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.

Age Group Representative Age

(Midpoint of Age Group)

Average Swim Distance

(meters)

20–29 25 3913.5 30–39 35 3728.8 40–49 45 3579.4 Representative Age (Midpoint of Age Group)
Average Swim Distance (meters)
50–59 55 3361.9 60–69 65 3000.1 70–79 75 2649.0 80–89 85 2118.4

a. Find the equation of the least-squares line with x 5 representative age and y 5 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.