{VERSION 4 0 "SUN SPARC SOLARIS" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 256 "terminal" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "terminal" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "terminal" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "terminal" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE " " -1 264 "terminal" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "terminal" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 "ter minal" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "terminal" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "terminal" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 269 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 271 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 272 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 275 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 276 "terminal" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 277 "terminal" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 278 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 279 "terminal" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 280 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 281 "terminal" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 282 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 283 "terminal" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 287 "terminal" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 288 "terminal" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 289 "terminal" 1 18 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 290 "terminal" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 292 "terminal" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 293 "terminal" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 294 "terminal" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 295 "terminal" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{PSTYLE "Normal " -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "terminal" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE " " 0 258 1 {CSTYLE "" -1 -1 "terminal" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(stats):\n" } {TEXT 261 44 "This loads the statistics functions library." }{TEXT 262 0 "" }{TEXT 256 0 "" }{TEXT 257 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "Xvalues:=[1,2,3,4]; Yvalues:=[1.7,1.8,2.3,3.2];\n" } {TEXT -1 0 "" }{TEXT 258 0 "" }{TEXT -1 0 "" }{TEXT 259 0 "" }{TEXT 260 136 "The above is one of many formats for entering the data.\nWhat we are doing is creating two arrays, which will be put into a single \+ array." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(XvaluesG7&\"\"\"\"\"#\"\" $\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(YvaluesG7&$\"# " 0 "" {MPLTEXT 1 0 53 "bestfit :=fit[leastsquare[[x,y]]]([Xvalues,Yvalues]);\n" }{TEXT -1 0 "" } {TEXT 263 0 "" }{TEXT 264 84 "The above is the command that determines the best-fit line, here unoriginally named." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(bestfitG/%\"yG,&$\"\"\"\"\"!F)*&$\"+++++]!#5F)%\"xGF )F)" }}}{EXCHG {PARA 256 "> " 1 "" {MPLTEXT 1 0 18 "?fit[leastsquare] \n" }{TEXT 287 0 "" }{TEXT 265 0 "" }{TEXT 266 172 "The command used p reviously used the default for \"leastsquare\", which in this case\nme rely generated a line. This request for help on \"leastsquare\" will \+ give other options." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "yb:= subs(bestfit,y);\n" }{TEXT 288 0 "" }{TEXT 267 0 "" }{TEXT 268 90 "Str ictly speaking, we have generated an equation that represents a line, \+ not the \"bestfit " }{TEXT 289 1 "y" }{TEXT 290 91 "\" as a function o f x. This command substitutes the equation to give yb as a function o f x." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ybG,&$\"\"\"\"\"!F'*&$\"+++ ++]!#5F'%\"xGF'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "Yb:=rh s(bestfit);\n" }{TEXT -1 0 "" }{TEXT 282 0 "" }{TEXT 283 113 "An alter native is to set another variable equal to the right-hand side of the \+ equation determining the same line." }{TEXT -1 0 "" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%#YbG,&$\"\"\"\"\"!F'*&$\"+++++]!#5F'%\"xGF'F'" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "plot(yb,x=0..5);\n" }{TEXT -1 0 "" }{TEXT 269 0 "" }{TEXT 270 1 "T" }{TEXT 292 48 "his is the com mand that plots the best-fit line." }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7S7$$\"\"!F)$\"\"\"F)7$$\"3GLLL3x&) *3\"!#=$\"3jmmT&)G\\a5!#<7$$\"3umm\"H2P\"Q?F/$\"3TLek`o!>5\"F27$$\"3ML L$eRwX5$F/$\"3pm;z>)G_:\"F27$$\"32ML$3x%3yTF/$\"3im;aQU!*37F27$$\"3emm \"z%4\\Y_F/$\"3LLeRZXKi7F27$$\"3`LLeR-/PiF/$\"3cm\"z>,_=J\"F27$$\"3\\* **\\il'pisF/$\"3\"**\\7G$[8j8F27$$\"3>MLe*)>VB$)F/$\"3gm\"z%*frhT\"F27 $$\"3X++DJbw!Q*F/$\"33+Dcw#Q!p9F27$$\"3%ommTIOo/\"F2$\"3ULL3_\"=M_\"F2 7$$\"3YLL3_>jU6F2$\"3$omTg(fJr:F27$$\"37++]i^Z]7F2$\"3&****\\7eP_i\"F2 7$$\"32++](=h(e8F2$\"3#****\\Pf!Qz;F27$$\"3/++]P[6j9F2$\"3-++v=ubJF27 $$\"3gmmm\"pW`(>F2$\"3TLL$eMsw)>F27$$\"3K+]i!f#=$3#F2$\"3;+DJ&H\"fT?F2 7$$\"3>+](=xpe=#F2$\"3))*\\Pf)[$H4#F27$$\"37nm\"H28IH#F2$\"3LL$ek`1l9# F27$$\"3um;zpSS\"R#F2$\"3eLe*[.-d>#F27$$\"3GLL3_?`(\\#F2$\"3Um;/Egw[AF 27$$\"3fL$e*)>pxg#F2$\"3zm\"z%*f%)QI#F27$$\"33+]Pf4t.FF2$\"3.+voza'=N# F27$$\"3uLLe*Gst!GF2$\"34n;zWho.CF27$$\"3/+++DRW9HF2$\"3C++]i>AdCF27$$ \"39++DJE>>IF2$\"32+]i:jf4DF27$$\"3F+]i!RU07$F2$\"38+DJ&>r-c#F27$$\"3+ ++v=S2LKF2$\"3++]P4q`;EF27$$\"3Jmmm\"p)=MLF2$\"3:LL$eM%4nEF27$$\"3B++] (=]@W$F2$\"37++v$4v5s#F27$$\"35L$e*[$z*RNF2$\"3bm\"zWn*)*pFF27$$\"3e++ ]iC$pk$F2$\"3H++DJiYBGF27$$\"3Zm;H2qcZPF2$\"3,Lek.NytGF27$$\"3O+]7.\"f F&QF2$\"3S+Dc^&zj#HF27$$\"3Xmm;/OgbRF2$\"3XLL3-=!y(HF27$$\"3w**\\ilAFj SF2$\"3))*\\7G8O;.$F27$$\"3yLLL$)*pp;%F2$\"3*omm;*\\[$3$F27$$\"3(RL$3x e,tUF2$\"3)pmT&Qz]OJF27$$\"3Cn;HdO=yVF2$\"3hLekG=4*=$F27$$\"3`+++D>#[Z %F2$\"3E++]i4TPKF27$$\"3RnmT&G!e&e%F2$\"3qL$3F9!z#H$F27$$\"3\"RLLL)Qk% o%F2$\"3'pmm;%>KULF27$$\"37+]iSjE!z%F2$\"3/+DJqJ8&R$F27$$\"3a+]P40O\"* [F2$\"3F+voa-oXMF27$$\"\"&F)$\"3++++++++NF2-%'COLOURG6&%$RGBG$\"#5!\" \"F(F(-%+AXESLABELSG6$Q\"x6\"Q!6\"-%%VIEWG6$;F(Fdz%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }{MPLTEXT 1 0 43 "dpoints:=[[Xvalues[n], Yvalues[n]]$n=1..4];\n" }{TEXT -1 0 "" }{TEXT 271 0 "" }{TEXT 272 1 "I " }{TEXT 293 89 "n order to plot the data points, we have to create an other array from the previous array." }}{PARA 257 "" 0 "" {TEXT 275 79 "There is a compact way to do both at once, but we don't need to be that fancy.)" }}{PARA 258 "" 0 "" {TEXT -1 134 "In the above command, the dollar sign \"$\" is used to iterate the assigning of the values \+ from the previous arrays into the new arrays." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(dpointsG7&7$\"\"\"$\"# " 0 "" {MPLTEXT 1 0 34 "plot( dpoints,x=0..5,style=point);\n" }{TEXT 294 0 "" }{TEXT 276 0 "" } {TEXT 277 56 "Of course, plotting the data points is of advantage, ... " }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVESG6$ 7&7$$\"\"\"\"\"!$\"3%**************p\"!#<7$$\"\"#F*$\"3/+++++++=F-7$$ \"\"$F*$\"3#)*************H#F-7$$\"\"%F*$\"3;+++++++KF--%'COLOURG6&%$R GBG$\"#5!\"\"$F*F*FD-%+AXESLABELSG6$Q\"x6\"Q!6\"-%&STYLEG6#%&POINTG-%% VIEWG6$;FD$\"\"&F*%(DEFAULTG" 1 5 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "plot([dpoints,yb],x=0..5,style=[point,line],color=[ma genta,blue]);\n" }{TEXT -1 0 "" }{TEXT 278 0 "" }{TEXT 279 78 "... and plotting the data and the best-fit line simultaneously is best of all ." }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVESG6 %7&7$$\"\"\"\"\"!$\"3%**************p\"!#<7$$\"\"#F*$\"3/+++++++=F-7$$ \"\"$F*$\"3#)*************H#F-7$$\"\"%F*$\"3;+++++++KF--%'COLOURG6&%$R GBG$\"*++++\"!\")$F*F*FA-%&STYLEG6#%&POINTG-F$6%7S7$FDF(7$$\"3GLLL3x&) *3\"!#=$\"3jmmT&)G\\a5F-7$$\"3umm\"H2P\"Q?FP$\"3TLek`o!>5\"F-7$$\"3MLL $eRwX5$FP$\"3pm;z>)G_:\"F-7$$\"32ML$3x%3yTFP$\"3im;aQU!*37F-7$$\"3emm \"z%4\\Y_FP$\"3LLeRZXKi7F-7$$\"3`LLeR-/PiFP$\"3cm\"z>,_=J\"F-7$$\"3\\* **\\il'pisFP$\"3\"**\\7G$[8j8F-7$$\"3>MLe*)>VB$)FP$\"3gm\"z%*frhT\"F-7 $$\"3X++DJbw!Q*FP$\"33+Dcw#Q!p9F-7$$\"3%ommTIOo/\"F-$\"3ULL3_\"=M_\"F- 7$$\"3YLL3_>jU6F-$\"3$omTg(fJr:F-7$$\"37++]i^Z]7F-$\"3&****\\7eP_i\"F- 7$$\"32++](=h(e8F-$\"3#****\\Pf!Qz;F-7$$\"3/++]P[6j9F-$\"3-++v=ubJF-7 $$\"3gmmm\"pW`(>F-$\"3TLL$eMsw)>F-7$$\"3K+]i!f#=$3#F-$\"3;+DJ&H\"fT?F- 7$$\"3>+](=xpe=#F-$\"3))*\\Pf)[$H4#F-7$$\"37nm\"H28IH#F-$\"3LL$ek`1l9# F-7$$\"3um;zpSS\"R#F-$\"3eLe*[.-d>#F-7$$\"3GLL3_?`(\\#F-$\"3Um;/Egw[AF -7$$\"3fL$e*)>pxg#F-$\"3zm\"z%*f%)QI#F-7$$\"33+]Pf4t.FF-$\"3.+voza'=N# F-7$$\"3uLLe*Gst!GF-$\"34n;zWho.CF-7$$\"3/+++DRW9HF-$\"3C++]i>AdCF-7$$ \"39++DJE>>IF-$\"32+]i:jf4DF-7$$\"3F+]i!RU07$F-$\"38+DJ&>r-c#F-7$$\"3+ ++v=S2LKF-$\"3++]P4q`;EF-7$$\"3Jmmm\"p)=MLF-$\"3:LL$eM%4nEF-7$$\"3B++] (=]@W$F-$\"37++v$4v5s#F-7$$\"35L$e*[$z*RNF-$\"3bm\"zWn*)*pFF-7$$\"3e++ ]iC$pk$F-$\"3H++DJiYBGF-7$$\"3Zm;H2qcZPF-$\"3,Lek.NytGF-7$$\"3O+]7.\"f F&QF-$\"3S+Dc^&zj#HF-7$$\"3Xmm;/OgbRF-$\"3XLL3-=!y(HF-7$$\"3w**\\ilAFj SF-$\"3))*\\7G8O;.$F-7$$\"3yLLL$)*pp;%F-$\"3*omm;*\\[$3$F-7$$\"3(RL$3x e,tUF-$\"3)pmT&Qz]OJF-7$$\"3Cn;HdO=yVF-$\"3hLekG=4*=$F-7$$\"3`+++D>#[Z %F-$\"3E++]i4TPKF-7$$\"3RnmT&G!e&e%F-$\"3qL$3F9!z#H$F-7$$\"3\"RLLL)Qk% o%F-$\"3'pmm;%>KULF-7$$\"37+]iSjE!z%F-$\"3/+DJqJ8&R$F-7$$\"3a+]P40O\"* [F-$\"3F+voa-oXMF-7$$\"\"&F*$\"3++++++++NF--F>6&F@FDFDFA-FF6#%%LINEG-% +AXESLABELSG6$Q\"x6\"Q!6\"-%%VIEWG6$;FDFd\\l%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "describe[linearcorrelation]( Xvalues,Yvalues);\n" }{TEXT -1 0 "" }{TEXT 295 0 "" }{TEXT -1 0 "" } {TEXT 280 0 "" }{TEXT 281 62 "Of course, the correlation coefficient i s part of the game ..." }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+9Za:%*!# 5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "11 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }