(*^ ::[ Information = "This is a Mathematica Notebook file. It contains ASCII text, and can be transferred by email, ftp, or other text-file transfer utility. It should be read or edited using a copy of Mathematica or MathReader. If you received this as email, use your mail application or copy/paste to save everything from the line containing (*^ down to the line containing ^*) into a plain text file. On some systems you may have to give the file a name ending with ".ma" to allow Mathematica to recognize it as a Notebook. The line below identifies what version of Mathematica created this file, but it can be opened using any other version as well."; FrontEndVersion = "Macintosh Mathematica Notebook Front End Version 2.2"; MacintoshStandardFontEncoding; fontset = title, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e8, 24, "Times"; fontset = subtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, bold, e6, 18, "Times"; fontset = subsubtitle, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeTitle, center, M7, italic, e6, 14, "Times"; fontset = section, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, grayBox, M22, bold, a20, 18, "Times"; fontset = subsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, blackBox, M19, bold, a15, 14, "Times"; fontset = subsubsection, inactive, noPageBreakBelow, nohscroll, preserveAspect, groupLikeSection, whiteBox, M18, bold, a12, 12, "Times"; fontset = text, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = smalltext, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Times"; fontset = input, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeInput, M42, N23, bold, L-5, 12, "Courier"; fontset = output, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier"; fontset = message, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, R65535, L-5, 12, "Courier"; fontset = print, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, L-5, 12, "Courier"; fontset = info, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeOutput, M42, N23, B65535, L-5, 12, "Courier"; fontset = postscript, PostScript, formatAsPostScript, output, inactive, noPageBreakInGroup, nowordwrap, preserveAspect, groupLikeGraphics, M7, l34, w282, h287, 12, "Courier"; fontset = name, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, italic, 10, "Geneva"; fontset = header, inactive, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = leftheader, inactive, L2, 12, "Times"; fontset = footer, inactive, noKeepOnOnePage, preserveAspect, center, M7, 12, "Times"; fontset = leftfooter, inactive, L2, 12, "Times"; fontset = help, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 10, "Times"; fontset = clipboard, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = completions, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special1, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special2, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special3, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special4, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; fontset = special5, inactive, nohscroll, noKeepOnOnePage, preserveAspect, M7, 12, "Times"; paletteColors = 128; currentKernel; ] :[font = section; inactive; preserveAspect; startGroup] Ancova Program for solving the Johnson-Neyman Problem for 1 and 2 Covariates :[font = subsubsection; inactive; preserveAspect] Steve Hunka, University of Alberta, Edmonton, AB, Canada, T6G 2G5, e-mail: steve.hunka@ualberta.ca :[font = subsection; inactive; preserveAspect; fontSize = 12] Program Description: The program handles the 1 and 2 covariate case of analysis of covariance when homogeneity of regression coefficients does not exist. Arguments to the program are the data matrix and a vector of the number of observations per group. Parameters are estimated using the general linear model approach. The significance of each covariate is tested, and a plot is made of the regression lines or planes. In the case of one covariate the unknown is solved directly and plotted to show the boundaries for the region of significance. In the two covariate case, the polynomial surface is plotted including a plot of the surface defining the region of significance as well as a contour plot identifying various levels of the significance regions as a function of the two covariates. Revised: June 1995 :[font = subsubsection; inactive; preserveAspect] References: S. Hunka. Using Mathematica to solve Johnson-Neyman Problems, Mathematica in Education, Vol. 3, No. 3, 32-36, Summer 1994. S. Hunka. Identifying regions of significance in ANCOVA problems having non-homogeneous regressions. Br. Jr. Math. Stat. Psych., 48, 161-188, 1995. R.F. Potthoff. Johnson-Neyman Technique, in Encyclopedia of Statistical Sciences, Eds. S. Kotz and N.L. Johnson, 4, 299-303, John Wiley & Sons, New York, 1983. ;[s] 5:0,0;28,1;39,0;74,1;85,0;444,-1; 2:3,13,9,Times,1,12,0,0,0;2,13,9,Times,3,12,0,0,0; :[font = subsection; inactive; preserveAspect; fontSize = 12] Program Name: ancvjn[d_,ng_] Calling arguments: d_ is the data matrix in which each row is an observation holding the dependent variable followed by one or two covariates. The rows are ordered by groups. ng_ is a vector in which each element is the number of observations in each group. Functions called: getMp, cradd, ssk, knTrst, plotLines, plotRp, int3dplot,chkPts, as described below. Packages: Statistics`ContinuousDistributions` :[font = subsubsection; inactive; preserveAspect] Interactive Input: In the 1 covariate case the user inputs an alpha level for the desired region of significance and if a particular value of the covariate is to be tested for significance, the value to be used. In the 2 covariate case the following are requested of the user: 1) an alpha value for the surface plot 2) the minimum and maximum values of each covariate for plotting purposes 3) the number of plot points 4) a vector of alpha values for the contour plot and whether shading is desired 5) to replot at a different of alpha using sequence starting at (1) 6) calculate significance of a covariate pair of values :[font = subsubsection; inactive; preserveAspect] Program Output: 1) the parameter estimates 2) a test of SSmcfm (at covariate values of zero) including contrast used 3) test of regression homogeneity for each covariate 4) symbolic contrast matrix to test SSmcfm for covariate adjustment to p and q 5) points of significance for user selected alpha values 6) plot of regression lines or planes 7) a plots of the polynomial or polynomial surfaces 8) contour plot of user selected regions of significance (2 covariate case only) 9) the polynomial representing SSmcfm for defining region of significance :[font = subsection; inactive; preserveAspect] Package calls, Functions, and Program follow: :[font = input; preserveAspect] <Identity, PlotStyle->{RGBColor[Random[Real,{0,1}], Random[Real,{0,1}], Random[Real,{0,1}]]}]], {i,1,np}]; Show[pobj,DisplayFunction->$DisplayFunction, AxesLabel->{"x","y"}, PlotLabel->ttl ]; ]; (*end Module*) :[font = subsubsection; inactive; preserveAspect; startGroup] plotRp[p_,rng_,ttl_] plots regression planes in one 3d cube. The arguments are defined as follows: p is a matrix in which each row represents the parameters of each plane, i.e., {{c,x1,x2},{c,x1,x2}..{}}, and rng is a matrix of order (2,2) in which each row gives the range (min,max) for x1 and x2 over which each plane is to be plotted.ttl is a title,e.g, title="yourtitle". :[font = input; preserveAspect; endGroup] plotRp[p_,rng_,ttl_]:= Module[{i,pobj,np,xv,ev}, pobj=List[]; np=Length[p]; (*# param/grp*) xv={1,x1,x2}; (*symbolic const & covars*) ex=p.xv; Do[ AppendTo[pobj, Plot3D[ex[[i]],{x1,rng[[1]][[1]],rng[[1]][[2]]}, {x2,rng[[2]][[1]],rng[[2]][[2]]}, DisplayFunction->Identity]], {i,1,np}]; Show[pobj,DisplayFunction->$DisplayFunction, AxesLabel->{"x1","x2","y"}, PlotLabel->ttl ]; ]; (*end Module*) :[font = subsubsection; inactive; preserveAspect] int3dplot[pmm_,ss_,mse_,dfc_,dfe_] is used to plot the expression ss having unknowns p and q. The argument pmm is a vector containing the minimum and maximum values of p and q respectively; ss is the expression; mse is means square error; dfc is degrees of freedom for contrast; dfe is error degrees of freedom. For each variable p and q (x1 and x2) the user is presented with the currently set minimum and maximum values and allowed to change them. The user could save the expression output by ancvjn2, and after defining the matrix for pmm, use the function to further explore the polynomial surface and regions of significance of ss-siglev independently of ancvjn. :[font = input; preserveAspect; startGroup] int3dplot[pmm_,ss_,mse_,dfc_,dfe_]:= Module[{rpq,pp,vminmax,q1,mw,vw,par,q3,q2,q4,pobj, siglev,alf}, rpq="y"; pp=10; q4="Do you want to replot with new values? y/n"; vminmax=pmm; q1="Type a value of to use.It currently is "; mw=Flatten[Table[{"minimum ","maximum "},{2}]]; vw={"x1 ","x1 ","x2 ","x2 "}; While[rpq=="y", alf=Input["Type alpha for surface plot, e.g.,.05"]; Print["Alpha=",alf]; siglev=mse dfc Quantile[FRatioDistribution[dfc,dfe],1-alf]; Print["Point of Signficance (c): MSe x dfc x F=",siglev]; par=List[]; Do[ q2=StringInsert[q1,vw[[i]],17];(*insert x1 or x2*) q2=StringInsert[q2,mw[[i]],8];(*insert min or max*) q2=StringJoin[q2,ToString[vminmax[[i]]]]; par=Append[par,Input[q2]]; ,{i,1,4}]; (*end Do *) vminmax=par; Print["Plot ranges are:",par]; q3="How many PlotPoints do you want? Currently it is "; q3=StringJoin[q3,ToString[pp]]; pp=Input[q3]; Print["PlotPoints=",pp]; pobj=Plot3D[ss-siglev, {p,par[[1]],par[[2]]},{q,par[[3]],par[[4]]}, PlotPoints->pp, AxesLabel->{"x1","x2","ss-c"}, PlotLabel->"Polynomial Surface of ss-c"]; Show[pobj,PlotRange->{-1,0}, PlotLabel->"Polynomial Surface at ss-c=0"]; (* now do contour plot *) alf=Input["Type alpha for contours, e.g.,{.05,.01}"]; Print["Alpha=",alf]; siglev=mse dfc Quantile[FRatioDistribution[dfc,dfe],1-alf]; Print["Points of Signficance: MSe x dfc x F are"]; Print[siglev]; cs="y"==InputString["Contour shading? y/n"]; ContourPlot[ss, {p,par[[1]],par[[2]]},{q,par[[3]],par[[4]]}, Contours->siglev, ContourShading->cs, FrameLabel->{"x1","x2"},ColorFunction->Hue, PlotLabel->"Regions of Signficance"]; rpq=InputString[q4]; (*quest to repeat *) ]; (*end While*) ]; (* end Module *) :[font = message; inactive; preserveAspect] Syntax::newl: The newline character after " siglev=mse dfc " is understood as a multiplication operator. :[font = message; inactive; preserveAspect; endGroup] Syntax::newl: The newline character after " siglev=mse dfc " is understood as a multiplication operator. :[font = subsubsection; inactive; preserveAspect; startGroup] chkPts[x,b,mse,dfe,ng] calculates the probability in testing SSmcfm associated with a particular set of covariate values input by user. x is X'X where X is the design matrix; b is a vector of parameter estimates; mse is the mean square error; dfe is the degree of freedom for mse; ng is the number of groups. chkPts calls knTrst and ssk. :[font = input; preserveAspect; endGroup] chkPts[x_,b_,mse_,dfe_,ng_]:= Module[{cpat,rpq,con,ms,dfc,f,fdist,prob}, rpq="y"; Print[""];Print["Probability of Covariate set points"]; While[rpq=="y", cpat=Join[{1}, Input["Type vector of covariate values,eg.{2,3}"]]; con=knTrst[cpat,ng]; Print["Contrast Matrix"];Print[con]; dfc=Length[con]; ms=ssk[con,x,b]/dfc; (*get Mean square *) f=ms/mse; Print["MS=",ms,",df=",dfc,",F=",f]; fdist=FRatioDistribution[dfc,dfe]; prob=1-CDF[fdist,f]; Print["Probability=",prob]; rpq=InputString["Do you have more values? y/n"]; ];(*end While*) ];(*end Module*) :[font = subsection; inactive; preserveAspect] The Mathematica program. ;[s] 3:0,0;4,1;15,0;25,-1; 2:2,16,12,Times,1,14,0,0,0;1,16,12,Times,3,14,0,0,0; :[font = input; preserveAspect; startGroup] ancvjn[d_,ng_]:= (*Johnson-Neyman Ancova*) Module[{nt,ngrp,x,y,ncv,xtx,dm,b,dfc,dfe,j,mse,con, concv,ss1,f1,fdist,prob,ss2,siglev,b1,mnx,dt, soln,pobj,title,alf}, y=Flatten[Take[Transpose[d],1]]; x=Drop[Transpose[d],1]; nt=Length[d];(*N total*) ngrp=Length[ng]; ncv=-1+Last[Dimensions[d]];(*# covariates *) x=Transpose[ Partition[Join[Table[1,{nt}],Flatten[x]],nt]]; (*now set up the design matrix*) dm=cradd[getMp[1,x,ng],getMp[2,x,ng]]; Do[dm=cradd[dm,getMp[j,x,ng]],{j,3,ngrp}]; xtx=Transpose[dm].dm; b=N[Inverse[xtx].Transpose[dm].y]; Print["Mu-Model Parameter Estimates"]; Print[TableForm[b,TableSpacing->{0}, TableHeadings->Automatic]]; ssmcfm=(b.xtx.b)-(Apply[Plus,y]^2)/nt; dfm=Length[xtx]-1;Print[""]; Print["SSmcfm=",ssmcfm," dfm=",dfm]; dfe=Dimensions[dm].{1,-1}; mse=((y.y)-b.Transpose[dm].y)/dfe; Print["Mean Square Error=",mse," dfe=",dfe]; f1=(ssmcfm/dfm)/mse;Print["Fmodel=",f1]; fdist=FRatioDistribution[dfm,dfe]; prob=1-CDF[fdist,f1]; Print["Probability=",prob]; (*now plot the lines or planes*) dt=Transpose[d]; (*for convenience*) mnx=List[]; Do[AppendTo[mnx,Min[dt[[i]]]]; AppendTo[mnx,Max[dt[[i]]]],{i,2,Length[dt]}]; Print["Covariate Range"]; Print[mnx]; (*Plot regression lines or planes *) Which[ncv==1, title="Regression Lines"; b1=Partition[Flatten[b],2]; plotLines[b1,mnx,title], ncv==2, title="Regression Planes"; b1=Partition[Flatten[b],3]; plotRp[b1,Table[mnx,{2}],title];, ncv>2, Print["#cov>2,so no plots"]; ]; (*end Which*) (*now test each cov regr coeff*) con=Join[{1,0},Table[0,{ncv-1}]]; Do[con=RotateRight[con,1]; concv=knTrst[con,ngrp]; Print["Contrast matrix covariate ",j]; Print[TableForm[concv,TableSpacing->{0,4}]]; ss1=ssk[concv,xtx,b]; dfc=Length[concv]; Print["SS covariate=",ss1," dfc=",dfc]; f1=(ss1/dfc)/mse; Print["F1=",f1]; Needs["Statistics`ContinuousDistributions`"]; fdist=FRatioDistribution[dfc,dfe]; prob=1-CDF[fdist,f1]; Print["Probability=",prob]; ,{j,1,ncv}];(*end do*) (*Now do the symbolic processing*) concv=knTrst[Join[{1},Take[{p,q},ncv]],ngrp]; Print["Symbolic Contrast Matrix"]; Print[TableForm[concv,TableSpacing->{0,4}]]; ss2=Simplify[ssk[concv,xtx,b]]; (*symbolic sum of squares*) (*Do 2D plot & Solve, or 3D plots*) Which[ncv==1, alf=Input["Type the level of alpha, e.g.,.05"]; Print["Alpha=",alf]; siglev=mse dfc Quantile[FRatioDistribution[dfc,dfe],1-alf]; Print["Point of Signficance: MSe x dfc x F=",siglev]; Plot[ss2-siglev,{p,mnx[[1]],mnx[[2]]}, PlotLabel->"Quadratic Plot", AxesLabel->{"x","ss-c"}]; soln=Solve[ss2-siglev==0,p]; Print["Solution to Quadratic is",soln];, ncv==2, int3dplot[mnx,ss2,mse,dfc,dfe]; ]; (*end Which*) If["y"==InputString["Check covariate point sets? y/n"], chkPts[xtx,b,mse,dfe,ngrp]]; Return[ss2]; ]; (*end module *) :[font = message; inactive; preserveAspect; endGroup] Syntax::newl: The newline character after " siglev=mse dfc " is understood as a multiplication operator. :[font = subsubsection; inactive; preserveAspect] Data matrix: {y,cov1,cov2} one observation per row as shown below for 2 covariate case. :[font = input; preserveAspect; startGroup] data={{7,4,5},{10,6,5},{9,8,9},{11,9,8},{14,12,11}, {6,4,3},{7,6,7},{8,8,7},{8,10,11},{9,12,10}, {6,4,3},{6,6,7},{5,7,6},{5,10,11},{4,13,12}} :[font = output; output; inactive; preserveAspect; endGroup] {{7, 4, 5}, {10, 6, 5}, {9, 8, 9}, {11, 9, 8}, {14, 12, 11}, {6, 4, 3}, {7, 6, 7}, {8, 8, 7}, {8, 10, 11}, {9, 12, 10}, {6, 4, 3}, {6, 6, 7}, {5, 7, 6}, {5, 10, 11}, {4, 13, 12}} ;[o] {{7, 4, 5}, {10, 6, 5}, {9, 8, 9}, {11, 9, 8}, {14, 12, 11}, {6, 4, 3}, {7, 6, 7}, {8, 8, 7}, {8, 10, 11}, {9, 12, 10}, {6, 4, 3}, {6, 6, 7}, {5, 7, 6}, {5, 10, 11}, {4, 13, 12}} :[font = input; preserveAspect; startGroup] ssjn=ancvjn[data,{5,5,5}] (*2 covariate case*) :[font = print; inactive; preserveAspect] Mu-Model Parameter Estimates 1 5.21795 2 1.52564 3 -0.910256 4 4.82353 5 0.402941 6 -0.0588235 7 7.01 8 -0.47 9 0.25 SSmcfm=96.1563 dfm=8 Mean Square Error=0.196164 dfe=6 Fmodel=61.273 Probability=0.0000344107 Covariate Range {4, 13, 3, 12} Contrast matrix covariate 1 0 1 0 0 -1 0 0 0 0 0 0 0 0 1 0 0 -1 0 SS covariate=9.00972 dfc=2 F1=22.9648 Probability=0.00154245 Contrast matrix covariate 2 0 0 1 0 0 -1 0 0 0 0 0 0 0 0 1 0 0 -1 SS covariate=2.78457 dfc=2 F1=7.09756 Probability=0.0262249 Symbolic Contrast Matrix 1 p q -1 -p -q 0 0 0 0 0 0 1 p q -1 -p -q Alpha=0.05 Point of Signficance (c): MSe x dfc x F=2.01784 Plot ranges are:{0, 15, 0, 15} PlotPoints=15 Alpha={0.05, 0.01, 0.001, 0.0001} Points of Signficance: MSe x dfc x F are {2.01784, 4.28609, 10.5929, 24.1804} Alpha=0.01 Point of Signficance (c): MSe x dfc x F=4.28609 Plot 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.35941 L s P p .001 w .04239 .38 m .0459 .3787 L s P p .001 w .04085 .38973 m .04436 .38844 L s P p .001 w .0393 .39952 m .04281 .39824 L s P p .001 w .03773 .40938 m .04125 .4081 L s P p .001 w .03458 .42928 m .0381 .42802 L s P p .001 w .03299 .43933 m .03651 .43807 L s P p .001 w .03138 .44945 m .03491 .4482 L s P p .001 w .02977 .45963 m .0333 .45838 L s P p .001 w .06016 .2679 m .06364 .26653 L s P p .001 w .02651 .4802 m .03004 .47896 L s P [(y)] -0.02691 .40064 1 -0.37036 Mshowa P 0 0 m 1 0 L 1 .82055 L 0 .82055 L closepath clip newpath p .002 w .06024 .26735 m .02494 .49015 L s .02494 .49015 m .40296 .79562 L s .40296 .79562 m .41001 .59401 L s .41001 .59401 m .06024 .26735 L s .67932 .02494 m .94594 .43277 L s .94594 .43277 m .97506 .64585 L s .97506 .64585 m .69286 .25814 L s .69286 .25814 m .67932 .02494 L s .06024 .26735 m .02494 .49015 L s .02494 .49015 m .69286 .25814 L s .69286 .25814 m .67932 .02494 L s .67932 .02494 m .06024 .26735 L s .41001 .59401 m .94594 .43277 L s .94594 .43277 m .97506 .64585 L s .97506 .64585 m .40296 .79562 L s .40296 .79562 m .41001 .59401 L s P p .002 w .428 .57266 m .44788 .58668 L .41457 .5886 L p .505 .75 .983 r F P s P p .002 w .41457 .5886 m .39441 .57473 L .428 .57266 L p .505 .75 .983 r F P s P p .002 w .46221 .57054 m .48181 .58472 L .44788 .58668 L p .505 .75 .983 r F P s P p .002 w .44788 .58668 m .428 .57266 L .46221 .57054 L p .505 .75 .983 r F P s P p .002 w .40755 .55824 m .428 .57266 L .39441 .57473 L p .505 .75 .983 r F P s P p .002 w .39441 .57473 m .37369 .56048 L .40755 .55824 L p .505 .75 .983 r F P s P p .002 w .42675 .61471 m .4468 .63304 L .41282 .64073 L p .632 .743 .928 r F P s P p .002 w .41282 .64073 m .39249 .62264 L .42675 .61471 L p .632 .743 .928 r F P s P p .002 w .49707 .56839 m .51637 .58273 L .48181 .58472 L p .505 .75 .983 r F P s P p .002 w .48181 .58472 m .46221 .57054 L .49707 .56839 L p .505 .75 .983 r F P s P p .002 w .44206 .55596 m .46221 .57054 L .428 .57266 L p .505 .75 .983 r F P s P p .002 w .428 .57266 m .40755 .55824 L .44206 .55596 L p .505 .75 .983 r F P s P p .002 w .42625 .6317 m .44637 .65164 L .41203 .66411 L p .685 .742 .894 r F P s P p .002 w .41203 .66411 m .39162 .64444 L .42625 .6317 L p .685 .742 .894 r F P s P p .002 w .46153 .60666 m .48129 .62523 L .4468 .63304 L p .632 .743 .928 r F P s P p .002 w .4468 .63304 m .42675 .61471 L .46153 .60666 L p .632 .743 .928 r F P s P p .002 w .38653 .54341 m .40755 .55824 L .37369 .56048 L p .505 .75 .983 r F P s P p .002 w .37369 .56048 m .35238 .54582 L .38653 .54341 L p .505 .75 .983 r F P s P p .002 w .53259 .56619 m .55157 .5807 L .51637 .58273 L p .505 .75 .983 r F P s P p .002 w .51637 .58273 m .49707 .56839 L .53259 .56619 L p .505 .75 .983 r F P s P p .002 w .40619 .59591 m .42675 .61471 L .39249 .62264 L p .632 .743 .928 r F P s P p .002 w .39249 .62264 m .37166 .60408 L .40619 .59591 L p .632 .743 .928 r F P s P p .002 w .46129 .61881 m .48111 .63902 L .44637 .65164 L p .685 .742 .894 r F P s P p .002 w .44637 .65164 m .42625 .6317 L .46129 .61881 L p .685 .742 .894 r F P s P p .002 w .49682 .5985 m .51629 .6173 L .48129 .62523 L p .632 .743 .928 r F P s P p .002 w .48129 .62523 m .46153 .60666 L .49682 .5985 L p .632 .743 .928 r F P s P p .002 w .47722 .55363 m .49707 .56839 L .46221 .57054 L p .505 .75 .983 r F P s P p .002 w .46221 .57054 m .44206 .55596 L .47722 .55363 L p .505 .75 .983 r F P s P p .002 w .49676 .60576 m .51627 .62625 L .48111 .63902 L p .685 .742 .894 r F P s P p .002 w .48111 .63902 m .46129 .61881 L .49676 .60576 L p .685 .742 .894 r F P s P p .002 w .40564 .61127 m .42625 .6317 L .39162 .64444 L p .685 .742 .894 r F P s P p .002 w .39162 .64444 m .37071 .62429 L .40564 .61127 L p .685 .742 .894 r F P s P p .002 w .44126 .58762 m .46153 .60666 L .42675 .61471 L p .632 .743 .928 r F P s P p .002 w .42675 .61471 m .40619 .59591 L .44126 .58762 L p .632 .743 .928 r F P s P p .002 w .42133 .54096 m .44206 .55596 L .40755 .55824 L p .505 .75 .983 r F P s P p .002 w .40755 .55824 m .38653 .54341 L .42133 .54096 L p .505 .75 .983 r F P s P p .002 w .56879 .56396 m .58743 .57863 L .55157 .5807 L p .505 .75 .983 r F P s P p .002 w .55157 .5807 m .53259 .56619 L .56879 .56396 L p .505 .75 .983 r F P s P p .002 w .53265 .59021 m .55181 .60926 L .51629 .6173 L p .632 .743 .928 r F P s P p .002 w .51629 .6173 m .49682 .5985 L .53265 .59021 L p .632 .743 .928 r F P s P p .002 w .53266 .59255 m .55185 .61333 L .51627 .62625 L p .685 .742 .894 r F P s P p .002 w .51627 .62625 m .49676 .60576 L .53266 .59255 L p .685 .742 .894 r F P s P p .002 w .38511 .57663 m .40619 .59591 L .37166 .60408 L p .632 .743 .928 r F P s P p .002 w .37166 .60408 m .35029 .58505 L .38511 .57663 L p .632 .743 .928 r F P s P p .002 w .44099 .5981 m .46129 .61881 L .42625 .6317 L p .685 .742 .894 r F P s P p .002 w .42625 .6317 m .40564 .61127 L .44099 .5981 L p .685 .742 .894 r F P s P p .002 w .3649 .52816 m .38653 .54341 L .35238 .54582 L p .505 .75 .983 r F P s P p .002 w .35238 .54582 m .33047 .53074 L .3649 .52816 L p .505 .75 .983 r F P s P p .002 w .51306 .55127 m .53259 .56619 L .49707 .56839 L p .505 .75 .983 r F P s P p .002 w .49707 .56839 m .47722 .55363 L .51306 .55127 L p .505 .75 .983 r F P s P p .002 w .47685 .57921 m .49682 .5985 L .46153 .60666 L p .632 .743 .928 r F P s P p .002 w .46153 .60666 m .44126 .58762 L .47685 .57921 L p .632 .743 .928 r F P s P p .002 w .569 .57918 m .58786 .60025 L .58164 .60251 L p .685 .742 .894 r F P s P p .002 w .58164 .60251 m .55181 .60926 L p .56227 .59259 L .632 .743 .928 r F P s P p .002 w .58164 .60251 m .55185 .61333 L p .56227 .59259 L .685 .742 .894 r F P s P p .56227 .59259 m .569 .57918 L .58164 .60251 L .685 .742 .894 r F P p .002 w .56904 .58179 m .58788 .60109 L .58164 .60251 L p .632 .743 .928 r F P s P p .56227 .59259 m .56904 .58179 L .58164 .60251 L .632 .743 .928 r F P p .002 w .55181 .60926 m .53265 .59021 L .54984 .58623 L p .632 .743 .928 r F P s P p .002 w .55185 .61333 m .53266 .59255 L .54984 .58623 L p .685 .742 .894 r F P s P p .002 w .54984 .58623 m .569 .57918 L p .56227 .59259 L .685 .742 .894 r F P s P p .55181 .60926 m .54984 .58623 L .56227 .59259 L .632 .743 .928 r F P p .55185 .61333 m .54984 .58623 L .56227 .59259 L .685 .742 .894 r F P p .002 w .54984 .58623 m .56904 .58179 L p .56227 .59259 L .632 .743 .928 r F P s P p .002 w .4568 .53845 m .47722 .55363 L .44206 .55596 L p .505 .75 .983 r F P s P p .002 w .44206 .55596 m .42133 .54096 L .4568 .53845 L p .505 .75 .983 r F P s P p .002 w .60569 .56168 m .62398 .57653 L .58743 .57863 L p .505 .75 .983 r F P s P p .002 w .58743 .57863 m .56879 .56396 L .60569 .56168 L p .505 .75 .983 r F P s P p .002 w .47677 .58476 m .49676 .60576 L .46129 .61881 L p .685 .742 .894 r F P s P p .002 w .46129 .61881 m .44099 .5981 L .47677 .58476 L p .685 .742 .894 r F P s P p .002 w .38452 .59034 m .40564 .61127 L .37071 .62429 L p .685 .742 .894 r F P s P p .002 w .37071 .62429 m .34929 .60364 L .38452 .59034 L p .685 .742 .894 r F P s P p .002 w .42046 .56809 m .44126 .58762 L .40619 .59591 L p .632 .743 .928 r F P s P p .002 w .40619 .59591 m .38511 .57663 L .42046 .56809 L p .632 .743 .928 r F P s P p .002 w .513 .57066 m .53265 .59021 L .49682 .5985 L p .632 .743 .928 r F P s P p .002 w .49682 .5985 m .47685 .57921 L .513 .57066 L p .632 .743 .928 r F P s P p .002 w .39999 .52552 m .42133 .54096 L .38653 .54341 L p .505 .75 .983 r F P s P p .002 w .38653 .54341 m .3649 .52816 L .39999 .52552 L p .505 .75 .983 r F P s P p .002 w .5496 .54885 m .56879 .56396 L .53259 .56619 L p .505 .75 .983 r F P s P p .002 w .53259 .56619 m .51306 .55127 L .5496 .54885 L p .505 .75 .983 r F P s P p .002 w .60579 .56565 m .62431 .58701 L .58786 .60025 L p .685 .742 .894 r F P s P p .002 w .58786 .60025 m .569 .57918 L .60579 .56565 L p .685 .742 .894 r F P s P p .002 w .513 .57126 m .53266 .59255 L .49676 .60576 L p .685 .742 .894 r F P s P p .002 w .49676 .60576 m .47677 .58476 L .513 .57126 L p .685 .742 .894 r F P s P p .002 w .60598 .57324 m .62449 .5928 L .58788 .60109 L p .632 .743 .928 r F P s P p .002 w .58788 .60109 m .56904 .58179 L .60598 .57324 L p .632 .743 .928 r F P s P p .002 w .42018 .57687 m .44099 .5981 L .40564 .61127 L p .685 .742 .894 r F P s P p .002 w .40564 .61127 m .38452 .59034 L .42018 .57687 L p .685 .742 .894 r F P s P p .002 w .36347 .55685 m .38511 .57663 L .35029 .58505 L p .632 .743 .928 r F P s P p .002 w .35029 .58505 m .32836 .56553 L .36347 .55685 L p .632 .743 .928 r F P s P p .002 w .34263 .51245 m .3649 .52816 L .33047 .53074 L p .505 .75 .983 r F P s P p .002 w .33047 .53074 m .30792 .51523 L .34263 .51245 L p .505 .75 .983 r F P s P p .002 w .49296 .5359 m .51306 .55127 L .47722 .55363 L p .505 .75 .983 r F P s P p .002 w .47722 .55363 m .4568 .53845 L .49296 .5359 L p .505 .75 .983 r F P s P p .002 w .64303 .55195 m .6612 .57361 L .65867 .57453 L p .685 .742 .894 r F P s P p .002 w .65867 .57453 m .62398 .57653 L p .63525 .56651 L .505 .75 .983 r F P s P p .002 w .65867 .57453 m .62431 .58701 L p .63525 .56651 L .685 .742 .894 r F P s P p .63525 .56651 m .64303 .55195 L .65867 .57453 L .685 .742 .894 r F P p .002 w .6433 .55935 m .66123 .57438 L .65867 .57453 L p .505 .75 .983 r F P s P p .63525 .56651 m .6433 .55935 L .65867 .57453 L .505 .75 .983 r F P p .002 w .62398 .57653 m .60569 .56168 L .61878 .56087 L p .505 .75 .983 r F P s P p .002 w .62431 .58701 m .60579 .56565 L .61878 .56087 L p .685 .742 .894 r F P s P p .002 w .61878 .56087 m .64303 .55195 L p .63525 .56651 L .685 .742 .894 r F P s P p .62398 .57653 m .61878 .56087 L .63525 .56651 L .505 .75 .983 r F P p .62431 .58701 m .61878 .56087 L .63525 .56651 L .685 .742 .894 r F P p .002 w .61878 .56087 m .6433 .55935 L p .63525 .56651 L .505 .75 .983 r F P s P p .002 w .45636 .55941 m .47685 .57921 L .44126 .58762 L p .632 .743 .928 r F P s P p .002 w .44126 .58762 m .42046 .56809 L .45636 .55941 L p .632 .743 .928 r F P s P p .002 w .54967 .55759 m .569 .57918 L .54984 .58623 L p .685 .742 .894 r F P s P p .002 w .54984 .58623 m .53265 .59021 L p .53855 .58045 L .632 .743 .928 r F P s P p .002 w .54984 .58623 m .53266 .59255 L p .53855 .58045 L .685 .742 .894 r F P s P p .53855 .58045 m .54967 .55759 L .54984 .58623 L .685 .742 .894 r F P p .002 w .5497 .56198 m .56904 .58179 L .54984 .58623 L p .632 .743 .928 r F P s P p .53855 .58045 m .5497 .56198 L .54984 .58623 L .632 .743 .928 r F P p .002 w .53265 .59021 m .513 .57066 L .51739 .56962 L p .632 .743 .928 r F P s P p .002 w .53266 .59255 m .513 .57126 L .51739 .56962 L p .685 .742 .894 r F P s P p .002 w .51739 .56962 m .54967 .55759 L p .53855 .58045 L .685 .742 .894 r F P s P p .53265 .59021 m .51739 .56962 L .53855 .58045 L .632 .743 .928 r F P p .53266 .59255 m .51739 .56962 L .53855 .58045 L .685 .742 .894 r F P p .002 w .51739 .56962 m .5497 .56198 L p .53855 .58045 L .632 .743 .928 r F P s P p .002 w .45628 .56323 m .47677 .58476 L .44099 .5981 L p .685 .742 .894 r F P s P p .002 w .44099 .5981 m .42018 .57687 L .45628 .56323 L p .685 .742 .894 r F P s P p .002 w .36287 .56888 m .38452 .59034 L .34929 .60364 L p .685 .742 .894 r F P s P p .002 w .34929 .60364 m .32734 .58248 L .36287 .56888 L p .685 .742 .894 r F P s P p .002 w .43578 .52283 m .4568 .53845 L .42133 .54096 L p .505 .75 .983 r F P s P p .002 w .42133 .54096 m .39999 .52552 L .43578 .52283 L p .505 .75 .983 r F P s P p .002 w .60569 .56168 m .56879 .56396 L p .58416 .54901 L .505 .75 .983 r F P s P p .002 w .60579 .56565 m .569 .57918 L p .58416 .54901 L .685 .742 .894 r F P s P p .002 w .5868 .54375 m .5944 .55252 L p .58416 .54901 L .685 .742 .894 r F P s P p .002 w .5944 .55252 m .60569 .56168 L p .58416 .54901 L .505 .75 .983 r F P s P p .002 w .5944 .55252 m .60579 .56565 L p .58416 .54901 L .685 .742 .894 r F P s P p .002 w .58685 .54639 m .5944 .55252 L p .58416 .54901 L .505 .75 .983 r F P s P p .002 w .56879 .56396 m .5496 .54885 L .57818 .54696 L p .505 .75 .983 r F P s P p .56879 .56396 m .57818 .54696 L .58416 .54901 L .505 .75 .983 r F P p .002 w .569 .57918 m .54967 .55759 L .57818 .54696 L p .685 .742 .894 r F P s P p .002 w .57818 .54696 m .5868 .54375 L p .58416 .54901 L .685 .742 .894 r F P s P p .569 .57918 m .57818 .54696 L .58416 .54901 L .685 .742 .894 r F P p .002 w .57818 .54696 m .58685 .54639 L p .58416 .54901 L .505 .75 .983 r F P s P p .002 w .6435 .56456 m .66166 .58439 L .62449 .5928 L p .632 .743 .928 r F P s P p .002 w .62449 .5928 m .60598 .57324 L .6435 .56456 L p .632 .743 .928 r F P s P p .002 w .39912 .54804 m .42046 .56809 L .38511 .57663 L p .632 .743 .928 r F P s P p .002 w .38511 .57663 m .36347 .55685 L .39912 .54804 L p .632 .743 .928 r F P s P p .002 w .513 .57066 m .47685 .57921 L p .49002 .55561 L .632 .743 .928 r F P s P p .002 w .513 .57126 m .47677 .58476 L p .49002 .55561 L .685 .742 .894 r F P s P p .002 w .49283 .54943 m .50618 .56388 L p .49002 .55561 L .685 .742 .894 r F P s P p .002 w .50618 .56388 m .513 .57066 L p .49002 .55561 L .632 .743 .928 r F P s P p .002 w .50618 .56388 m .513 .57126 L p .49002 .55561 L .685 .742 .894 r F P s P p .002 w .49282 .5506 m .50618 .56388 L p .49002 .55561 L .632 .743 .928 r F P s P p .002 w .47685 .57921 m .45636 .55941 L .48427 .55266 L p .632 .743 .928 r F P s P p .47685 .57921 m .48427 .55266 L .49002 .55561 L .632 .743 .928 r F P p .002 w .47677 .58476 m .45628 .56323 L .48427 .55266 L p .685 .742 .894 r F P s P p .002 w .48427 .55266 m .49283 .54943 L p .49002 .55561 L .685 .742 .894 r F P s P p .47677 .58476 m .48427 .55266 L .49002 .55561 L .685 .742 .894 r F P p .002 w .48427 .55266 m .49282 .5506 L p .49002 .55561 L .632 .743 .928 r F P s P p .002 w .68074 .53808 m .69855 .56004 L .6612 .57361 L p .685 .742 .894 r F P s P p .002 w .6612 .57361 m .64303 .55195 L .68074 .53808 L p .685 .742 .894 r F P s P p .002 w .37803 .50962 m .39999 .52552 L .3649 .52816 L p .505 .75 .983 r F P s P p .002 w .3649 .52816 m .34263 .51245 L .37803 .50962 L p .505 .75 .983 r F P s P p .002 w .52984 .5333 m .5496 .54885 L .51306 .55127 L p .505 .75 .983 r F P s P p .002 w .51306 .55127 m .49296 .5359 L .52984 .5333 L p .505 .75 .983 r F P s P p .002 w .69921 .57219 m .66123 .57438 L p .6794 .55891 L .505 .75 .983 r F P s P p .002 w .69941 .57584 m .66166 .58439 L p .6794 .55891 L .632 .743 .928 r F P s P p .002 w .6816 .55575 m .68613 .56085 L p .6794 .55891 L .632 .743 .928 r F P s P p .002 w .68613 .56085 m .69921 .57219 L p .6794 .55891 L .505 .75 .983 r F P s P p .002 w .68613 .56085 m .69941 .57584 L p .6794 .55891 L .632 .743 .928 r F P s P p .002 w .68166 .55698 m .68613 .56085 L p .6794 .55891 L .505 .75 .983 r F P s P p .002 w .66123 .57438 m .6433 .55935 L .67428 .55744 L p .505 .75 .983 r F P s P p .66123 .57438 m .67428 .55744 L .6794 .55891 L .505 .75 .983 r F P p .002 w .66166 .58439 m .6435 .56456 L .67428 .55744 L p .632 .743 .928 r F P s P p .002 w .67428 .55744 m .6816 .55575 L p .6794 .55891 L .632 .743 .928 r F P s P p .66166 .58439 m .67428 .55744 L .6794 .55891 L .632 .743 .928 r F P p .002 w .67428 .55744 m .68166 .55698 L p .6794 .55891 L .505 .75 .983 r F P s P p .002 w .39884 .55511 m .42018 .57687 L .38452 .59034 L p .685 .742 .894 r F P s P p .002 w .38452 .59034 m .36287 .56888 L .39884 .55511 L p .685 .742 .894 r F P s P p .002 w .58698 .55316 m .60598 .57324 L .56904 .58179 L p .632 .743 .928 r F P s P p .002 w .56904 .58179 m .5497 .56198 L .58698 .55316 L p .632 .743 .928 r F P s P p .002 w .34126 .53655 m .36347 .55685 L .32836 .56553 L p .632 .743 .928 r F P s P p .002 w .32836 .56553 m .30587 .54549 L .34126 .53655 L p .632 .743 .928 r F P s P p .002 w .43533 .53909 m .45636 .55941 L .42046 .56809 L p .632 .743 .928 r F P s P p .002 w .42046 .56809 m .39912 .54804 L .43533 .53909 L p .632 .743 .928 r F P s P p .002 w .31971 .49629 m .34263 .51245 L .30792 .51523 L p .505 .75 .983 r F P s P p .002 w .30792 .51523 m .28471 .49926 L .31971 .49629 L p .505 .75 .983 r F P s P p .002 w 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r F P s P p .002 w .50618 .56388 m .49283 .54943 L p .51447 .56812 L .685 .742 .894 r F P s P p .002 w .49282 .5506 m .52986 .54164 L p .51447 .56812 L .632 .743 .928 r F P s P p .002 w .50618 .56388 m .49282 .5506 L p .51447 .56812 L .632 .743 .928 r F P s P p .002 w .43527 .54116 m .45628 .56323 L .42018 .57687 L p .685 .742 .894 r F P s P p .002 w .42018 .57687 m .39884 .55511 L .43527 .54116 L p .685 .742 .894 r F P s P p .002 w .34067 .54687 m .36287 .56888 L .32734 .58248 L p .685 .742 .894 r F P s P p .002 w .32734 .58248 m .30483 .56079 L .34067 .54687 L p .685 .742 .894 r F P s P p .002 w .62485 .54421 m .6435 .56456 L .60598 .57324 L p .632 .743 .928 r F P s P p .002 w .60598 .57324 m .58698 .55316 L .62485 .54421 L p .632 .743 .928 r F P s P p .002 w .37721 .52746 m .39912 .54804 L .36347 .55685 L p .632 .743 .928 r F P s P p .002 w .36347 .55685 m .34126 .53655 L .37721 .52746 L p .632 .743 .928 r F P s P p .002 w .41413 .50673 m .43578 .52283 L .39999 .52552 L p .505 .75 .983 r F P s P p .002 w .39999 .52552 m .37803 .50962 L .41413 .50673 L p .505 .75 .983 r F P s P p .002 w .56733 .52129 m .5868 .54375 L .57818 .54696 L p .685 .742 .894 r F P s P p .002 w .57818 .54696 m .5496 .54885 L p .55817 .54011 L .505 .75 .983 r F P s P p .002 w .57818 .54696 m .54967 .55759 L p .55817 .54011 L .685 .742 .894 r F P s P p .55817 .54011 m .56733 .52129 L .57818 .54696 L .685 .742 .894 r F P p .002 w .56745 .53065 m .58685 .54639 L .57818 .54696 L p .505 .75 .983 r F P s P p .55817 .54011 m .56745 .53065 L .57818 .54696 L .505 .75 .983 r F P p .002 w .5496 .54885 m .52984 .5333 L .53684 .53281 L p .505 .75 .983 r F P s P p .002 w .54967 .55759 m .52985 .53545 L .53684 .53281 L p .685 .742 .894 r F P s P p .002 w .53684 .53281 m .56733 .52129 L p .55817 .54011 L .685 .742 .894 r F P s P p .5496 .54885 m .53684 .53281 L .55817 .54011 L .505 .75 .983 r F P p .54967 .55759 m .53684 .53281 L .55817 .54011 L .685 .742 .894 r F P p .002 w .53684 .53281 m .56745 .53065 L 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.742 .894 r F P s P p .002 w .73636 .54631 m .71891 .52403 L .75758 .50981 L p .685 .742 .894 r F P s P p .002 w .66246 .51555 m .68074 .53808 L .64303 .55195 L p .685 .742 .894 r F P s P p .002 w .64303 .55195 m .62439 .52974 L .66246 .51555 L p .685 .742 .894 r F P s P p .002 w .37696 .53279 m .39884 .55511 L .36287 .56888 L p .685 .742 .894 r F P s P p .002 w .36287 .56888 m .34067 .54687 L .37696 .53279 L p .685 .742 .894 r F P s P p .002 w .56748 .53255 m .58698 .55316 L .5497 .56198 L p .632 .743 .928 r F P s P p .002 w .5497 .56198 m .52986 .54164 L .56748 .53255 L p .632 .743 .928 r F P s P p .002 w .31845 .5157 m .34126 .53655 L .30587 .54549 L p .632 .743 .928 r F P s P p .002 w .30587 .54549 m .28277 .52493 L .31845 .5157 L p .632 .743 .928 r F P s P p .002 w .35541 .49325 m .37803 .50962 L .34263 .51245 L p .505 .75 .983 r F P s P p .002 w .34263 .51245 m .31971 .49629 L .35541 .49325 L p .505 .75 .983 r F P s P p .002 w .52984 .5333 m .49296 .5359 L p .5053 .52201 L .505 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.55744 m .6433 .55935 L p .65251 .55117 L .505 .75 .983 r F P s P p .002 w .67428 .55744 m .6435 .56456 L p .65251 .55117 L .632 .743 .928 r F P s P p .65251 .55117 m .66332 .53511 L .67428 .55744 L .632 .743 .928 r F P p .002 w .66359 .54132 m .68166 .55698 L .67428 .55744 L p .505 .75 .983 r F P s P p .65251 .55117 m .66359 .54132 L .67428 .55744 L .505 .75 .983 r F P p .002 w .6433 .55935 m .62484 .54388 L .62679 .54375 L p .505 .75 .983 r F P s P p .002 w .6435 .56456 m .62485 .54421 L .62679 .54375 L p .632 .743 .928 r F P s P p .002 w .62679 .54375 m .66332 .53511 L p .65251 .55117 L .632 .743 .928 r F P s P p .6433 .55935 m .62679 .54375 L .65251 .55117 L .505 .75 .983 r F P p .6435 .56456 m .62679 .54375 L .65251 .55117 L .632 .743 .928 r F P p .002 w .62679 .54375 m .66359 .54132 L p .65251 .55117 L .505 .75 .983 r F P s P p .002 w .41373 .51822 m .43533 .53909 L .39912 .54804 L p .632 .743 .928 r F P s P p .002 w .39912 .54804 m .37721 .52746 L .41373 .51822 L p .632 .743 .928 r F P s P p .002 w .79673 .4954 m .81341 .51832 L .77464 .5324 L p .685 .742 .894 r F P s P p .002 w .77464 .5324 m .75758 .50981 L .79673 .4954 L p .685 .742 .894 r F P s P p .002 w .70102 .50118 m .71891 .52403 L .68074 .53808 L p .685 .742 .894 r F P s P p .002 w .68074 .53808 m .66246 .51555 L .70102 .50118 L p .685 .742 .894 r F P s P p .002 w .75964 .53769 m .77669 .55834 L .73775 .56716 L p .632 .743 .928 r F P s P p .002 w .73775 .56716 m .72031 .54679 L .75964 .53769 L p .632 .743 .928 r F P s P p .002 w .60528 .50696 m .62439 .52974 L .5868 .54375 L p .685 .742 .894 r F P s P p .002 w .5868 .54375 m .56733 .52129 L .60528 .50696 L p .685 .742 .894 r F P s P p .002 w .41372 .51852 m .43527 .54116 L .39884 .55511 L p .685 .742 .894 r F P s P p .002 w .39884 .55511 m .37696 .53279 L .41372 .51852 L p .685 .742 .894 r F P s P p .002 w .3179 .5243 m .34067 .54687 L .30483 .56079 L p .685 .742 .894 r F P s P p .002 w .30483 .56079 m .28174 .53854 L .3179 .5243 L p .685 .742 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r F P s P p .002 w .58685 .54639 m .56745 .53065 L .57859 .52986 L p .505 .75 .983 r F P s P p .002 w .58698 .55316 m .56748 .53255 L .57859 .52986 L p .632 .743 .928 r F P s P p .002 w .57859 .52986 m .6057 .52331 L p .59807 .53548 L .632 .743 .928 r F P s P p .58685 .54639 m .57859 .52986 L .59807 .53548 L .505 .75 .983 r F P p .58698 .55316 m .57859 .52986 L .59807 .53548 L .632 .743 .928 r F P p .002 w .57859 .52986 m .60582 .52794 L p .59807 .53548 L .505 .75 .983 r F P s P p .002 w .7607 .5521 m .77742 .56768 L .73793 .56996 L p .505 .75 .983 r F P s P p .002 w .73793 .56996 m .72079 .55457 L .7607 .5521 L p .505 .75 .983 r F P s P p .002 w .35471 .50632 m .37721 .52746 L .34126 .53655 L p .632 .743 .928 r F P s P p .002 w .34126 .53655 m .31845 .5157 L .35471 .50632 L p .632 .743 .928 r F P s P p .002 w .70241 .52587 m .72031 .54679 L .6816 .55575 L p .632 .743 .928 r F P s P p .002 w .6816 .55575 m .66332 .53511 L .70241 .52587 L p .632 .743 .928 r F P s P p .002 w .39182 .49015 m .41413 .50673 L .37803 .50962 L p .505 .75 .983 r F P s P p .002 w .37803 .50962 m .35541 .49325 L .39182 .49015 L p .505 .75 .983 r F P s P p .002 w .54735 .49826 m .56733 .52129 L .53684 .53281 L p .685 .742 .894 r F P s P p .002 w .53684 .53281 m .52984 .5333 L p .53189 .53111 L .505 .75 .983 r F P s P p .002 w .53684 .53281 m .52985 .53545 L p .53189 .53111 L .685 .742 .894 r F P s P p .53189 .53111 m .54735 .49826 L .53684 .53281 L .685 .742 .894 r F P p .002 w .56745 .53065 m .53684 .53281 L p .54426 .51997 L .505 .75 .983 r F P s P p .002 w .54745 .51137 m .55982 .52446 L p .54271 .51952 L .632 .743 .928 r F P s P p .53189 .53111 m .54271 .51952 L .53684 .53281 L .505 .75 .983 r F P p .54271 .51952 m .54747 .51443 L .54426 .51997 L .505 .75 .983 r F P p .54271 .51952 m .54426 .51997 L .53684 .53281 L .505 .75 .983 r F P p .002 w .50951 .51274 m .54735 .49826 L p .53189 .53111 L .685 .742 .894 r F P s P p .002 w .52334 .52819 m .50951 .51274 L p .53189 .53111 L .685 .742 .894 r F P s P p .002 w .52967 .51577 m .54745 .51137 L p .54271 .51952 L .632 .743 .928 r F P s P p .002 w .50949 .51728 m .52967 .51577 L p .53189 .53111 L .505 .75 .983 r F P s P p .002 w .52967 .51577 m .54747 .51443 L p .54271 .51952 L .505 .75 .983 r F P s P p .53189 .53111 m .52967 .51577 L .54271 .51952 L .505 .75 .983 r F P p .002 w .52984 .5333 m .52334 .52819 L p .53189 .53111 L .505 .75 .983 r F P s P p .002 w .52334 .52819 m .50949 .51728 L p .53189 .53111 L .505 .75 .983 r F P s P p .002 w .52985 .53545 m .52334 .52819 L p .53189 .53111 L .685 .742 .894 r F P s P p .002 w .52986 .54164 m .50948 .52076 L .52967 .51577 L p .632 .743 .928 r F P s P p .52986 .54164 m .52967 .51577 L .54271 .51952 L .632 .743 .928 r F P p .002 w .56748 .53255 m .52986 .54164 L p .54271 .51952 L .632 .743 .928 r F P s P p .002 w .55982 .52446 m .56745 .53065 L p .54426 .51997 L .505 .75 .983 r F P s P p .002 w .55982 .52446 m .56748 .53255 L p .54271 .51952 L .632 .743 .928 r F P s P p .002 w 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p .48976 .50426 L .505 .75 .983 r F P s P p .002 w .4948 .50572 m .50948 .52076 L p .48641 .5033 L .632 .743 .928 r F P s P p .002 w .48853 .50078 m .4948 .50572 L p .48976 .50426 L .505 .75 .983 r F P s P p .002 w .64454 .51392 m .66332 .53511 L .62679 .54375 L p .632 .743 .928 r F P s P p .002 w .62679 .54375 m .62484 .54388 L p .62541 .54336 L .505 .75 .983 r F P s P p .002 w .62679 .54375 m .62485 .54421 L p .62541 .54336 L .632 .743 .928 r F P s P p .62541 .54336 m .64454 .51392 L .62679 .54375 L .632 .743 .928 r F P p .002 w .64497 .52518 m .66359 .54132 L .62679 .54375 L p .505 .75 .983 r F P s P p .62541 .54336 m .64497 .52518 L .62679 .54375 L .505 .75 .983 r F P p .002 w .6057 .52331 m .64454 .51392 L p .62541 .54336 L .632 .743 .928 r F P s P p .002 w .62484 .54388 m .62359 .54283 L p .62541 .54336 L .505 .75 .983 r F P s P p .002 w .62485 .54421 m .62359 .54283 L p .62541 .54336 L .632 .743 .928 r F P s P p .002 w .62359 .54283 m .6057 .52331 L p .62541 .54336 L .632 .743 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.4846 L .34459 .48116 L p .632 .743 .928 r F P s P p .002 w .34459 .48116 m .36372 .47352 L p .35981 .48895 L .685 .742 .894 r F P s P p .35471 .50632 m .34459 .48116 L .36195 .49005 L .632 .743 .928 r F P p .36195 .49005 m .36372 .47352 L .36763 .47486 L .685 .742 .894 r F P p .35452 .50989 m .35981 .48895 L .36195 .49005 L .685 .742 .894 r F P p .35981 .48895 m .36372 .47352 L .36195 .49005 L .685 .742 .894 r F P p .002 w .36372 .47352 m .36891 .47145 L p .36763 .47486 L .685 .742 .894 r F P s P p .002 w .36372 .47352 m .36883 .47306 L p .36763 .47486 L .505 .75 .983 r F P s P p .002 w .34561 .44697 m .36891 .47145 L .36372 .47352 L p .685 .742 .894 r F P s P p .002 w .36372 .47352 m .33209 .47638 L p .33911 .4651 L .505 .75 .983 r F P s P p .002 w .34459 .48116 m .33159 .4846 L p .3351 .4763 L .632 .743 .928 r F P s P p .002 w .36372 .47352 m .34459 .48116 L p .33911 .4651 L .685 .742 .894 r F P s P p .3351 .4763 m .33911 .4651 L .34459 .48116 L .685 .742 .894 r F P p .33911 .4651 m .34561 .44697 L .36372 .47352 L .685 .742 .894 r F P p .33911 .4651 m .34135 .4615 L .36372 .47352 L .505 .75 .983 r F P p .002 w .30806 .45899 m .33209 .47638 L .29609 .47963 L p .505 .75 .983 r F P s P p .002 w .33159 .4846 m .29503 .49428 L p .30781 .46233 L .632 .743 .928 r F P s P p .002 w .33148 .48639 m .29453 .50115 L p .30781 .46233 L .685 .742 .894 r F P s P p .002 w .30783 .46227 m .30797 .46242 L p .30781 .46233 L .685 .742 .894 r F P s P p .002 w .30797 .46242 m .33159 .4846 L p .30781 .46233 L .632 .743 .928 r F P s P p .002 w .30797 .46242 m .33148 .48639 L p .30781 .46233 L .685 .742 .894 r F P s P p .002 w .30783 .46228 m .30797 .46242 L p .30781 .46233 L .632 .743 .928 r F P s P p .002 w .33209 .47638 m .30806 .45899 L .31838 .458 L p .505 .75 .983 r F P s P p .33209 .47638 m .31838 .458 L .32766 .46118 L .505 .75 .983 r F P p .002 w .31838 .458 m .34561 .44697 L p .33911 .4651 L .685 .742 .894 r F P s P p .33209 .47638 m .32651 .45722 L .34135 .4615 L .505 .75 .983 r F P p .002 w .33159 .4846 m .30797 .46242 L p .3351 .4763 L .632 .743 .928 r F P s P p .002 w .33148 .48639 m .30783 .46227 L .31838 .458 L p .685 .742 .894 r F P s P p .33148 .48639 m .31838 .458 L .33911 .4651 L .685 .742 .894 r F P p .002 w .31838 .458 m .32651 .45722 L p .32766 .46118 L .505 .75 .983 r F P s P p .002 w .32651 .45722 m .34531 .45212 L p .34135 .4615 L .632 .743 .928 r F P s P p .002 w .36883 .47306 m .36372 .47352 L p .34135 .4615 L .505 .75 .983 r F P s P p .002 w .36082 .46711 m .36883 .47306 L p .34135 .4615 L .505 .75 .983 r F P s P p .3351 .4763 m .34135 .4615 L .34459 .48116 L .632 .743 .928 r F P p .34135 .4615 m .34531 .45212 L .34505 .46256 L .632 .743 .928 r F P p .34135 .4615 m .34505 .46256 L .34459 .48116 L .632 .743 .928 r F P p .002 w .34531 .45212 m .36082 .46711 L p .34505 .46256 L .632 .743 .928 r F P s P p .002 w .38388 .43146 m .40683 .45631 L .36891 .47145 L p .685 .742 .894 r F P s P p .002 w .36891 .47145 m .34561 .44697 L .38388 .43146 L p 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.4763 L .632 .743 .928 r F P s P p .3351 .4763 m .32651 .45722 L .34135 .4615 L .632 .743 .928 r F P p .002 w .30797 .46242 m .30783 .46228 L p .3351 .4763 L .632 .743 .928 r F P s P p .002 w .34459 .48116 m .33148 .48639 L p .3351 .4763 L .685 .742 .894 r F P s P p .002 w .34512 .45544 m .36082 .46711 L p .34135 .4615 L .505 .75 .983 r F P s P p .002 w .36875 .47476 m .34459 .48116 L p .34505 .46256 L .632 .743 .928 r F P s P p .002 w .36082 .46711 m .36875 .47476 L p .34505 .46256 L .632 .743 .928 r F P s P p .002 w .34459 .48116 m .36875 .47476 L p .36195 .49005 L .632 .743 .928 r F P s P p .002 w .35452 .50989 m .33148 .48639 L .34459 .48116 L p .685 .742 .894 r F P s P p .35452 .50989 m .34459 .48116 L .35981 .48895 L .685 .742 .894 r F P p .002 w .52686 .48962 m .54745 .51137 L .52967 .51577 L p .632 .743 .928 r F P s P p .002 w .52967 .51577 m .50949 .51728 L p .51468 .51145 L .505 .75 .983 r F P s P p .002 w .52967 .51577 m .50948 .52076 L p .51468 .51145 L .632 .743 .928 r F P 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L .48003 .50146 L .632 .743 .928 r F P p .4512 .50348 m .45789 .49508 L .45187 .50371 L .505 .75 .983 r F P p .45789 .49508 m .46691 .48376 L .45829 .4952 L .505 .75 .983 r F P p .45789 .49508 m .45829 .4952 L .45187 .50371 L .505 .75 .983 r F P p .002 w .42918 .4805 m .46724 .46552 L p .4512 .50348 L .685 .742 .894 r F P s P p .002 w .45003 .50308 m .42918 .4805 L p .4512 .50348 L .685 .742 .894 r F P s P p .002 w .42963 .48694 m .46703 .47726 L p .45789 .49508 L .632 .743 .928 r F P s P p .002 w .42898 .48699 m .42963 .48694 L p .4512 .50348 L .505 .75 .983 r F P s P p .002 w .42963 .48694 m .46691 .48376 L p .45789 .49508 L .505 .75 .983 r F P s P p .4512 .50348 m .42963 .48694 L .45789 .49508 L .505 .75 .983 r F P p .002 w .45095 .50379 m .45003 .50308 L p .4512 .50348 L .505 .75 .983 r F P s P p .002 w .45003 .50308 m .42898 .48699 L p .4512 .50348 L .505 .75 .983 r F P s P p .002 w .45095 .50407 m .45003 .50308 L p .4512 .50348 L .685 .742 .894 r F P s P p .002 w .45084 .50884 m 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L p .632 .743 .928 r F P s P p .002 w .82351 .49724 m .84019 .51905 L .79959 .52845 L p .632 .743 .928 r F P s P p .002 w .79959 .52845 m .78248 .50694 L .82351 .49724 L p .632 .743 .928 r F P s P p .002 w .56581 .47977 m .58603 .50184 L .54745 .51137 L p .632 .743 .928 r F P s P p .002 w .54745 .51137 m .52686 .48962 L .56581 .47977 L p .632 .743 .928 r F P s P p .002 w .29503 .49428 m .27096 .47228 L .30775 .4623 L p .632 .743 .928 r F P s P p .29503 .49428 m .30775 .4623 L .30781 .46233 L .632 .743 .928 r F P p .002 w .29453 .50115 m .27055 .47738 L .30775 .4623 L p .685 .742 .894 r F P s P p .002 w .30775 .4623 m .30783 .46227 L p .30781 .46233 L .685 .742 .894 r F P s P p .29453 .50115 m .30775 .4623 L .30781 .46233 L .685 .742 .894 r F P p .002 w .30775 .4623 m .30783 .46228 L p .30781 .46233 L .632 .743 .928 r F P s P p .002 w .24666 .44477 m .27176 .46247 L .23618 .46588 L p .505 .75 .983 r F P s P p .002 w .23618 .46588 m .2108 .44841 L .24666 .44477 L p .505 .75 .983 r F P s 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L .49728 .34774 L p .632 .743 .928 r F P s P p .002 w .21756 .3287 m .24463 .35485 L .20582 .36645 L p .632 .743 .928 r F P s P p .002 w .20582 .36645 m .17842 .34071 L .21756 .3287 L p .632 .743 .928 r F P s P p .002 w .10851 .34734 m .13797 .36811 L .10095 .37283 L p .505 .75 .983 r F P s P p .002 w .10095 .37283 m .0712 .35237 L .10851 .34734 L p .505 .75 .983 r F P s P p .002 w .28162 .37434 m .30822 .39467 L .26933 .3991 L p .505 .75 .983 r F P s P p .002 w .26933 .3991 m .24238 .37906 L .28162 .37434 L p .505 .75 .983 r F P s P p .002 w .45475 .40134 m .47847 .42122 L .43773 .42536 L p .505 .75 .983 r F P s P p .002 w .43773 .42536 m .41358 .40577 L .45475 .40134 L p .505 .75 .983 r F P s P p .002 w .62788 .42834 m .64874 .44778 L .60613 .45163 L p .505 .75 .983 r F P s P p .002 w .60613 .45163 m .58479 .43247 L .62788 .42834 L p .505 .75 .983 r F P s P p .002 w .80103 .45534 m .81902 .47433 L .77455 .47789 L p .505 .75 .983 r F P s P p .002 w .77455 .47789 m .75602 .45917 L 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L p .632 .743 .928 r F P s P p .002 w .29992 .27863 m .32588 .30762 L .28556 .325 L p .685 .742 .894 r F P s P p .002 w .28556 .325 m .2592 .29646 L .29992 .27863 L p .685 .742 .894 r F P s P p .002 w .19155 .28513 m .21907 .31404 L .17949 .33136 L p .685 .742 .894 r F P s P p .002 w .17949 .33136 m .1516 .30292 L .19155 .28513 L p .685 .742 .894 r F P s P p .002 w .75732 .34042 m .77665 .36675 L .73263 .37841 L p .632 .743 .928 r F P s P p .002 w .73263 .37841 m .7128 .35249 L .75732 .34042 L p .632 .743 .928 r F P s P p .002 w .47367 .3211 m .49728 .34774 L .45569 .35957 L p .632 .743 .928 r F P s P p .002 w .45569 .35957 m .43166 .33335 L .47367 .3211 L p .632 .743 .928 r F P s P p .002 w .18967 .30176 m .21756 .3287 L .17842 .34071 L p .632 .743 .928 r F P s P p .002 w .17842 .34071 m .15019 .31419 L .18967 .30176 L p .632 .743 .928 r F P s P p .002 w .25411 .35331 m .28162 .37434 L .24238 .37906 L p .505 .75 .983 r F P s P p .002 w .24238 .37906 m .21452 .35835 L .25411 .35331 L p 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.742 .894 r F P s P p .002 w .66844 .24093 m .68925 .27066 L .6461 .2884 L p .685 .742 .894 r F P s P p .002 w .6461 .2884 m .6248 .25914 L .66844 .24093 L p .685 .742 .894 r F P s P p .002 w .5594 .24746 m .58179 .2771 L .53939 .29481 L p .685 .742 .894 r F P s P p .002 w .53939 .29481 m .51655 .26564 L .5594 .24746 L p .685 .742 .894 r F P s P p .002 w .45033 .254 m .4743 .28355 L .43265 .30122 L p .685 .742 .894 r F P s P p .002 w .43265 .30122 m .40825 .27213 L .45033 .254 L p .685 .742 .894 r F P s P p .002 w .34122 .26054 m .36677 .29001 L .32588 .30762 L p .685 .742 .894 r F P s P p .002 w .32588 .30762 m .29992 .27863 L .34122 .26054 L p .685 .742 .894 r F P s P p .002 w .23208 .26709 m .2592 .29646 L .21907 .31404 L p .685 .742 .894 r F P s P p .002 w .21907 .31404 m .19155 .28513 L .23208 .26709 L p .685 .742 .894 r F P s P p .002 w .69237 .32577 m .7128 .35249 L .66907 .36434 L p .632 .743 .928 r F P s P p .002 w .66907 .36434 m .64816 .33805 L .69237 .32577 L p .632 .743 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w .82904 .43149 m .84707 .45143 L .80103 .45534 L p .505 .75 .983 r F P s P p .002 w .80103 .45534 m .78242 .4357 L .82904 .43149 L p .505 .75 .983 r F P s P p .002 w .73739 .31327 m .75732 .34042 L .7128 .35249 L p .632 .743 .928 r F P s P p .002 w .7128 .35249 m .69237 .32577 L .73739 .31327 L p .632 .743 .928 r F P s P p .002 w .44933 .29364 m .47367 .3211 L .43166 .33335 L p .632 .743 .928 r F P s P p .002 w .43166 .33335 m .4069 .30633 L .44933 .29364 L p .632 .743 .928 r F P s P p .002 w .56 .29593 m .58271 .32343 L .53961 .33569 L p .632 .743 .928 r F P s P p .002 w .53961 .33569 m .51644 .30863 L .56 .29593 L p .632 .743 .928 r F P s P p .002 w .75763 .20369 m .77744 .23439 L .73303 .25265 L p .685 .742 .894 r F P s P p .002 w .73303 .25265 m .71271 .22244 L .75763 .20369 L p .685 .742 .894 r F P s P p .002 w .64701 .21031 m .66844 .24093 L .6248 .25914 L p .685 .742 .894 r F P s P p .002 w .6248 .25914 m .60289 .22902 L .64701 .21031 L p .685 .742 .894 r F P s P p .002 w 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m .38313 .24219 L .34122 .26054 L p .685 .742 .894 r F P s P p .002 w .34122 .26054 m .31492 .2302 L .35725 .21135 L p .685 .742 .894 r F P s P p .002 w .60437 .28299 m .6266 .31094 L .58271 .32343 L p .632 .743 .928 r F P s P p .002 w .58271 .32343 m .56 .29593 L .60437 .28299 L p .632 .743 .928 r F P s P p .002 w .31254 .26308 m .3393 .29136 L .29798 .30404 L p .632 .743 .928 r F P s P p .002 w .29798 .30404 m .27083 .27621 L .31254 .26308 L p .632 .743 .928 r F P s P p .002 w .71683 .28527 m .73739 .31327 L .69237 .32577 L p .632 .743 .928 r F P s P p .002 w .69237 .32577 m .6713 .29823 L .71683 .28527 L p .632 .743 .928 r F P s P p .002 w .42423 .26531 m .44933 .29364 L .4069 .30633 L p .632 .743 .928 r F P s P p .002 w .4069 .30633 m .38137 .27846 L .42423 .26531 L p .632 .743 .928 r F P s P p .002 w .26654 .32604 m .29462 .34814 L .25411 .35331 L p .505 .75 .983 r F P s P p .002 w .25411 .35331 m .22565 .33155 L .26654 .32604 L p .505 .75 .983 r F P s P p .002 w .4478 .35431 m 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.26531 L p .632 .743 .928 r F P s P p .002 w .42423 .26531 m .39832 .23608 L .44245 .22219 L p .632 .743 .928 r F P s P p .002 w .64798 .12621 m .67021 .15926 L .62493 .17877 L p .685 .742 .894 r F P s P p .002 w .62493 .17877 m .60217 .14627 L .64798 .12621 L p .685 .742 .894 r F P s P p .002 w .53307 .13308 m .55705 .16603 L .51259 .1855 L p .685 .742 .894 r F P s P p .002 w .51259 .1855 m .48812 .15309 L .53307 .13308 L p .685 .742 .894 r F P s P p .002 w .55774 .22436 m .58142 .25414 L .53657 .26755 L p .632 .743 .928 r F P s P p .002 w .53657 .26755 m .51239 .23827 L .55774 .22436 L p .632 .743 .928 r F P s P p .002 w .46647 .32624 m .49182 .349 L .4478 .35431 L p .505 .75 .983 r F P s P p .002 w .4478 .35431 m .42196 .33191 L .46647 .32624 L p .505 .75 .983 r F P s P p .002 w .65325 .35536 m .67527 .37761 L .62909 .38258 L p .505 .75 .983 r F P s P p .002 w .62909 .38258 m .6065 .36069 L .65325 .35536 L p .505 .75 .983 r F P s P p .002 w .67372 .22654 m .69562 .25638 L .64957 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p .505 .75 .983 r F P s P p .002 w .74322 .39433 m .72256 .37252 L .77101 .3673 L p .505 .75 .983 r F P s P p .002 w .60396 .21018 m .62713 .24047 L .58142 .25414 L p .632 .743 .928 r F P s P p .002 w .58142 .25414 m .55774 .22436 L .60396 .21018 L p .632 .743 .928 r F P s P p .002 w .72121 .21234 m .74255 .24269 L .69562 .25638 L p .632 .743 .928 r F P s P p .002 w .69562 .25638 m .67372 .22654 L .72121 .21234 L p .632 .743 .928 r F P s P p .002 w .62506 .09212 m .64798 .12621 L .60217 .14627 L p .685 .742 .894 r F P s P p .002 w .60217 .14627 m .57871 .11276 L .62506 .09212 L p .685 .742 .894 r F P s P p .002 w .51207 .32042 m .53691 .34357 L .49182 .349 L p .505 .75 .983 r F P s P p .002 w .49182 .349 m .46647 .32624 L .51207 .32042 L p .505 .75 .983 r F P s P p .002 w .70114 .34991 m .72256 .37252 L .67527 .37761 L p .505 .75 .983 r F P s P p .002 w .67527 .37761 m .65325 .35536 L .70114 .34991 L p .505 .75 .983 r F P s P p .002 w .53327 .1936 m .55774 .22436 L .51239 .23827 L p 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.03447 .45099 L s P p .001 w .02945 .46163 m .03298 .46039 L s P p .001 w .02796 .47108 m .03149 .46984 L s P p .001 w .02645 .48058 m .02998 .47935 L s P [(ss-c)] -0.02691 .40064 1 -0.37036 Mshowa P 0 0 m 1 0 L 1 .82055 L 0 .82055 L closepath clip newpath p .002 w .06024 .26735 m .02494 .49015 L s .02494 .49015 m .40296 .79562 L s .40296 .79562 m .41001 .59401 L s .41001 .59401 m .06024 .26735 L s .67932 .02494 m .94594 .43277 L s .94594 .43277 m .97506 .64585 L s .97506 .64585 m .69286 .25814 L s .69286 .25814 m .67932 .02494 L s .06024 .26735 m .02494 .49015 L s .02494 .49015 m .69286 .25814 L s .69286 .25814 m .67932 .02494 L s .67932 .02494 m .06024 .26735 L s .41001 .59401 m .94594 .43277 L s .94594 .43277 m .97506 .64585 L s .97506 .64585 m .40296 .79562 L s .40296 .79562 m .41001 .59401 L s P p .907 .803 .733 r .0015 w .38672 .63279 .40836 .64131 .4449 .58352 .42433 .56376 Metetra .664 .741 .907 r .42433 .56376 .4449 .58352 .48026 .57288 .46 .55285 Metetra .664 .741 .907 r .46 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.40323 .54349 Metetra .664 .741 .907 r .40323 .54349 .42433 .56376 .46 .55285 .43922 .53229 Metetra .664 .741 .907 r .43922 .53229 .46 .55285 .49618 .54178 .47572 .52093 Metetra .664 .741 .907 r .47572 .52093 .49618 .54178 .53287 .53056 .51275 .50941 Metetra .664 .741 .907 r .51275 .50941 .53287 .53056 .57007 .51917 .5503 .49773 Metetra .664 .741 .907 r .5503 .49773 .57007 .51917 .60781 .50763 .58841 .48587 Metetra .664 .741 .907 r .58841 .48587 .60781 .50763 .6461 .49591 .62707 .47384 Metetra .664 .741 .907 r .62707 .47384 .6461 .49591 .68494 .48403 .66629 .46163 Metetra .664 .741 .907 r .66629 .46163 .68494 .48403 .72435 .47197 .7061 .44925 Metetra .937 .567 .193 r .7061 .44925 .72435 .47197 .76434 .45974 .76184 .6495 Metetra .539 .291 .488 r .76184 .6495 .76434 .45974 .82414 .65945 .80582 .63756 Metetra .645 .763 .934 r .80582 .63756 .82414 .65945 .86832 .64767 .85052 .62544 Metetra .645 .763 .934 r .85052 .62544 .86832 .64767 .91321 .63571 .89594 .61311 Metetra .645 .763 .934 r .89594 .61311 .91321 .63571 .95884 .62355 .94212 .60058 Metetra .927 .799 .699 r .34099 .62002 .36429 .62557 .40323 .54349 .38125 .52998 Metetra .736 .828 .922 r .38125 .52998 .40323 .54349 .43922 .53229 .41789 .5112 Metetra .664 .741 .907 r .41789 .5112 .43922 .53229 .47572 .52093 .45472 .49954 Metetra .664 .741 .907 r .45472 .49954 .47572 .52093 .51275 .50941 .49209 .48771 Metetra .664 .741 .907 r .49209 .48771 .51275 .50941 .5503 .49773 .53 .4757 Metetra .664 .741 .907 r .53 .4757 .5503 .49773 .58841 .48587 .56847 .46352 Metetra .664 .741 .907 r .56847 .46352 .58841 .48587 .62707 .47384 .60751 .45116 Metetra .664 .741 .907 r .60751 .45116 .62707 .47384 .66629 .46163 .64714 .43862 Metetra .943 .579 .226 r .64714 .43862 .66629 .46163 .7061 .44925 .69869 .63941 Metetra .534 .283 .481 r .69869 .63941 .7061 .44925 .76184 .6495 .74246 .62731 Metetra .645 .763 .934 r .74246 .62731 .76184 .6495 .80582 .63756 .78695 .61502 Metetra .645 .763 .934 r .78695 .61502 .80582 .63756 .85052 .62544 .83217 .60252 Metetra .645 .763 .934 r .83217 .60252 .85052 .62544 .89594 .61311 .87814 .58982 Metetra .645 .763 .934 r .87814 .58982 .89594 .61311 .94212 .60058 .92488 .5769 Metetra .935 .8 .687 r .31669 .61663 .34099 .62002 .38125 .52998 .35852 .51738 Metetra .8 .839 .881 r .35852 .51738 .38125 .52998 .41789 .5112 .39599 .48954 Metetra .664 .741 .907 r .39599 .48954 .41789 .5112 .45472 .49954 .43316 .47756 Metetra .664 .741 .907 r .43316 .47756 .45472 .49954 .49209 .48771 .47087 .46541 Metetra .664 .741 .907 r .47087 .46541 .49209 .48771 .53 .4757 .50915 .45308 Metetra .664 .741 .907 r .50915 .45308 .53 .4757 .56847 .46352 .54799 .44056 Metetra .664 .741 .907 r .54799 .44056 .56847 .46352 .60751 .45116 .58742 .42786 Metetra .664 .741 .907 r .58742 .42786 .60751 .45116 .64714 .43862 .62744 .41496 Metetra .943 .579 .226 r .62744 .41496 .64714 .43862 .69869 .63941 .67823 .61692 Metetra .645 .763 .934 r .67823 .61692 .69869 .63941 .74246 .62731 .7225 .60446 Metetra .645 .763 .934 r .7225 .60446 .74246 .62731 .78695 .61502 .7675 .59178 Metetra .645 .763 .934 r .7675 .59178 .78695 .61502 .83217 .60252 .81325 .5789 Metetra .645 .763 .934 r .81325 .5789 .83217 .60252 .87814 .58982 .85978 .5658 Metetra .645 .763 .934 r .85978 .5658 .87814 .58982 .92488 .5769 .9071 .55247 Metetra .943 .801 .674 r .29125 .616 .31669 .61663 .35852 .51738 .33498 .50541 Metetra .846 .838 .838 r .33498 .50541 .35852 .51738 .39599 .48954 .37349 .46729 Metetra .664 .741 .907 r .37349 .46729 .39599 .48954 .43316 .47756 .411 .45499 Metetra .664 .741 .907 r .411 .45499 .43316 .47756 .47087 .46541 .44907 .4425 Metetra .664 .741 .907 r .44907 .4425 .47087 .46541 .50915 .45308 .48771 .42983 Metetra .664 .741 .907 r .48771 .42983 .50915 .45308 .54799 .44056 .52694 .41696 Metetra .664 .741 .907 r .52694 .41696 .54799 .44056 .58742 .42786 .56676 .4039 Metetra .948 .589 .255 r .56676 .4039 .58742 .42786 .62744 .41496 .61311 .60639 Metetra .521 .264 .465 r .61311 .60639 .62744 .41496 .67823 .61692 .65714 .59375 Metetra .645 .763 .934 r .65714 .59375 .67823 .61692 .7225 .60446 .70192 .58089 Metetra .645 .763 .934 r .70192 .58089 .7225 .60446 .7675 .59178 .74745 .56783 Metetra .645 .763 .934 r .74745 .56783 .7675 .59178 .81325 .5789 .79375 .55453 Metetra .645 .763 .934 r .79375 .55453 .81325 .5789 .85978 .5658 .84084 .54102 Metetra .645 .763 .934 r .84084 .54102 .85978 .5658 .9071 .55247 .88875 .52726 Metetra .95 .801 .66 r .2645 .61881 .29125 .616 .33498 .50541 .31058 .49388 Metetra .876 .829 .797 r .31058 .49388 .33498 .50541 .37349 .46729 .35038 .44443 Metetra .664 .741 .907 r .35038 .44443 .37349 .46729 .411 .45499 .38824 .43179 Metetra .664 .741 .907 r .38824 .43179 .411 .45499 .44907 .4425 .42667 .41895 Metetra .664 .741 .907 r .42667 .41895 .44907 .4425 .48771 .42983 .46568 .40592 Metetra .664 .741 .907 r .46568 .40592 .48771 .42983 .52694 .41696 .50529 .39269 Metetra .95 .598 .283 r .50529 .39269 .52694 .41696 .56676 .4039 .54707 .59571 Metetra .515 .254 .457 r .54707 .59571 .56676 .4039 .61311 .60639 .59087 .58289 Metetra .645 .763 .934 r .59087 .58289 .61311 .60639 .65714 .59375 .6354 .56985 Metetra .645 .763 .934 r .6354 .56985 .65714 .59375 .70192 .58089 .68069 .55659 Metetra .645 .763 .934 r .68069 .55659 .70192 .58089 .74745 .56783 .72676 .54311 Metetra .645 .763 .934 r .72676 .54311 .74745 .56783 .79375 .55453 .77362 .5294 Metetra .645 .763 .934 r .77362 .5294 .79375 .55453 .84084 .54102 .8213 .51544 Metetra .645 .763 .934 r .8213 .51544 .84084 .54102 .88875 .52726 .86981 .50124 Metetra .957 .798 .644 r .23622 .62565 .2645 .61881 .31058 .49388 .28534 .48189 Metetra .893 .815 .764 r .28534 .48189 .31058 .49388 .35038 .44443 .32663 .42094 Metetra .664 .741 .907 r .32663 .42094 .35038 .44443 .38824 .43179 .36483 .40794 Metetra .664 .741 .907 r .36483 .40794 .38824 .43179 .42667 .41895 .40362 .39474 Metetra .664 .741 .907 r .40362 .39474 .42667 .41895 .46568 .40592 .44301 .38133 Metetra .951 .605 .308 r .44301 .38133 .46568 .40592 .50529 .39269 .4801 .58487 Metetra .507 .243 .448 r .4801 .58487 .50529 .39269 .54707 .59571 .52365 .57187 Metetra .645 .763 .934 r .52365 .57187 .54707 .59571 .59087 .58289 .56793 .55865 Metetra .645 .763 .934 r .56793 .55865 .59087 .58289 .6354 .56985 .61297 .5452 Metetra .645 .763 .934 r .61297 .5452 .6354 .56985 .68069 .55659 .65879 .53152 Metetra .645 .763 .934 r .65879 .53152 .68069 .55659 .72676 .54311 .7054 .5176 Metetra .645 .763 .934 r .7054 .5176 .72676 .54311 .77362 .5294 .75284 .50344 Metetra .645 .763 .934 r .75284 .50344 .77362 .5294 .8213 .51544 .80111 .48903 Metetra .645 .763 .934 r .80111 .48903 .8213 .51544 .86981 .50124 .85024 .47436 Metetra .96 .791 .628 r .20624 .63642 .23622 .62565 .28534 .48189 .25943 .46664 Metetra .894 .792 .74 r .25943 .46664 .28534 .48189 .32663 .42094 .3022 .39678 Metetra .664 .741 .907 r .3022 .39678 .32663 .42094 .36483 .40794 .34076 .38341 Metetra .664 .741 .907 r .34076 .38341 .36483 .40794 .40362 .39474 .37992 .36983 Metetra .664 .741 .907 r .37992 .36983 .40362 .39474 .44301 .38133 .4197 .35604 Metetra .951 .605 .308 r .4197 .35604 .44301 .38133 .4801 .58487 .45546 .5607 Metetra .645 .763 .934 r .45546 .5607 .4801 .58487 .52365 .57187 .49949 .54728 Metetra .645 .763 .934 r .49949 .54728 .52365 .57187 .56793 .55865 .54427 .53364 Metetra .645 .763 .934 r .54427 .53364 .56793 .55865 .61297 .5452 .58982 .51976 Metetra .645 .763 .934 r .58982 .51976 .61297 .5452 .65879 .53152 .63618 .50564 Metetra .645 .763 .934 r .63618 .50564 .65879 .53152 .7054 .5176 .68336 .49126 Metetra .645 .763 .934 r .68336 .49126 .7054 .5176 .75284 .50344 .73137 .47663 Metetra .645 .763 .934 r .73137 .47663 .75284 .50344 .80111 .48903 .78025 .46174 Metetra .645 .763 .934 r .78025 .46174 .80111 .48903 .85024 .47436 .83002 .44658 Metetra .916 .728 .633 r .17829 .61406 .20624 .63642 .25943 .46664 .23364 .4401 Metetra .863 .745 .732 r .23364 .4401 .25943 .46664 .3022 .39678 .27707 .37193 Metetra .664 .741 .907 r .27707 .37193 .3022 .39678 .34076 .38341 .316 .35817 Metetra .664 .741 .907 r .316 .35817 .34076 .38341 .37992 .36983 .35553 .3442 Metetra .951 .611 .331 r .35553 .3442 .37992 .36983 .4197 .35604 .3863 .54936 Metetra .491 .219 .428 r .3863 .54936 .4197 .35604 .45546 .5607 .43004 .53575 Metetra .645 .763 .934 r .43004 .53575 .45546 .5607 .49949 .54728 .47455 .52191 Metetra .645 .763 .934 r .47455 .52191 .49949 .54728 .54427 .53364 .51984 .50782 Metetra .645 .763 .934 r .51984 .50782 .54427 .53364 .58982 .51976 .56592 .49349 Metetra .645 .763 .934 r .56592 .49349 .58982 .51976 .63618 .50564 .61283 .4789 Metetra .645 .763 .934 r .61283 .4789 .63618 .50564 .68336 .49126 .66057 .46405 Metetra .645 .763 .934 r .66057 .46405 .68336 .49126 .73137 .47663 .70919 .44893 Metetra .645 .763 .934 r .70919 .44893 .73137 .47663 .78025 .46174 .75869 .43353 Metetra .645 .763 .934 r .75869 .43353 .78025 .46174 .83002 .44658 .80911 .41785 Metetra .92 .722 .617 r .1495 .5908 .17829 .61406 .23364 .4401 .21037 .38136 Metetra .717 .604 .73 r .21037 .38136 .23364 .4401 .27707 .37193 .25122 .34636 Metetra .664 .741 .907 r .25122 .34636 .27707 .37193 .316 .35817 .2905 .3322 Metetra .576 .712 .935 r .2905 .3322 .316 .35817 .35553 .3442 .32992 .32547 Metetra .944 .601 .341 r .32992 .32547 .35553 .3442 .3863 .54936 .35959 .52406 Metetra .645 .763 .934 r .35959 .52406 .3863 .54936 .43004 .53575 .40381 .51001 Metetra .645 .763 .934 r .40381 .51001 .43004 .53575 .47455 .52191 .4488 .49571 Metetra .645 .763 .934 r .4488 .49571 .47455 .52191 .51984 .50782 .4946 .48116 Metetra .645 .763 .934 r .4946 .48116 .51984 .50782 .56592 .49349 .54123 .46635 Metetra .645 .763 .934 r .54123 .46635 .56592 .49349 .61283 .4789 .58869 .45127 Metetra .645 .763 .934 r .58869 .45127 .61283 .4789 .66057 .46405 .63703 .43592 Metetra .645 .763 .934 r .63703 .43592 .66057 .46405 .70919 .44893 .68625 .42028 Metetra .645 .763 .934 r .68625 .42028 .70919 .44893 .75869 .43353 .73639 .40435 Metetra .645 .763 .934 r .73639 .40435 .75869 .43353 .80911 .41785 .78747 .38812 Metetra .922 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3.22626 p q + 3.63037 p q + 3 3 4 0.678389 q - 1.88933 p q + 0.366904 q )) / 2 3 4 (84087590 - 17090200 p + 17595663 p - 1598302 p + 907637 p - 2 3 21437990 q - 30069840 p q + 849540 p q - 3545750 p q + 2 2 2 2 3 19375230 q + 2567880 p q + 5445045 p q - 2389250 q - 3 4 3866000 p q + 1077500 q ) :[font = subsubsection; inactive; preserveAspect] Data matrix {y,cov1}; 1 covariate case :[font = input; preserveAspect; startGroup] data2={{5,3},{4,3},{4,4},{2,4},{2,5}, {3,2},{3,4},{3,5},{4,5},{4,7}, {6,5},{4,3},{6,4},{4,5},{7,6}} :[font = output; output; inactive; preserveAspect; endGroup] {{5, 3}, {4, 3}, {4, 4}, {2, 4}, {2, 5}, {3, 2}, {3, 4}, {3, 5}, {4, 5}, {4, 7}, {6, 5}, {4, 3}, {6, 4}, {4, 5}, {7, 6}} ;[o] {{5, 3}, {4, 3}, {4, 4}, {2, 4}, {2, 5}, {3, 2}, {3, 4}, {3, 5}, {4, 5}, {4, 7}, {6, 5}, {4, 3}, {6, 4}, {4, 5}, {7, 6}} :[font = input; preserveAspect; startGroup] ancvjn[data2,{5,5,5}] (*one covariate case*) :[font = print; inactive; preserveAspect] Mu-Model Parameter Estimates 1 8.28571 2 -1.28571 3 2.42424 4 0.212121 5 2.03846 6 0.730769 SSmcfm=21.3328 dfm=5 Mean Square Error=0.844507 dfe=9 Fmodel=5.05212 Probability=0.0175845 Covariate Range {2, 7} Contrast matrix covariate 1 0 1 0 -1 0 0 0 0 0 1 0 -1 SS covariate=7.57491 dfc=2 F1=4.48481 Probability=0.0445314 Symbolic Contrast Matrix 1 p -1 -p 0 0 0 0 1 p -1 -p Alpha=0.05 Point of Signficance: MSe x dfc x F=7.18928 Solution to Quadratic is{{p -> -24.1893}, {p -> 3.91089 - 1.51737 I}, {p -> 3.91089 + 1.51737 I}, {p -> 3.94129}} Probability of Covariate set points Contrast Matrix {{1, 5, -1, -5, 0, 0}, {0, 0, 1, 5, -1, -5}} MS=9.87132,df=2,F=11.6889 Probability=0.00314763 :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 34; pictureWidth = 282; pictureHeight = 174] %! %%Creator: Mathematica %%AspectRatio: .61803 MathPictureStart %% Graphics /Courier findfont 10 scalefont setfont % Scaling calculations -0.357143 0.190476 0.0681498 0.0748086 [ [(3)] .21429 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(10036.74991674992*(21.14320878564325 - 8.57359604189475*p + p^2)* (12.33093757497764 - 6.939118869274191*p + p^2))/ (483213 - 430740*p + 146570*p^2 - 22540*p^3 + 1325*p^4) ;[o] 2 2 10036.7 (21.1432 - 8.5736 p + p ) (12.3309 - 6.93912 p + p ) ------------------------------------------------------------ 2 3 4 483213 - 430740 p + 146570 p - 22540 p + 1325 p ^*)