Fixed half of the regression chapter.

regression/code/errorSurface.m

@@ -3,16 +3,17 @@ close all
 
 load('lin_regression.mat');
 
+% compute mean squared error for a range of sloopes and intercepts:
 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);
+        error_surf(i,j) = lsqError(x, y, [slopes(i), intercepts(j)]);
     end
 end
 
-% plot the error surface
+% plot the error surface:
 figure()
 [N,M] = meshgrid(intercepts, slopes);
 s = surface(M,N,error_surf);

regression/code/lsqError.m

@@ -1,11 +1,13 @@
-function error = lsqError(parameter, x, y)
+function error = lsqError(x, y, parameter)
 % Objective function for fitting a linear equation to data.
 %
-% Arguments: parameter, vector containing slope and intercept (1st and 2nd element) 
-%            x, the input values
-%            y, the measured system output
+% Arguments: x, the input values
+%            y, the corresponding measured output values
+%            parameter, vector containing slope and intercept 
+%                       as the 1st and 2nd element 
 %
-% Retruns: the estimation error in terms of the mean sqaure error
+% Returns: the estimation error in terms of the mean sqaure error
 
 y_est = x .* parameter(1) + parameter(2);
 error = meanSquareError(y, y_est);
+end

regression/code/meanSquareError.m

@@ -1,9 +1,10 @@
 function error = meanSquareError(y, y_est)
-% Function calculates the mean sqauare error between observed and predicted values.
+% Mean squared error between observed and predicted values.
 %
-% Agruments:    y, the observed values
-%               y_est, the predicted values.
+% Arguments:    y, vector of observed values.
+%               y_est, vector of predicted values.
 %
-% Returns:      the error in the mean-square-deviation sense.
+% Returns:      the error in the mean-squared-deviation sense.
 
-error = mean((y - y_est).^2);
+  error = mean((y - y_est).^2);
+end