[32 pts] 4. An education economist is analyzing the amount of annual tuition (and fees) paid by university students. The economist believes that the tuition amount is closely related to the number of students attending the university (i.e., the enrollment). She reasons that higher enrollment allows the university to defray costs across a greater number of people, thus allowing the average tuition bill to be lower at more-populated universities. The economist therefore considers the model: very (5) (6) War (9) Var (4) +3 En Tuition B B2 Enrollment + e = (a) Before collecting a sample of data, reflect on the ensuing regression line. In particular, consider the p-value associated with the y-intercept (that would show up in the lower table of the Stata output). For this particular model, do you anticipate a high p-value or a low p-value? Please provide two or three sentences of explanation. A sample of n = 6 different universities provides the following (both tuition and enrollment are recorded in thousands): Enrollment (in thousands) 6 8 14 18 24 35 W Tuition (in thousands) Y Y Y3 Y4 Ys Yo Ang alamong Notice that the Y-values of the sample are not shown; their precise values are unnecessary for this exercise. (b) Suppose the ensuing regression line is Tuition = 58.913 -1.48 Enrollment with MSE= 76.665. Construct a hypothesis test on whether the average tuition paid by students at universities which enroll 15,000 students (i.e., Enrollment = 15) exceeds $28,000. Determine the p-value of the test. (c) Now consider a different sample of size n = 6 which uses the same X-values but different Y-values as compared to the above sample. With this sample, the regression line is Tuition = 51.456-1.16 Enrollment. Further, the variance of the Y-values (using the sample variance formula) is Var(Y) = 269.367. Determine the R-value for this regression line. high