Rankings of research universities. Refer to the College Choice 2015 Rankings of National Research Universities, Exercise 2.43 (p. 95). 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() = 0  1, to the data for all 50 top-ranked schools. Interpret the estimates of the slope and y-intercept.

Exercise 2.43

Rankings of research universities. Based on factors (e.g., academic reputation, financial aid offerings, overall cost, and success of graduates in the post-college job market) that actual college freshmen said were most important to their college decision, College Choice developed their 2015 Rankings of National Research Universities. Data for the top 50 universities are saved in the TOPUNIV file. Several are listed in the accompanying table above. TOPUNIV Rank University Public/ Private Academic Reputation Score (100-pt. scale) Average Financial Aid Awarded Average Net Cost to Attend Median Salary During Early Career % High Meaning* % STEM† Degrees 1 Harvard University Private 99 $41,555 $14,455 $61,400 65% 28% 5 Yale University Private 97 $39,771 $18,479 $60,300 68% 21% 20 University of California Berkeley Public 79 $16,141 $16,178 $59,500 50% 31% 23 University of Virginia Public 76 $16,834 $12,672 $54,700 52% 24% 27 Carnegie Mellon University Private 76 $24,263 $33,257 $64,700 46% 51% 47 Pepperdine University Private 60 $29,926 $25,345 $48,300 51% 4% *% high meaning represents the percentage of alumni who say their work makes the world a better place; †% STEM represents the percentage of degrees awarded in science, technology, engineering, or mathematics.

a. The average financial aid awarded values were determined by recording the financial aid awarded to each freshman who attended the university in 2015. Does this statistic represent a population or sample mean? Interpret this value for Harvard University.

b. The median salary during early career values were determined by recording the salaries of a random selection of alumni with 0 to 5 years of experience. Does this statistic represent a population or sample median? Interpret this value for Harvard University.

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