Historical tuition and fees. You can find data on past tuition and fees at several colleges by doing a Google search on "historical tuition and fees." Select one of the colleges you find and determine whether the data show the same pattern as you observed in Exercise 28.24 (page 28-51). You should try to find data going back at least 20 years (at the time we searched, we were able to find data for Clemson University, Montana State University, Western Washington University, Oregon State University, and University of Tennessee). The data may not be in spreadsheet format, and you may have to enter or cut and paste it into a spreadsheet to carry out your analysis.
Exercise 28.24:
24 Tuition and fees at a small liberal arts college. Information regarding tuition and fees at the University of Virginia from 1970 to 2011 is provided in Table 28.7.9 Use statistical software to answer the following questions. TUITION
(a) Find the simple linear regression equation for predicting tuition and fees from year, and save the residuals and fitted values.
(b) The value of tuition and fees in 1971 is missing from the data set. Use the least-squares line to estimate this value.
(c) Does the estimate obtained in part (b) intuitively make sense to you? That is, are you happy with this estimate? Explain.
(d) Plot the residuals against year. What does the plot tell you about the adequacy of the linear fit?
(e) Will this linear model overestimate or underestimate the tuition and fees at this college in the 1990s?
(f) Since the residual plot shows a quadratic trend, it might be helpful to add a quadratic term to this model. Fit the quadratic regression model and provide the estimated model.
(g) Does the quadratic model provide a better fit than the linear model?
(h) Would you be willing to make inferences based on the quadratic model? Explain.