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:

1. 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.
2. 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).
3. c)Write down the estimated regression equation.
4. d)Interpret the R2 in context.
5. e)How does your new slope estimate for Waist compare to the one you found in part a)? Explain why they may differ.
6. 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).
7. g)Which of the two predictions in part f) (i.e. which of the two models) would you trust more? Explain your choice.

|Waist (in.) 32 36 38 33 39 40 41 35 38 38 Weight (III) 175 181 200 159 196 192 205 173 187 188 Body Fat (96) 6 21 15 6 22 31 32 21 25 30 Waist (in.) 33 40 36 32 44 33 41 34 34 44 Weight (lb) 188 240 175 168 246 160 215 159 146 219 Body Fat (96) 10 20 22 38 10 27 12 10 28