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7. Consider the data set given in Chapter 25, Exercise 53: Body fat, again. From the related exercise in Homework 3, recall that we found
7. Consider the data set given in Chapter 25, Exercise 53: Body fat, again. From the related exercise in Homework 3, recall that we found an R2 = 0.485 if we regress BodyFat on Weight. On the other hand, we found an R2 = 0.787 if we regress BodyFat on Waist, which indicated that Waist is a better predictor. Answer the following questions:
- a)Redo the simple regression of BodyFat on Waist, and calculate a 95% confidence interval for the slope coefficient. Show your work, and inter- pret the CI in context.
- b)Now run a multiple regression, by including both Waist as well as Weight as explanatory variables. Show your regression output (i.e. estimated coefficients, standard errors, t-statistics, p-values, and R2).
- c)Write down the estimated regression equation.
- d)Interpret the R2 in context.
- e)How does your new slope estimate for Waist compare to the one you found in part a)? Explain why they may differ.
- f)Consider an individual with a waist size of 40 inches and a weight of 250 lb. Predict this persons body fat percentage based on the simple regression from part a), and based on the multiple regression in part b).
- g)Which of the two predictions in part f) (i.e. which of the two models) would you trust more? Explain your choice.
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