Lumber Cutters — Lumber cutters wish to use readily available measurements to estimate the number of board feet of lumber in a tree. Assume they measure the diameter of the tree in inches at waist height. Develop a model that predicts board feet as a function of diameter in inches. Use the following data for your test:

The variable x is the diameter of a ponderosa pine in inches, and y is the number of board feet divided by 10.

a. Consider two separate assumptions, allowing each to lead to a model. Completely analyze each model.

i. Assume that all trees are right-circular cylinders and are approximately the same height.

ii. Assume that all trees are right-circular cylinders and that the height of the tree is proportional to the diameter.

b. Which model appears to be better? Why? Justify your conclusions.

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