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? Here's a scatter plot:

And here's the simple regression:

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 we've 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:

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.)

Transcribed Image Text:

40 退30t 叶 120 160 240 200 Weight (lb) 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 270 5.32 <0.0001 Weight 0.18937 0.0153 124 <0.0001 Dependent variable is: Pct BF R-squared 72.5% R-squared (adjusted) 72.2% = 4.376 with 250-4-246 degrees of freedom Source Regression 12418.7 Residual Sum of Squares df Mean Square F-ratio 216 3 4139.57 246 4710.11 19.1468 ariable Coefficient SE(Coeff) t-ratio P-value Intercept 31.4830 11.54 .7 0.0068 Waist Height Weight 2.31848 0.1820 12.7 <0.0001 0.224932 0.1583 1.42 0.1567 -0.100572 0.0310 3.25 0.0013