Question 1 (15 points total ) Consider the following multiple regression model : (1 ) (a) (5 points) To estimate the model using the OLS, we need more observations that the number of coefficients (betas ) in the model . In other words, it must be that n > k. Since we have & = 4 coefficients in this model $ 18 28 , and ,), we need at least n = 5 observations. (b) (5 points ) Since there exists an exact relationship between X,, and X, we have perfect collinearity, and hence we cannot estimate the model using OLS. (c) (5 points ) Slope coefficients show the marginal effects of regressors X2 :..; Xxi on the average value of the dependent variable Y Question 2 (50 points total ) Suppose that you've been hired to work as an analyst at a sports consultancy firm . Your task is to evaluate the effectiveness of players on the client's team. Your observe the following data on seven players at the end of the season: Player # Season Goals Total Field Time (minutes) Y1 = 3 X = 120 2 12 =5 X2 = 340 3 Y3 = 8 X3 = 560 4 Y = 15 *4 = 590 5 Y's = 27 Xs = 780 6 Y6 = 45 X's = 1120 Y, = 46 X5 = 1800 Table 1: Player Effectiveness: Goals vs Field Time You decide to use these data to estimate the following regression model: (2) and obtain the following OLS estimates