The data set cherry.dat, from Hand et al. (1994), contains measurements of diameter (inches), height (feet), and timber volume (cubic feet) for a sample of 31 black cherry trees. Diameter and height of trees are easily measured, but volume is more difficult to measure.

a. Plot volume vs. diameter for the 31 trees.

b. Suppose that these trees are an SRS from a forest of N = 2967 trees and that the sum of the diameters for all trees in the forest is tx = 41,835 inches. Use ratio estimation to estimate the total volume for all trees in the forest. Give a 95% CI.

c. Use regression estimation to estimate the total volume for all trees in the forest.

Give a 95% CI.