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:
x 17 19 20 23 25 28 32 38 39 41
y 19 25 32 57 71 113 123 252 259 294
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 seperate 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.