Regression with Gradient Descent in Low-level Matlab

I just finished writing my first machine learning algorithm in Matlab. The algorithm is based on gradient descent search for estimating parameters of linear regression (but can be easily extended to quadratic or even higher-dimensional polynomials). It’s fairly easy if you know the theory behind the model. So, first a very brief theory portion. This isn’t a tutorial on statistics. Go read a book if you don’t know about regression.