I have a question about problem 3:

part1: I'm having trouble writing an expression for the likelihood of a set of observations, given an assumed number of coefficients. I believe I understand the intuition (below), but I'm not sure about how to express it in formula. If my intuition is correct, I could live without a nice formula, but it would be a heck of a lot easier to implement, if I had a nice likelihood formula.

part2: Intuition: Treat the set of Y_i's as distributed as a Gaussian with different means (depending on X_i's), but with the same variance. Use the least squares solution as the MLE for a model containing a specific set of variables. Use the resultant RSS to estimate the variance of Y. Given (1) the expected Y (treated as mean) (2) the actual Y and (3) the estimated variance of Y, we have enough to determine the (maximum) likelihood of the observation assuming our model has the right parameters. Does this make sense?