3-D Least Squares Fit

by Yufang Hao

Purpose: Given data in x, y, z, find and plot the best linear least-squares fit to it.

> restart; with(stats[fit]);

> x_data := [12,13,16,15,11]:

> y_data := [5,3,4,2,6]:

> z_data := [7,9,6,8,6]:

The best linear least-squares fit to the given data can be easily found by the leastsquare() command. For more information, please refer to the help page ?stats[fit] command.

> leastsquare[[x,y,z]]([x_data,y_data,z_data]);

> f := unapply(rhs(%),x,y);

The following manipulations make sure that the plot contains every data point.

> x_max := max(seq(x_data[i],i=1..nops(x_data))):
x_min := min(seq(x_data[i],i=1..nops(x_data))):

> y_max := max(seq(y_data[i],i=1..nops(y_data))):
y_min := min(seq(y_data[i],i=1..nops(y_data))):

> with(plots):

Warning, the name changecoords has been redefined

> data_points := pointplot3d( {seq([x_data[i],y_data[i],z_data[i]], i=1..nops(z_data)) }, symbol=circle, color=blue):

> best_curve := plot3d(f(x,y), x=x_min..x_max, y=y_min..y_max, style=wireframe):

> display3d([best_curve, data_points], labels=['x','y','z'], axes=normal, orientation=[145,45]);