Assignment #12

Regression Analysis for Tree Data

by

Vicki Tarleton

The data in the table below represents data from the lumber industry. The information listed approximates the number of board feet of lumber per tree in a forest for a given age.

 Age of Tree 100s of Board Feet 20 1 40 6 60 80 33 100 56 120 88 140 160 182 180 200 320

In order to evaluate and interpret the data, a scatterplot is formed for the above data.

The graph appears to be quadratic in form. Based on this information, a regression equation can be made to approximate the path of the curve.

Using excel to help predict values, a possible regression equation would be

.

Using this equation, the estimated values based on the age of the tree are as follows:

 Age of Tree 100s of Board Feet Predicted Values 20 1 0.01 40 6 3.58 60 15.15 80 33 34.72 100 56 62.28 120 88 97.85 140 141.42 160 182 192.99 180 252.56 200 320 320.12

The scatterplot below depicts how the values, using prediction equation, follow the path of the original curve.

Predictions based on the Regression Equation

 If the age of the tree is . . . Prediction for100s of board feet 5 2.59 110 79.07 230 436.48 400 1435.80

The correlation coefficient for the tree data is .94135. Because this coefficient is so close to +1, there is a strong positive relationship between the age of the tree and the number of board feet that can be obtained from the tree. This was evident by the graphic display of the data.