Diabetes and obesity are serious health concerns in the

Chapter 11, Problem 1E

(choose chapter or problem)

Diabetes and obesity are serious health concerns in the United States and much of the developed world. Measuring the amount of body fat a person carries is one way to monitor weight control progress, but measuring it accurately involves either expensive X-ray equipment or a pool in which to dunk the subject. Instead body mass index (BMI) is often used as a proxy for body fat because it is easy to measure: BMI = mass \((k g)(\text { height }(m))^{2}=703 \text { mass }(l b)(\text { height }(i n))^{2}\). In a study of 250 men at Bingham Young University, both BMI and body fat were measured. Researchers found the following summary statistics:

                                            \(\sum_{t=i}^{=} x_{i}=6322.28 \sum_{i=1}^{5} x_{i}^{2}=162674.18\)

                                                       \(\sum_{i=i}^{\infty} y_{i}=4757.90 \sum_{i=1}^{3} y_{i}^{2}=107679.27\)

                                            \(\sum_{i=1}^{3} y_{i}^{2}=125471.10\)

(a) Calculate the least squares estimates of the slope and intercept. Graph the regression line.

(b) Use the equation of the fitted line to predict what body fat would be observed, on average, for a man with a BMI of 30 .

(c) Suppose that the observed body fat of a man with a BMI of 25 is 25%. Find the residual for that observation.

(d) Was the prediction for the BMI of 25 in part (c) an overestimate or underestimate? Explain briefly.

Equation Transcription:

Text Transcription:

(kg)(height(m))^2=703 mass(lb) (height(in))^2

Sum over t=i ^infty x_i=6322.28 sum over i=1 ^5 x_i ^2=162674.18

Sum overt=iyi=4757.90 sum over i=1 ^3 y_i^2=107679.27

Sum over i=1 ^3 y_i^2=125471.10