Using 2011 data on 141 U.S. public research universities, we examine the relationship between academic cost per student, \(A C A\) (real total academic cost per student in thousands of dollars) and full-time enrollment FTESTU (in thousands of students).

a. The least squares fitted relation is \(\widehat{A C A}=14.656+0.266 F T E S T U\). What is the economic interpretation of the estimated parameters? Why isn't the intercept zero?

b. In 2011 Louisiana State University (LSU) had a full-time student enrollment of 27,950. Using the fitted related in part (a), compute the predicted value of \(A C A\).

c. The actual value of \(A C A\) for LSU that year was 21.403. Calculate the least squares residual for LSU? Does the model overpredict or underpredict ACA for LSU?

d. The sample mean (average) full-time enrollment in U.S. public research universities in 2011 was \(22,845.77\). What was the sample mean of academic cost per student?