Chapter 12.3, Problem 12.20ACI

Rankings of research universities. Refer to the College Choice 2015 Rankings of National Research Universities, Exercise 11.29 (p. 633). 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 (y) 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 α = .05.

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