For a study of University of Georgia female athletes, the prediction equation relating y = total body weight (in pounds) to x1 = height (in inches) and x2 = percent body fat is ŷ = -121 + 3.50 x1 + 1.35x2.
(a) Find the predicted total body weight for a female athlete at the mean values of 66 and 18 for x1 and x2.
(b) An athlete with x1 = 66 and x2 = 18 has actual weight y = 115 pounds. Find the residual, and interpret it.
(a) ŷ= -121 + 3.50 x1 + 1.35 x2 = -121 + 3.50 (66) + 1.35 (18) = 134.3
(b) The residual = y – ŷ = 115 – 134.3 = -19.3. The actual total body weight is 19.3 pounds lower than predicted.