Normal Equation and pinv() in Matlab/Octave

Question

I'm studing the fundamentals of Machine Learning and, when I was reading about the use of Normal Equation in Matlab, I had a question.

If the Normal Equation is:

And

Is the Pseudo Inverse , so:

And pinv(X) compute the pseudo inverse of X .

Why, in Matlab/Octave, some people use:

theta = pinv(X'*X)*X'*y ...(4)

instead of

theta = pinv(X)*y ...(5)

?

Is (4) not redundant? doesn't pinv(X) compute the pseudo inverse formula for us?

Thank you!

Answer 1

Has anybody found an answer to this? Even here under "Implementation" they use (4): http://mlwiki.org/index.php/Normal_Equation#Implementation