finished regression chapter

regression/code/errorSurface.m

@@ -0,0 +1,31 @@
+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')

regression/code/lsqError.m

@@ -1,4 +1,4 @@
-function error = lsq_error(parameter, x, y)
+function error = lsqError(parameter, x, y)
 % Objective function for fitting a linear equation to data.
 %
 % Arguments: parameter, vector containing slope and intercept (1st and 2nd element) 

regression/code/lsqGradient.m

@@ -0,0 +1,7 @@
+function gradient = lsqGradient(parameter, x, y)
+h = 1e-6;
+
+partial_m = (lsqError([parameter(1)+h, parameter(2)],x,y) - lsqError(parameter,x,y))/ h;
+partial_n = (lsqError([parameter(1), parameter(2)+h],x,y) - lsqError(parameter,x,y))/ h;
+
+gradient = [partial_m, partial_n];

regression/code/lsq_gradient.m

@@ -1,7 +0,0 @@
-function gradient = lsq_gradient(parameter, x, y)
-h = 1e-6;
-
-partial_m = (lsq_error([parameter(1)+h, parameter(2)],x,y) - lsq_error(parameter,x,y))/ h;
-partial_n = (lsq_error([parameter(1), parameter(2)+h],x,y) - lsq_error(parameter,x,y))/ h;
-
-gradient = [partial_m, partial_n];