Because it is difficult to measure body fat, researchers have considered different ways to predict body fat based on other characteristics. One model proposed in the paper “A Comparison Between Multiple Regression Models an CUNBAE Equation to Predict Body Fat in Adults” (PLOS ONE [2015]: 1–15) included three predictor variables. The variables in the model were

y = Percentage of body fat mass

x₁ = log of body mass index (log(kg/m²))

x₂ = log of age (log(years))

x₃ = Sex (0 = male, 1 = female)

The estimated regression equation based on a sample of n = 3200 was

y = 296.07 + 76.91x₁ + 6.65x² + 11.40x³

Suppose that SSRegr = 540,000 and SSResid = 180,000 (these values were not given in the paper but are consistent with other given information).

a. Interpret the values of b₂ and b₃.

b. What proportion of observed variability in percentage of body fat mass can be explained by the model relationship?

c. Estimate the value of σ.

d. Calculate the value of adjusted R². How does it compare to the value of R2 calculated in Part (b)?