Table 52 compares the SAT scores and acceptance rates of applicants to 10 of the most selective U.S. colleges and universities. The data do not include students who participated in the early-decision application process.

For students who score x points, let y be the percentage of applicants who are accepted.
a. Construct a scatterplot.
b. Describe the four characteristics of the association. Compute and interpret r as part of your analysis.
c. Construct a residual plot for the regression line that models the association. Does it support any of the conclusions you made in part (b)? If so, which one(s)?
d. Estimate the SAT score and the residual represented by the lowest dot in the residual plot. What does this tell you about the corresponding data point in the scatterplot and the regression line?
e. Because r is so close to 1, a student concludes that there is a strong, linear association. What would you tell the student?

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Table 52 SAT Scores and Acceptance Rates Score Used to Represent SAT Score Group (points) SAT Score Group (points) 1100-1190 1200-1290 1300-1390 1400-1490 1500-1600 Percent 1145 1245 1345 1445 1550 10 17 31 48 72