# For a study of University of Georgia female athletes, the prediction equation relating y = total

**QUESTION:**

For a study of University of Georgia female athletes, the prediction equation relating y = total body weight (in pounds) to x_{1} = height (in inches) and x_{2} = percent body fat is ŷ = -121 + 3.50 x_{1} + 1.35x_{2}.

(a) Find the predicted total body weight for a female athlete at the mean values of 66 and 18 for x_{1} and x_{2}.

(b) An athlete with x_{1} = 66 and x_{2} = 18 has actual weight y = 115 pounds. Find the residual, and interpret it.

**ANSWER:**

(a) ŷ= -121 + 3.50 x_{1} + 1.35 x_{2 }= -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.

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