clear
close all

load('lin_regression.mat');

slopes = -5:0.25:5;
intercepts = -30:1:30;
error_surf = zeros(length(slopes), length(intercepts));
for i = 1:length(slopes)
    for j = 1:length(intercepts)
        error_surf(i,j) = lsqError([slopes(i), intercepts(j)], x, y);
    end
end

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

set(gcf, 'paperunits', 'centimeters', 'papersize', [15, 15], ... 
    'paperposition', [0., 0., 15, 15])
saveas(gcf, 'error_surface', 'pdf')