The paper Effects of Age and Gender on Physical Performance(Age [ 2007]: 77 85) describes a study

The paper €œEffects of Age and Gender on Physical Performance€(Age [ 2007]: 77€“ 85) describes a study investigating the relationship between age and swimming performance. Data on age and 1 hour 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 regression line using x = 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 average swim distance?
c. Would it be reasonable to use the least squares regression line from Part (a) to predict the average swim distance for women ages 40 to 49 by substituting the representative age of 45 into the equation of the least squares regression line? Explain why or why not.

Transcribed Image Text:

imidpltod Average swim Representative Age group) 25 35 45 Age Group 20-29 30-39 40-49 50-59 60-59 70-79 80-89 Distance (meters) 3.913.5 3.728.8 35794 3361.9 3,000.1 2.649.0 2,1184 65 75 85