Question

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Thank you!

Suppose that a researcher studying the weight of female college athletes wants to predict the weights based on height, measured in inches, and the percentage of body fat of an athlete. The researcher calculates the regression equation as (weight) 4.358 (height) 0.713 (percent body fat)-85.095. If a female athlete is 65 inches tall, has a 16 percentage of body fat, and a weight of 210.005. What is the residual? 1) -84.673 2) 0.422 3) We do not know the observations in the data set, so we cannot answer that question. 4) 144.583 5) -0.422 Suppose that a researcher studying the weight of female college athletes wants to predict the weights based on height, measured in inches, the percentage of body fat of an athlete, and age. The researcher calculates the regression equation as (weight) 3.267*(height)0.855* (percent body fat) 1.194"(age)-83.404. If a female athlete is 67 inches tall, has a 17 percentage of body fat, is 22 years old, and has a weight of 227.64, the residual is 103.888 Choose the correct interpretation of the residual. 1 The weight of the athlete is 227.64 pounds larger than what we would expect. 2) The height of the athlete is 103.888 inches larger than what we would expect. 3) The weight of the athlete is 103.888 pounds larger than what we would expect. 4) The weight of the athlete is 103.888 pounds less than what we would expect 5) The height of the athlete is 103.888 inches less than what we would expect.

Answer 1

#1.
Regression equation,
weight = 4.358*(height) + 0.713*(percent body fat) - 85.095

For height = 65 and percent body fat = 16
predicted value of weight = 4.358*65 + 0.713*16 - 85.095
= 209.583

observed weight = 210.005

Residual = observed value - predicted value
= 210.005 - 209.583
= 0.422

Option (2)

#2.
observed weight = 227.64 and residual = 103.888

residual = observed - predicted

The weight of the athlete is 103.888 pounds larger than what we would expect

Option (3)