% RegressMultEx2.m
%
% Calculations for multiple regression example.

% Multiple regression fit of tensile strength of steel versus composition,
%  C % and Cr %.

% Create the matrix of x values (and 1's).
X = [ 1, 0.08, 14.5; 1, 0.12, 16.0; 1, 0.12, 18.0; 1, 0.20, 23.0];

% Create y pts.
y = [415, 450, 450, 515]';

% Print values.
data = [X,y]

% Now compute the multiple regression solution.
Xplus = pinv(X)

% Find the hyperplane fit.
ba_soln = Xplus * y

% Print out the pts predicted by the fit.
fit = [X,X * ba_soln]

hold off

% Make 3D plot.
miny = 400;
maxy = 525;
plot3(data(:,2)',data(:,3)',data(:,4)','+k')
xlabel('x1'), ylabel('x2'), zlabel('y')
axis([0, 0.25, 0, 25, miny, maxy])
grid on
hold on
for index = 1 : length(y)
  plot3([data(index,2);data(index,2)], ...
        [data(index,3);data(index,3)], ...
        [miny,data(index,4)],'-g')
end

plot3(fit(:,2)',fit(:,3)',fit(:,4)','or')

hold off