In an experiment to study factors influencing wood specific gravity (“Anatomical Factors...

In an experiment to study factors influencing wood specific gravity (“Anatomical Factors Influencing Wood Specific Gravity of Slash Pines and the Implications for the Development of a High-Quality Pulpwood,” TAPPI, 1964: 401–404), a sample of 20 mature wood samples was obtained, and measurements were taken on the number of fibers/mm² in springwood (x₁), number of fibers/mm² in summerwood (x₂), % springwood (x₃), light absorption in springwood (x₄), and light absorption in summerwood (x₅).

a. Fitting the regression function resulted in . Does the data indicate that there is a linear relationship between specific gravity and at least one of the predictors? Test using α = .01.

b. When x₂ is dropped from the model, the value of R² remains at .769. Compute adjusted R² for both the full model and the model with x₂ deleted.

c. When x₁, x₂, and x₄ are all deleted, the resulting value of R² is .654. The total sum of squares is SSE = .0196610 . Does the data suggest that all of x₁, x₂, and x₄ have zero coefficients in the true regression model? Test the relevant hypotheses at level .05.