The paper “Effects of Age and Gender on Physical Performance” (Age [2007]: 77–85) describes a study of the relationship between age and 1-hour swimming performance. Data on age and swim distance for over 10,000 men participating in a national long-distance 1-hour swimming competition are summarized in the accompanying table.
a. Find the equation of the least-squares line with x 5 representative age and y = average swim distance.
b. Compute the seven residuals and use them to construct a residual plot. What does the residual plot suggest about the appropriateness of using a line to describe the relationship between representative age and swim distance?
c. Would it be reasonable to use the least-squares line from Part (a) to predict the average swim distance for women age 40 to 49 by substituting the representative age of 45 into the equation of the least-squares line? Explain.

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