first steps of the gradient descent chapter

regression/code/lsq_error.m

@@ -1,6 +1,11 @@
 function error = lsq_error(parameter, x, y)
-% parameter(1) is the slope
-% parameter(2) is the intercept
+% 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
+%
+% Retruns: the estimation error in terms of the mean sqaure error
 
-f_x = x .* parameter(1) + parameter(2);
-error = mean((f_x - y).^2);
+y_est = x .* parameter(1) + parameter(2);
+error = meanSquareError(y, y_est);

regression/code/mean_square_error.m

@@ -0,0 +1,9 @@
+function error = meanSquareError(y, y_est)
+% Function calculates the mean sqauare error between observed and predicted values.
+%
+% Agruments:    y, the observed values
+%               y_est, the predicted values.
+%
+% Returns:      the error in the mean-square-deviation sense.
+
+error = mean((y - y_est).^2);