The provost at a major university would like to develop a model to examine the relationship between the salaries of full time associate professors at the institution and the following independent variables: an associate professor’s performance rating on a scale of 1– 20, his or her gender, student approval rating on a scale of 0– 100%, age, years of teaching experience, and college (arts and sciences, or business). The provost has collected these data from a random sample of associate professors, which can be found in the Excel file faculty salaries. xlsx.

a. Check for the presence of multicollinearity between the independent variables. If it is present, take the necessary steps to eliminate it.

b. Construct a regression model using all the independent variables remaining after part a.

c. Interpret the meaning of each of the regression coefficients.

d. Test the significance of the overall regression model using α = 0.01. e. Using the p values, identify which independent variables are significant with α = 0.01.

f. Construct a regression model using a general stepwise regression to predict an associate professor’s salary using the independent variables from part b. Use α = 0.01 for the p value to enter and remove independent variables.

g. Predict the salary of a female associate professor in the business college who is 41 years old with 11 years of teaching experience, a performance score of 17, and a student approval rating of 88.3%.

h. Use PH_Stat to construct a 99% confidence interval for the average salary of an associate professor described in part f using the general stepwise regression results and interpret its meaning.

i. Use PH_Stat to construct a 99% prediction interval for the salary of an associate professor described in part f using the general stepwise regression results and interpret its meaning.

j. Perform a residual analysis to verify that the conditions for the regression model are met for the model developed in part f.