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 a 5 3.3 b 5 .0046 aabbg a 5 3.3 b 5 .0046 Q 5 aeba egb P

Q 5 aabbgP 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 .

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 .

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.

d. The mean and standard deviation of x3 were 52.540 and 5.4447, respectively, whereas those of x5 were 89.195 and 3.6660, respectively. When the model involving these two standardized variables was fit, the estimated regression equation was . What value of specific gravity would you predict for a wood sample with % and % light absorption in ?

e. The estimated standard deviation of the estimated coefficient of (i.e., for of the standardized model) was

.0046. Obtain a 95% CI for b3.

f. Using the information in parts

(d) and (e), what is the estimated coefficient of x3 in the unstandardized model

(using only predictors x3 and x5), and what is the estimated standard deviation of the coefficient estimator

(i.e., for in the unstandardized model)?

g. The estimate of s for the two-predictor model is , whereas the estimated standard deviation of when and (i.e., when and ) is .00482. Compute a 95%

PI for specific gravity when % and %

light absorption in summerwood 5 88.9.

springwood 5