The ability to estimate the volume of a tree based on a simple measurement, such as the diameter of the tree, is important to the lumber industry, ecologists, and conservationists. Data on volume, in cubic feet, and diameter at breast height, in inches, for 70 shortleaf pines was reported in C. Bruce and F. X. Schumacher’s Forest Mensuration (New York: McGraw-Hill, 1935) and analyzed by A. C. Akinson in the article “Transforming Both Sides of a Tree” (The American Statistician, Vol. 48, pp. 307–312). The data are provided on the Weiss Stats CD.
a. Obtain and interpret the standard error of the estimate.
b. Obtain a residual plot and a normal probability plot of the residuals.
c. Decide whether you can reasonably consider Assumptions 1–3 for regression inferences met by the two variables under consideration.