2. (18 points) Suppose you are interested in how students' learning, as measured by test scores, is related to class size. You have data on 420 school districts in California, and for each district, you can compute the average reading and math test scores of fth graders, avgscore, and the student-teacher ratio, str. The variable avgscore has a mean of 654 and a standard deviation of 19, and the variable str has a mean of 19.6 and a standard deviation of 1.9. You regress test score on studentteacher ratio and obtain the following estimated regression line and R2: avgscore = 698.9 2.28 str, R2 = 0.05 2.1. What is the predicted average test score for a district with a student-teacher ratio of 20? 2.2. What is the predicted average test score for a district with a student-teacher ratio of 30? 2.3. Based solely on the information in this question, which of the two predictions do you think is more informative or reliable? (a) The prediction for a district with a student-teacher ratio of 20 (b) The prediction for a district with a student-teacher ratio of 30 (c) The predictions are equally reliable 2.4. What are the units of R2? (a) test score (b) class size (c) (test score) x (class size) (d) There are no units 2.5. Suppose the test score variable is measured on a 01000 scale and you rescaled it to a 0100 scale. What would happen to the total sum of squares, SST? (a) SST would increase (b) SST would decrease (c) SST would not change 2.6. Suppose the test score variable is measured on a 01000 scale and you rescaled it to a 0100 scale. What would happen to the variance of the residuals? (a) The variance of the residuals would increase (b) The variance of the residuals would decrease (c) The variance of the residuals would not change