In this lecture we will review/present distribution theory related to the sampling distribution of the MLEs, in particular, Student-t and Chi-Squared distributions.
Readings: Christensen Chapter 2, Appendex C
In this lecture we will review the Student t distribution and $\chi^2$ distribution and then find the sampling distributions of the MLEs. We will provide proof of why the residual sum of squares has a $\chi^2$ distribution and how the degrees of freedom are obtained. We will use these results to find confidence intervals for coefficients, the mean function, and predictions. Finally we will look at an example using the prostate data from the lasso2 package (See code link above).