Question

considering the propirtionality constant k, for the model W = k*(l*l*g), derive the equation for the least squares estimate of k.

Length, (in.) | 14.5 12.5 17.25 14.5 12.625 17.75 14.125 12.625 Girth, g (in.)9.75 8.375 11.0 9.75 8.5 12.5 9.0 8.5 Weight, W (oz) 27 17 41 26 17 49 23 16

Answer 1

MATLAB Code:

close all
clear
clc

% W = k*l*l*g
l = [14.5 12.5 17.25 14.5 12.625 17.75 14.125 12.625];
g = [9.75 8.375 11.0 9.75 8.5 12.5 9.0 8.5];
W = [27 17 41 26 17 49 23 16];

k = (l.*l.*g)' \ W'

scatter(l.*l.*g, W), hold on
plot(l.*l.*g, k*l.*l.*g)
legend('Data Points', 'Fit', 'Location', 'northwest')
xlabel('l*l*g'), ylabel('W')

Output:

k =
0.012583877271936

Plot:

50 O Data Points Fit 45 40 35 30 25 20 15 1000 1500 2500 Il g 2000 3000 3500 4000