Question: The principle objective of many data collection exercises in forestry is developing
models that predict the volume and general value of trees in a forested tract. Volume is
approximated using the formula:
, where r is half the Mean Diameter at
Breast Height (MDBH). Breast height is defined as 4.5 feet above ground. While walking a
stand of trees it is fairly easy to estimate the number of trees per acre and the height of the trees.
Information on the age of the stand can be obtained from planting records. It is time consuming
to collect data on the MDBH and so it is desirable to have a model for predicting the MDBH for
a stand of trees.
Data Collection: For 20 stands of pine trees the following characteristics are recorded.
 Mean Height of Pine trees (MHP) in feet.
 Number of Pine trees (NoP) per acre.
 Age of Pine trees (AGE) in years.
 Mean Diameter at Breast Height (MDBH) in inches. Breast height is defined as 4.5 feet
above ground.
Foresters often use variables derived from these basic measurements as their explanatory
variables. In particular:
 X1 = MHP
 X2 = AGE*NoP
 X3 = MHP/NoP
Data:
X1
51.5
41.3
36.7
32.2
39.0
29.8
51.2
46.8
61.8
55.8
37.3
54.2
32.5
56.3
52.8
47.0
53.0
50.3
50.5
57.7
X2
9500
12600
7150
6240
6760
7320
12600
10640
18600
11730
10400
13650
5830
12920
10540
13500
9920
11680
9520
10560
X3
0.10300
0.04589
0.05646
0.06708
0.07500
0.04885
0.07314
0.06158
0.06645
0.08087
0.04662
0.08336
0.06132
0.08279
0.08516
0.05222
0.08548
0.06890
0.07426
0.12021
MDBH
7.0
5.0
6.2
5.2
6.2
5.2
6.2
6.4
6.4
6.4
5.4
6.4
5.4
6.7
6.7
5.9
6.9
6.9
6.9
7.9