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. In Exercise 5.34 from Section 5.3, a plot of the residuals from the least-squares line showed a curved pattern that suggested that a quadratic curve would do a better job of summarizing the relationship between x representative age and y average swim distance. Find the equation of the least-squares quadratic curve and use it to predict average swim distance at 40 years of age. y^ 5 3843.027 1 10.619x 2 0.360x2 y^ 5 3691.293 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 50–59 55 3361.9 60–69 65 3000.1 70–79 75 2649.0 80–89 85 2118.4