Body fat, revisited The data set on body fat contains 15 body measurements on 250 men

Chapter 28, Problem 21

(choose chapter or problem)

Body fat, revisited The data set on body fat contains 15 body measurements on 250 men from 22 to 81 years old. Is average %Body Fat related to Weight? Heres a scatterplot: And heres the simple regression: Dependent variable is Pct BF R-squared = 38.1, R-squared (adjusted) = 37.9, s = 6.538 with 250 - 2 = 248 degrees of freedom Variable Coefficient SE(Coeff) t-Ratio P-Value Intercept -14.6931 2.760 -5.32 60.0001 Weight 0.18937 0.0153 12.4 60.0001 a) Is the coefficient of %Body Fat on Weight statistically distinguishable from 0? (Perform a hypothesis test.) b) What does the slope coefficient mean in this regression? We saw before that the slopes of both Waist size and Height are statistically significant when entered into a multiple regression equation. What happens if we add Weight to that regression? Recall that weve already checked the assumptions and conditions for regression on Waist size and Height in the chapter. Here is the output from a regression on all three variables: Dependent variable is Pct BF R-squared = 72.5, R-squared (adjusted) = 72.2, s = 4.376 with 250 - 4 = 246 degrees of freedom Source Sum of Squares df Mean Square F-Ratio Regression 12418.7 3 4139.57 216 Residual 4710.11 246 19.1468 Variable Coefficient SE(Coeff) t-Ratio P-Value Intercept -31.4830 11.54 -2.73 0.0068 Waist 2.31848 0.1820 12.7 60.0001 Height -0.224932 0.1583 -1.42 0.1567 Weight -0.100572 0.0310 -3.25 0.0013 c) Interpret the slope for Weight. How can the coefficient for Weight in this model be negative when its coefficient was positive in the simple regression model? d) What does the P-value for Height mean in this regression? (Perform the hypothesis test.)