# solution

Rankings of research universities. Refer to the analysis of data from College Choice 2015 Rankings of National Research Universities, Exercise 12.20 (p. 726). You fit a first-order multiple regression model to predict academic reputation score (y) using financial aid awarded (x1), net cost (x2), early career salary 1×32, work makes a better place percentage (x4), and percentage of STEM degrees x5. Now use statistical software to find and interpret a 95% prediction interval for the academic reputation score of a university with the following characteristics: x1 = \$23,368, x2 = \$32,868, x3 = \$49,100, x4 = 46%, and x5 = 12%.

Exercise 12.20

Rankings of research universities. Refer to the College Choice 2015 Rankings of National Research Universities, Exercise 11.29 (p. 657). Data on academic reputation score, average financial aid awarded, average net cost to attend, median salary during early career, percentage of alumni who feel their work makes a better place, 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 reproduced in the table. Consider a first-order multiple regression model to predict academic reputation score 1y2 using financial aid awarded (x1), net cost (x2), early career salary (x3), work makes a better place percentage (x4), and percentage of STEM degrees (x5). a. Use statistical software to fit the model to the data. Give the least squares prediction equation.

b. Find and give a practical interpretation of the standard deviation of the model, s.

c. Find and give a practical interpretation of the coefficient of determination, R2 .

d. Conduct a test of the overall adequacy of the model using Â = .05.

e. Find a 90% confidence interval for the b coefficient associated with work makes a better place percentage (x4). Interpret the result

Exercise 11.29

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(y) = 0 + 1 x, to the data for all 50 top-ranked schools. Interpret the estimates of the slope and y-intercept. ##### "Looking for a Similar Assignment? Get Expert Help at an Amazing Discount!" ##### Looking for a Similar Assignment? Our Experts can help. Use the coupon code SAVE30 to get your first order at 30% off!

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