Question

A research paper 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 3738.8 40–49 45 3579.4 50–59 55 3361.9 60–69 65 3000.1 70–79 75 2659.0 80–89 85 2118.4 (a) Find the equation of the least-squares line with x = representative age and y = average swim distance. (Round your numerical values to three decimal places.) ŷ = + x (b) Compute the seven residuals. (Round your answers to three decimal places.) Representative Age (x) Residual (meters) 25 35 45 55 65 75 85

Answer 1

a)

from above least square regression line : Yhat=4791.696+(-29.015)x

b)

for residual =actual-predicted value

residual are:

et=(y-ŷ)
-152.821
-37.371
93.379
166.029
94.379
43.429
-207.021