Refer to the College Choice 2015 Rankings of National Research Universities, Exercise 2.43. Recall that data on academic reputation score, financial aid awarded, net cost to attend, median salary during early career, percentage of alumni who feel their work makes a better place in which to live, and percentage of science, technology, engineering, and math (STEM) degrees awarded for the top 50 research universities are saved in the file. Information on the top 10 schools are listed in the table on the next page.

a. Select one of the variables as the dependent variable, y, and another as the independent variable, x. Use your knowledge of the subject area and common sense to help you select the variables.

b. Fit the simple linear model, E(y) = β0 + β1x, to the data for all 50 top-ranked schools. Interpret the estimates of the slope and y-intercept.

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Academic Rep. Score 99 pts. Financial Rank University Early Pay Better Place Aid Cost STEM $41,555 34,641 38,522 37,934 39,771 31,445 38,148 35,539 33,191 $14,455 20,629 19,233 21,274 18,479 22,645 20,490 21,821 24,134 22,973 65% 55 62 28% 79 $61,400 Harvard MIT 92 2 Stanford 65,900 60,200 60,300 72,600 94 Columbia 29 21 4 56 5 Yale 97 91 91 66 45 55 59 63 CalTech Dartmouth Penn Duke Johns Hopkins 20 19 35 26 60,300 60,600 57,500 92 92 89 10 34,469