How old is that tree?
One can determine how old a tree is by counting its rings, but that requires cutting the tree down. Can we estimate the tree s age simply from its diameter? A forester measured 27 trees of the same species that had been cut down, and counted the rings to determine the ages of the trees.
| Diameter (in.) |
Age (yr) |
Diameter (in.) |
Age (yr) |
| 1.8 |
4 |
10.3 |
23 |
| 1.8 |
5 |
14.3 |
25 |
| 2.2 |
8 |
13.2 |
28 |
| 4.4 |
8 |
9.9 |
29 |
| 6.6 |
8 |
13.2 |
30 |
| 4.4 |
10 |
15.4 |
30 |
| 7.7 |
10 |
17.6 |
33 |
| 10.8 |
12 |
14.3 |
34 |
| 7.7 |
13 |
15.4 |
35 |
| 5.5 |
14 |
11 |
38 |
| 9.9 |
16 |
15.4 |
38 |
| 10.1 |
18 |
16.5 |
40 |
| 12.1 |
20 |
16.5 |
42 |
| 12.8 |
22 |
|
|
a) Find the correlation between Diameter and Age. Does this suggest that a linear model may be appropriate? Explain.
b) Create a scatterplot and describe the association.
c) Create the linear model.
d) Check the residuals. Explain why a linear model is probably not appropriate.
e) If you used this model, would it generally overestimate or underestimate the ages of very large trees? Explain.