a forester wishes to predict the volume in cubic

Question

A forester wishes to predict the volume (in cubic feet) of usable lumber in a certain species of trees from the height (in feet) and diameter (in inches) of the trees. The height and diameter of 31 trees of a certain species were measured, the trees were cut down, and the volume of usable lumber was determined. The multiple linear regression model

Volume = β₀ + β₁(Diameter) + β₂(Height) + β_i

is assumed to hold, where the deviations i are independent and Normally distributed with mean 0 and standard deviation . This model is fit to the data using the method of least squares using statistical software, and the following parameter estimates and their standard errors are obtained.

Based on these results, a 99% confidence interval for β₀ is found to be -57.99 ± 23.87. We may conclude

A. if we tested the hypotheses H 0: β₀ = 0, H_a: β₀ ≠ 0, the P-value would be less than 0.01.
B. the estimate of β₀ would tell us the volume of a tree of this species when height and diameter are 0.
C. Both choices are correct.