The numbers of men€™s colleges, not including seminaries, are shown in Table 53 for various years.

Let f (x) be the number of men€™s colleges at x years since 1960.
a. Construct a scatterplot.
b. Find a regression equation.
c. Describe the four characteristics of the association. Compute and interpret an appropriate correlation coefficient as part of your analysis.
d. Find f(45). What does it mean in this situation? Have you performed interpolation or extrapolation?
e. Find f(65). What does it mean in this situation? Have you performed interpolation or extrapolation? How much faith do you have in your result? Explain.

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Table 53 Numbers of Men's Colleges Year 1967 1975 1985 1995 2012 Number of Men's Colleges 145 80 27