1a forester wishes to predict the volume in cubic

Question

1. A forester wishes to predict the volume (in cubic feet) of usable lumber in a certain species of tree 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 ANOVA table is obtained.

The value of MSE is

A. 15.069.
B. 421.921.
C. 3842.08.

2. A forester wishes to predict the volume (in cubic feet) of usable lumber in a certain species of tree 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 ANOVA table is obtained.

 

We wish to test the hypotheses

H₀: 1 = 2 = 0, H_a: at least one of the j is not 0.

using the ANOVA F test. The value of the F statistic is

A. 0.071.
B. 18.21.
C. 254.97.