Access the data about mean tuitions at colleges, which are available at MyMathLab and at the Pearson Downloadable Student Resources for Math & Stats website. Do not access the other data about individual tuitions. Let y be the mean tuition at private, nonprofit, four-year colleges and w be the mean tuition at public, four-year colleges, both in dollars at x years since 1970.
a. Construct a scatterplot that describes the association between years and mean tuitions at private, nonprofit, four-year colleges. Also construct a scatterplot that describes the association between years and mean tuitions at public, four-year colleges.
b. Find a regression equation for each of the associations described in part (a).
c. Describe the four characteristics of each of the associations described in part (a). Compute and interpret an appropriate correlation coefficient as part of your analysis.
d. For each of the regression equations that you found in part (b), find and interpret the base.
e. Work with the entries in the appropriate column of the data table to find the mean one-year percentage change in mean tuition for private, nonprofit, four-year colleges for the period 1971–2015. Do the same for public, four-year colleges. Compare the two results with the two results you found in part (d).
f. Which type of college had a higher mean tuition in the academic year 2014–2015? Which type of college had the larger mean one-year percentage change in mean tuition for the period 1971–2015? Why do your two responses suggest that the two types of colleges will have equal mean tuitions at some point in the future? Do you have much faith that this will happen? Explain.