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) + βi
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.
![1678_multiple linear regression model.png](https://mywordsolution.com/CMSImages/1678_multiple%20linear%20regression%20model.png)
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) + βi
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.
![1678_multiple linear regression model.png](https://mywordsolution.com/CMSImages/1678_multiple%20linear%20regression%20model.png)
We wish to test the hypotheses
H0: 1 = 2 = 0, Ha: 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.