Lecture 4

We have derived the least squares estimators for parameters first principles of parameters in the simple linear regression and the simple linear regression through the origin. Each parameter and model was dealt with separately, but in fact we can derive a very general solution. More generally in the multiple regression setting where we might potentially include a large number of predictors it is more efficient to use vectors and matrices to define the regression model and find the parameter estimates. Here we review matrix algebra and derive important multiple regression formulae in matrix form.