{VERSION 5 0 "SUN SPARC SOLARIS" "5.0" } {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 } {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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "pts := [ [1,3], [2,4 .8], [3,7.1], [5,11.2], [6,13] ];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %$ptsG7'7$\"\"\"\"\"$7$\"\"#$\"#[!\"\"7$F($\"#rF-7$\"\"&$\"$7\"F-7$\" \"'\"#8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "plot(pts,style=p oint, symbol=box, scaling=constrained);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6(-%'CURVESG6$7'7$$\"\"\"\"\"!$\"\"$F*7$$\"\" #F*$\"3#)*************z%!#<7$F+$\"3k*************4(F27$$\"\"&F*$\"3$** ***********>6!#;7$$\"\"'F*$\"#8F*-%'COLOURG6&%$RGBG$\"#5!\"\"$F*F*FH-% 'SYMBOLG6#%$BOXG-%&STYLEG6#%&POINTG-%+AXESLABELSG6$Q!6\"FT-%(SCALINGG6 #%,CONSTRAINEDG-%%VIEWG6$%(DEFAULTGFgn" 1 5 3 1 10 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "guess the line y=2x+1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "plots[display]( \n plot(pts,style=point, symbol=box , scaling=constrained),\n plot(2*x+1,x=0..6,color=blue)\n);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6'-%'CURVESG6&7'7$$\"\" \"\"\"!$\"\"$F*7$$\"\"#F*$\"3#)*************z%!#<7$F+$\"3k************ *4(F27$$\"\"&F*$\"3$*************>6!#;7$$\"\"'F*$\"#8F*-%'COLOURG6&%$R GBG$\"#5!\"\"$F*F*FH-%'SYMBOLG6#%$BOXG-%&STYLEG6#%&POINTG-F$6$7S7$FHF( 7$$\"3%*******\\#HyI\"!#=$\"3********\\ech7F27$$\"33++]([kdW#FX$\"3!** ***\\(*G:*[\"F27$$\"3++++v;\\DPFX$\"3++++N$)4XZIu#F27$$\"39++]( Q=\"))**FX$\"3-++]xOi(*HF27$$\"3'****\\P'=pD6F2$\"3$*****\\FPQ^KF27$$ \"33+++lN?c7F2$\"3;+++IrS7NF27$$\"3,++]U$e6P\"F2$\"3.+++&o;Bu$F27$$\"3 6+++&>q0]\"F2$\"3x*******QS6+%F27$$\"3'******\\U80j\"F2$\"3O+++]o-hUF2 7$$\"34+++0ytb@F2$\"30+++g:WQ_F27$ $\"3'****\\(3wY_AF2$\"3#*****\\<_$\\]&F27$$\"3#)******HOTqBF2$\"3m**** **fs#3u&F27$$\"37++v3\">)*\\#F2$\"3E++]<#Q'**fF27$$\"3:++DEP/BEF2$\"3I ++]_u3YiF27$$\"3=++](o:;v#F2$\"3P+++v8B.lF27$$\"3=++v$)[opGF2$\"3Q++]n (p$RnF27$$\"3%*****\\i%Qq*HF2$\"3))*****\\#p2%*pF27$$\"3&****\\(QIKHJF 2$\"3!*****\\xgkesF27$$\"3#****\\7:xWC$F2$\"3$)****\\-V&*)[(F27$$\"37+ +]Zn%)oLF2$\"3E+++&\\$pPxF27$$\"3y******4FL(\\$F2$\"3e******>am%*zF27$ $\"3#)****\\d6.BOF2$\"3k*****\\JigC)F27$$\"3(****\\(o3lWPF2$\"3%***** \\Pw7&F2$\"3,++]5Q_D6 F;7$$\"3N++v)Q?QD&F2$\"32++vxSw]6F;7$$\"3G+++5jyp`F2$\"31+++is&R<\"F;7 $$\"3<++]Ujp-bF2$\"3.++]o#R0?\"F;7$$\"3++++gEd@cF2$\"3++++KXJC7F;7$$\" 39++v3'>$[dF2$\"3.++v@Rm\\7F;7$$\"37++D6EjpeF2$\"3.++DAl#RF\"F;F<-FB6& FDFHFH$\"*++++\"!\")-%+AXESLABELSG6%Q!6\"Fc]l-%%FONTG6#%(DEFAULTG-%(SC ALINGG6#%,CONSTRAINEDG-%%VIEWG6$;FHF=Fh]l" 1 2 0 1 10 0 2 9 1 4 1 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 100 "Let's use maple's built in least squares fitti ng. it lives in the stats library, which I will load:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(stats);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7*%&anovaG%)describeG%$fitG%+importdataG%'randomG%*stat evalfG%*statplotsG%*transformG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 42 "Need to transform our data a little, sigh." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "pts;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7'7$\"\"\" \"\"$7$\"\"#$\"#[!\"\"7$F&$\"#rF+7$\"\"&$\"$7\"F+7$\"\"'\"#8" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "pts[3][1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 " xvals:=[seq(pts[i][1], i=1..5)];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 " " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&xvalsG7'\"\"\"\"\"#\"\"$\"\"&\" \"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "yvals:=[seq(pts[i][2 ], i=1..5)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&yvalsG7'\"\"$$\"#[! \"\"$\"#rF)$\"$7\"F)\"#8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 " ?fit" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "fit[leastsquare[[x, y]]]([xvals,yvals]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"yG,&$\"+ cK-$4*!#5\"\"\"*&$\"+S\"eD.#!\"*F)%\"xGF)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PAGEBK }{PARA 0 "" 0 "" {TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "vdist := (m,b, p) -> m*p[1] \+ + b - p[2];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&vdistGf*6%%\"mG%\"bG %\"pG6\"6$%)operatorG%&arrowGF*,(*&9$\"\"\"&9&6#F1F1F19%F1&F36#\"\"#! \"\"F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "vdist(2,1, [1 ,3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 20 "vdist(2,1, [10,30]);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "E := (m,b, pts) -> sum( (vdist(m,b ,pts[i]) )^2 , i=1..5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"EGf*6%% \"mG%\"bG%$ptsG6\"6$%)operatorG%&arrowGF*-%$sumG6$*$)-%&vdistG6%9$9%&9 &6#%\"iG\"\"#\"\"\"/F;;F=\"\"&F*F*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "E(2,1,pts);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"\"* !\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "E(2.03,.909,pts);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+++]Gq!#6" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 5 "a:=2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aG \"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "a:=a;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"aG\"\"#" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "a;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "a:='a';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aGF$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "a ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"aG" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{MARK "25 0 0" 0 }{VIEWOPTS 1 1 0 3 2 1804 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }