Please help with these questions, thank you!!

Too (d) (3 points) Find 80 = using the formula derived in lecture 12: 0 = (XTX)-IXTY. Explicitly write out the matrix X for this problem and show all steps. (Hint: The intercept and coefficient of X 1 for OLS are the same as SLR in this special example. Check the remark at the end of the question to see why this is the case.) (e) (2 points) Show that MSE for the OLS is 0. What is the relationship between Y and span(X)? (As a sanity check, the sum of residuals should be 0.) Homework #6 10 (f) (3 points) Instead of using X.2 as a feature in our second model, we decided to transform it and use X?2 instead. That is, the dataset we use is modified as follows: Y bias X. 1 X?, (-1)2 = 1 Co 02 = 0 12 = 1 Accordingly, we calculate a single prediction using the new model as specified below: ynew = 0new + 0newx1+ 0new ? Is it possible to find a unique optimal solution in this case? If so, compute gnew and the corresponding value of MSE. If not, explain why this is not possible. Regardless of which way you answer, similar to part d), explicitly write out the matrix Knew for this problem and show all steps