Question 1 Consider the linear model with one response variable (Y) and two candidate pre- dictors (X 1,X2). For each variable, there are n = 12 observations. Regressing Y on only an intercept gives RSS 2 1221175. Suppose additionally that regressing Y on only X1 gives RSS 2 119718; regressing Y on only X2 gives RSS 2 116432, and regressing Y on both X1 and X 2 gives RSS 2 106836. (a) Perform a series of Ftests to select a model using Forward Selection: check if including one predictor is better than none. Then check if including both predictors is an improvement on just one. Use this \"best\" model for the rest of this problem. (Hint: the result will be a one-predictor model). (b) Suppose 3X1 2 11.12 and 3X2 2 1.81, and le = 29.32 and mX2 = 4.67. How wide of an interval would you need to be 95% \"sure\" that you've captured the response predicted by a new observation at $11, = 30 and / or $23, = 5'? (c) A colleague is confused by your solution to (b) because they tried to construct the same interval as you at :31p 2 60 and / or $21, = 10. Explain why you would expect your colleague's interval to be particularly wide. (d) Your colleague says that they can get a much better R2 by including X 1 , X 2, X f, X3, X 11, X 3. Explain why you might be skeptical of this model