[Ether]

Originally Posted by MikeE

for linear regression I solve the normal equation using Octave

Octave uses a polymorphic solver, that selects an appropriate matrix factorization depending on the properties of the matrix.

If the matrix is Hermitian with a real positive diagonal, the polymorphic solver will attempt Cholesky factorization.

Since the normal matrix N=A^TA satisfies this condition, Cholesky factorization will be used.

MLE is just an approach for getting the parameters from match data. For simplicity I assume a Gaussian distribution, use linear regression as an initial estimate of each team's mean and linear regression on the squared residuals as an initial estimate of each team's variance.

The solution of the normal equations is a maximum likelihood estimator only if the data follows a normal distribution. I was wondering what was the theoretical basis for assuming a normal distribution.