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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 25 "3-D Least Squares Fit :  \+
" }{TEXT 256 13 "by Yufang Hao" }}{PARA 0 "" 0 "" {TEXT -1 86 "Purpose
: Given data in x, y, z, find and plot the best linear least-squares f
it to it." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "restart; with(
stats[fit]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$%2leastmediansquareG
%,leastsquareG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "x_data :=
 [12,13,16,15,11]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "y_dat
a := [5,3,4,2,6]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "z_data
 := [7,9,6,8,6]:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 177 "The best lin
ear least-squares fit to the given data can be easily found by the lea
stsquare() command.  For more information, please refer to the help pa
ge ?stats[fit] command.  " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
45 "leastsquare[[x,y,z]]([x_data,y_data,z_data]);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#/%\"zG,(#\"%[%)\"$b%\"\"\"*&#\"#[\"#\"*F)%\"xGF)!\"\"*&
#\"$*[F(F)%\"yGF)F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "f :=
 unapply(rhs(%),x,y);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGf*6$%\"
xG%\"yG6\"6$%)operatorG%&arrowGF),(#\"%[%)\"$b%\"\"\"*&#\"#[\"#\"*F19$
F1!\"\"*&#\"$*[F0F19%F1F7F)F)F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
78 "The following manipulations make sure that the plot contains every
 data point." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "x_max := ma
x(seq(x_data[i],i=1..nops(x_data))):\nx_min := min(seq(x_data[i],i=1..
nops(x_data))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "y_max :=
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1..nops(y_data))):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(
plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changecoords
 has been redefined\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "d
ata_points := pointplot3d( \{seq([x_data[i],y_data[i],z_data[i]], i=1.
.nops(z_data)) \}, symbol=circle, color=blue):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 78 "best_curve := plot3d(f(x,y), x=x_min..x_max, y
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{MPLTEXT 1 0 94 "display3d([best_curve, data_points], labels=['x','y',
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