The percentage of body fat has been associated with many other variables, including weight, height, and neck, hip, chest, abdominal, thigh circumferences. For this problem, we will be using the bodyfat data set from the mplot R package. We have also created two new variables: BMI is a function of weight in pounds and height squared inches. The variable HARatio is the ratio of hip circumference to abdominal circumference and is therefore unitless. The problem does not require any coding; rather, we are providing summary graphs and lm output in the file MidtermProblem2.pdf under the Midterm assignment in Canvas. Use the information in this handout to answer parts (a) - (e).

a) Interpret the relationships for each of the four scatterplots of percentage Bodyfat on Weight, Height, BMI, and HARatio. Point out anything that stands out to you in addition to the average relationships.

b) Using the lm output, write out the equation for the regression of Bodyfat on Weight.

c) Interpret the estimated slope parameter for the regression of Bodyfat on Weight in the context of the problem.

d) Interpret the coefficient of determination for the regression of Bodyfat on Weight in the context of the problem.

e) We have provided the output for simple linear regression of Bodyfat on the four predictor variables we are considering. Of the four models, which model do you think is the best choice? Use all the information (scatterplots, lm output, residual plot, and histogram of the residuals) to support your choice. There may be more than one satisfactory answer, so do not fixate on that. We are looking for written answers that are in the context of the problem and that you support with more than a single piece of information provided. Limit your answer to a maximum of 250 words. You may use bullet points if that helps you organize your answer.

pa MidtermProblem2.pdf * + - X O X(+ | C:/Users/Owner/Downloads/MidtermProblem2.pdf ... 351 Microsoft Edge BEATHis PDF X148Ji/WHITES? X 15 Q V # Scatterplots 35 35 10 15 20 25 30 Body Fat (%) Body Fat (%) 5 10 15 20 25 30 10 60 70 80 90 100 110 120 66 68 70 72 74 Weight (kg) Height (in.) 5 10 15 20 25 30 35 15 20 25 Body Fat (%) Body Fat (%) 10 LO 20 25 30 25 0.95 1.05 1.15 1.25 BMI (Ib./in.^2) Hip:Ab Ratio 19:07 2022/2/10par MidtermProblem2.pdf * + - X C O X(+ | C:/Users/Owner/Downloads/MidtermProblem2.pdf ... PDE 35/ Microsoft Edge 12EATHis PDF X148Ji/WATER? X 2 15 Q - + V # Regression of Bodyfat on Weight Call : Im (formula = Bodyfat ~ Weight, data = bodyfat) Coefficients : Estimate Std. Error t value Pr (>/t/) (Intercept) -15. 84630 3. 57562 -4. 432 2. 01e-05 Weight 0. 43157 0 . 04358 9. 902 |t/) (Intercept) -16. 0197 20 . 4925 -0.782 0. 4358 Height 0 . 5006 0. 2912 1. 719 0. 0881 Residual standard error: 7.703 on 126 degrees of freedom Multiple R-squared: 0. 02291, Adjusted R-squared: 0. 01516 F-statistic: 2.955 on 1 and 126 DF, p-value: 0. 08807 Body Fat on Height 0o o LO Residuals Frequency 0 -5 O -10 00 0 -15 66 68 70 72 74 -15 -10 -5 0 5 10 15 20 Height (in.) Residuals 19:07 2022/2/10pa MidtermProblem2.pdf * + - X C O X1+ | C:/Users/Owner/Downloads/MidtermProblem2.pdf ... 35/ Microsoft Edge 12EATHis PDF X148Ji/WHITES? X 15 Q V # Regression of Bodyfat on BMI Call : Im (formula = Bodyfat ~ BMI, data = bodyfat) Coefficients : Estimate Std. Error t value Pr (>|t/) (Intercept) -25.9822 3. 9561 -6.568 1.21e-09 BMI 1. 7792 0 . 1547 : 7 11.503 |t|) (Intercept) 117.221 7. 068 16.58