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{SECT 0 {EXCHG {PARA 200 "" 0 "" {TEXT 202 8 "        " }}{PARA 200 ""
 0 "" {TEXT 202 59 "                        Discrete Least Squares Usi
ng MAPLE." }}{PARA 200 "" 0 "" {TEXT 203 0 "" }}}{EXCHG {PARA 201 "> "
 0 "" {MPLTEXT 1 204 8 "restart;" }}}{EXCHG {PARA 201 "> " 0 "" 
{MPLTEXT 1 204 12 "with(stats):" }}}{EXCHG {PARA 201 "> " 0 "" 
{MPLTEXT 1 204 27 "xvals:=[0,0.25,0.5,0.75,1];" }}{PARA 202 "" 1 "" 
{XPPMATH 20 "6#>I&xvalsG6\"7'\"\"!$\"#D!\"#$\"\"&!\"\"$\"#vF*\"\"\"" }
{TEXT 205 0 "" }}}{EXCHG {PARA 201 "> " 0 "" {MPLTEXT 1 204 38 "yvals:
=[1,1.284,1.6487, 2.117,2.7183];" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>
I&yvalsG6\"7'\"\"\"$\"%%G\"!\"$$\"&([;!\"%$\"%<@F*$\"&$=FF-" }{TEXT 
205 0 "" }}}{EXCHG {PARA 200 "" 0 "" {TEXT 202 34 "Trying with a quadr
atic polynomial" }{TEXT 203 0 "" }}}{EXCHG {PARA 201 "> " 0 "" 
{MPLTEXT 1 204 64 "z:=fit[leastsquare[[x,y],y=a*x^2+b*x+c,\{a,b,c\}]](
[xvals,yvals]);" }}{PARA 202 "" 1 "" {XPPMATH 20 "6#>I\"zG6\"/I\"yGF%,
(*$I\"xGF%\"\"#$\"+H9dO%)!#5F*$\"+r&G=k)F.$\"+Vr805!\"*\"\"\"" }{TEXT 
205 0 "" }}}{EXCHG {PARA 200 "" 0 "" {TEXT 202 32 "Let's try now a cub
ic polynomial" }}{PARA 200 "" 0 "" {TEXT 202 0 "" }}}{EXCHG {PARA 201 
"> " 0 "" {MPLTEXT 1 204 72 "z:=fit[leastsquare[[x,y],y=d*x^3+a*x^2+b*
x+c,\{d,a,b,c\}]]([xvals,yvals]);" }{MPLTEXT 1 204 0 "" }}{PARA 202 ""
 1 "" {XPPMATH 20 "6#>I\"zG6\"/I\"yGF%,**$I\"xGF%\"\"$$\"+KNL*y#!#5*$F
*\"\"#$\"+J6d_UF.F*$\"+M&4T,\"!\"*$\"+D92****F.\"\"\"" }{TEXT 205 0 ""
 }}}{EXCHG {PARA 200 "" 0 "" {TEXT 202 21 "Evaluation at a point" }}
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{MPLTEXT 1 204 21 "evalf(subs(x=1.7,z));" }}{PARA 202 "" 1 "" 
{XPPMATH 20 "6#/I\"yG6\"$\"+sfGB`!\"*" }{TEXT 205 0 "" }}}{EXCHG 
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