Compute Cost Multiple Variables

computeCostMulti.m

function J = computeCostMulti(X, y, theta)
%COMPUTECOSTMULTI Compute cost for linear regression with multiple variables
%   J = COMPUTECOSTMULTI(X, y, theta) computes the cost of using theta as the
%   parameter for linear regression to fit the data points in X and y

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta
%               You should set J to the cost.

	
J = (0.5/m) * (X*theta - y)' * (X*theta - y);



% =========================================================================

end

@punkytun
They are the exact same thing.
.^2 is an element-wise square function, which is the same thing as multiplying a function by it's inverse when it's a vector matrix.

The logic:
Given matrix A with dimensions mx1, A*A cant work because mx1 * mx1 has the wrong dimensions.
But A'*A gives you 1xm * mx1 - which gives you a 1x1 matrix, where every single element in the vector matrix is multiplied by itself.