Chest size might be a good predictor of body fat. Here's a scatter plot of %Body Fat vs. Chest Size.

A regression of %Body Fat on Chest Size gives the following equation:

a) Is the slope of %Body Fat on Chest Size statistically distinguishable from 0? (Perform a hypothesis test.)
b) What does the answer in part a mean about the relationship between %Body Fat and Chest Size?
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 Chest Size to that regression? Here is the output from a regression on all three variables:

c) Interpret the coefficient for Chest Size.
d) Would you consider removing any of the variables from this regression model? Why or why not?

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40 T 30 G320 10 100.0 112.5 25.0 87.5 Chest (in) Dependent variable is: Pct B R-squared# 49.196 R-squared (adjusted):+48.9% S 5.930 with 250 2 248 degrees of freedom Variable Coefficient SE(Coeff) t-ratio P-value Intercept -52.7122 4.654 13 <0.0001 Chest Size 0.712720 0.046 1. <0.0001 Dependent variable is: Pct BF R-squared 72.2% R-squared (adjusted)-:71.9% 4399 with 250-4 246 degrees of freedom Source Sum of Squares df Mean Square F-ratio P Regression 12368.9 3 4122.98 213 <0.0001 Residual 4759.87 246 19.3491 Variable Coefficient SE(Coeff) t-ratio P-value Intercept 2.07220 7.802 0.266 0.7908 Waist Height 0.561058 0.1094 <0.0001 Chest Size 0.233531 0.0832 281 0.0054 2.19939 0.1675 13.1 <0.0001