic /Times-Bold /Times-BoldItalic /Symbol /AvantGarde-Book /AvantGarde-BookOblique /AvantGarde-Demi /AvantGarde-DemiOblique /Bookman-Demi /Bookman-DemiItalic /Bookman-Light /Bookman-LightItalic /Helvetica-Narrow /Helvetica-Narrow-Bold /Helvetica-Narrow-BoldOblique /Helvetica-Narrow-Oblique /NewCenturySchlbk-Roman /NewCenturySchlbk-Bold /NewCenturySchlbk-Italic /NewCenturySchlbk-BoldItalic /Palatino-Roman /Palatino-Bold /Palatino-Italic /Palatino-BoldItalic /ZapfChancery-MediumItalic /ZapfDingbats ] def /Colors 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427 L 1484 423 L 1466 411 L 1457 408 L 1447 405 L 1429 404 L 1411 405 L 1401 408 L 1393 411 L 1375 420 L 1364 427 L 1356 433 L 1344 445 L 1338 453 L 1331 464 L 1321 482 L 1320 485 L 1315 501 L 1311 520 L 1309 538 L 1310 557 L 1312 575 L 1317 594 L 1320 602 L 1325 612 L 1336 631 L 1338 634 L 1354 650 L 1356 652 L 1375 661 L 1393 665 L 1411 664 L 1429 659 L 1447 651 L 1449 650 L 1466 637 L 1472 631 L 1484 618 L 1488 612 L 1498 594 L 1502 585 L 1506 575 L E (1755) 1508 566 0.5 T 501 224 501 185 S 865 224 865 185 S 1229 224 1229 185 S 1593 224 1593 185 S 1957 224 1957 185 S 501 224 1957 224 S (-40) 501 158 0.5 T (-20) 865 158 0.5 T (0) 1229 158 0.5 T (20) 1593 158 0.5 T (40) 1957 158 0.5 T 90 Sr 90 Sh 246 464 206 464 S 246 835 206 835 S 246 1207 206 1207 S 246 1578 206 1578 S 246 1950 206 1950 S 246 464 246 1950 S (-40) 180 464 0.5 T (-20) 180 835 0.5 T (0) 180 1207 0.5 T (20) 180 1578 0.5 T (40) 180 1950 0.5 T 0 Sr 0 Sh 0 Sd B 246 2190 M 246 224 L 2212 224 L 2212 2190 L 246 2190 L E 1 Sd B 1232 2117 M 1229 2113 L 1212 2099 L 1211 2098 L 1192 2084 L 1187 2080 L 1174 2069 L 1165 2062 L 1156 2053 L 1146 2043 L 1138 2035 L 1128 2024 L 1120 2014 L 1112 2006 L 1101 1993 L 1095 1987 L 1083 1974 L 1076 1969 L 1065 1960 L 1047 1957 L 1029 1961 L 1011 1969 L 1010 1969 L 992 1980 L 983 1987 L 974 1993 L 959 2006 L 956 2008 L 938 2023 L 936 2024 L 919 2038 L 914 2043 L 901 2054 L 892 2062 L 883 2069 L 871 2080 L 865 2085 L 850 2099 L 847 2102 L 831 2117 L E B 1345 2117 M 1338 2103 L 1336 2099 L 1325 2080 L 1320 2071 L 1314 2062 L 1303 2043 L 1302 2041 L 1291 2024 L 1284 2013 L 1278 2006 L 1265 1987 L 1265 1987 L 1252 1969 L 1247 1962 L 1238 1950 L 1229 1938 L 1224 1931 L 1211 1913 L 1211 1913 L 1198 1894 L 1192 1886 L 1186 1876 L 1176 1857 L 1174 1853 L 1167 1839 L 1159 1820 L 1156 1813 L 1151 1801 L 1143 1783 L 1138 1772 L 1134 1764 L 1125 1746 L 1120 1735 L 1115 1727 L 1103 1709 L 1101 1707 L 1086 1690 L 1083 1687 L 1065 1675 L 1052 1671 L 1047 1670 L 1029 1670 L 1019 1671 L 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