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.  

   
 

(x), %