The sheet UNIV&COL contains data on 80 colleges and universities. Among the variables included are the annual total cost (in thousands of dollars), the average total score on the SAT, and the room and board expenses (in thousands of dollars). Develop a model to predict the annual total cost based on SAT score and room and board expenses.
a. State the multiple regression equation.
b. Interpret the meaning of the slopes in the equation.
c. Predict the average annual total coast for a school that has an average SAT score of 1,100 and a room and board expense of $5,000.
d. Perform a residual analysis on the results and determine the adequacy of the fit of the model.
e. Determine whether there is a significant relationship between annual total cost and the two explanatory variables (SAT score and room and board expenses) at the 0.05 level of significance.
f. Determine the p-value in (e) and interpret its meaning.
g. At the 0.05 level of significance, determine whether each explanatory variable makes a significant contribution to the regression model. On the basis of these results, indicate the regression model that should be used in this problem.
h. Determine the p-values in (g) and interpret their meaning.
i. Set up a 95% confident interval estimate of the population slope between annual total cost and SAT score.
j. What other factors that are not included in the model might account for the strong positive relationship between annual total cost and SAT scores?