% generate data:
m = 0.75;
b = -40.0;
n = 20;
x = 120.0*rand(n, 1);
y = m*x + b + 15.0*randn(n, 1);

% compute mean squared error for a range of slopes and intercepts:
slopes = -5:0.25:5;
intercepts = -30:1:30;
error_surface = zeros(length(slopes), length(intercepts));
for i = 1:length(slopes)
    for j = 1:length(intercepts)
	      error_surf(i,j) = meanSquaredError([slopes(i), intercepts(j)], x, y);
    end
end

% plot the error surface:
figure()
[N,M] = meshgrid(intercepts, slopes);
surface(M, N, error_surface);
xlabel('slope', 'rotation', 7.5)
ylabel('intercept', 'rotation', -22.5)
zlabel('error')
set(gca,'xtick', (-5:2.5:5))
grid on
view(3)