The file UP-FBE contains satisfaction ratings, age, GPA, origin, and gender of 100 students at the business department in a university in Hungary. The overall satisfaction of the students is calculated as the sum of teaching quality, offered scholarships, affordable tuition fee, affordable housing, careers service, and graduate employment, so the minimum overall satisfaction level is 6 and the maximum is 42 .

Develop a regression model to predict the overall satisfaction, based on GPA and a dummy variable concerning origin (1 - international, 0 - national). For (a) through (1), do not include an interaction term.

Develop a regression model to predict the cost per person, based on a variable that represents the sum of the ratings for food, décor, and service and a dummy variable concerning location (center city versus metro area). For (a) through (m), do not include an interaction term.

a. State the multiple regression equation.

b. Interpret the regression coefficients.

c. Predict the mean overall satisfaction of an international student who has a 4.0 GPA and construct a \(95 \%\) confidence interval estimate and a \(95 \%\) prediction interval.

d. Perform a residual analysis on your model and determine whether the regression assumptions are valid.

e. Is there a significant relationship between overall satisfaction and the two independent variables (GPA and origin) at the 0.05 level of significance?

f. At the 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the most appropriate regression model for this set of data.

g. Construct a \(95 \%\) confidence interval estimate of the population slope between overall satisfaction and GPA.

h. Compare the slope in (b) with the slope for the simple linear regression model of Problem 13.5. Explain the difference in the results.

i. Compute and interpret the meaning of the coefficient of multiple determination.

j. Determine the adjusted \(r^{2}\).

k. Compare \(r^{2}\) with the \(r^{2}\) value computed in Problem 13.17 (b) on page 531.

l. Compute and interpret the coefficients of partial determination.

m. Add an interaction term to the model and, at the 0.05 level of significance, determine whether it makes a significant contribution to the model.

n. On the basis of the results (f) and (m), which model is most appropriate? Explain.

o. What conclusion can you reach about the effect of the GPA and origin of students on the overall satisfaction?

Problems 13.5

The file UP‐FBE contains satisfaction ratings, age, GPA, origin, and gender of 100 students at the business department in a university in Hungary. The overall satisfaction of the students is calculated as the sum of teaching quality, offered scholarships, affordable tuition fee, affordable housing, careers service, and graduate employment, so the minimum overall satisfaction level is 6 and the maximum is 42. You want to examine the relationship between students’ overall satisfaction with their GPA.

Problems 13.17 

You used the GPA to predict the overall satisfaction of university students (stored in UP‐FBE ).

b. Determine the standard error of the estimate.