Example on multiple linear regression model

Reference no: EM137972

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.

802_Example on Multiple linear regression model.gif

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.

Reference no: EM137972

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