Lumber Cutters – Lumber cutters wish to use readily available measurements to estimate the number of...

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:

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 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) For part a), use least squares to fit your proposed proportionality model. Compare your least-squares results with the model of the part a). Furthermore, find the bounds on the Chebyshev criterion and interpret the results.

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