In forestry, the diameter of a tree at breast height is used to model the height of the tree. Silviculturists working in British Columbia’s boreal forest conducted a series of spacing trials to predict the heights of several species of trees. The data are the breast height diameters (in centimeters) and heights (in meters) for a sample of 18 white spruce trees. B1 B2 18.9 20.0 15.5 16.8 19.4 20.2 20.0 20.0 29.8 20.2 19.8 18.0 20.3 17.8 20.0 19.2 22.0 22.3 16.6 18.8 15.5 16.9 13.7 16.3 27.5 21.4 20.3 19.2 22.9 19.8 14.1 18.5 10.1 12.1 5.8 8.0
In forestry, the diameter of a tree at breast height is used to model the height of the tree. Silviculturists working in British Columbia’s boreal forest conducted a series of spacing trials to predict the heights of several species of trees. The data are the breast height diameters (in centimeters) and heights (in meters) for a sample of 18 white spruce trees.
| B1 | B2 |
| 18.9 | 20.0 |
| 15.5 | 16.8 |
| 19.4 | 20.2 |
| 20.0 | 20.0 |
| 29.8 | 20.2 |
| 19.8 | 18.0 |
| 20.3 | 17.8 |
| 20.0 | 19.2 |
| 22.0 | 22.3 |
| 16.6 | 18.8 |
| 15.5 | 16.9 |
| 13.7 | 16.3 |
| 27.5 | 21.4 |
| 20.3 | 19.2 |
| 22.9 | 19.8 |
| 14.1 | 18.5 |
| 10.1 | 12.1 |
| 5.8 | 8.0 |
B1: Breast Height Diameter of White spruce (cm)
B2: Height (m)
a) Plot the relationship using
b) Compare the scatter plot in (a) with the
c) How much is the extent of the independent variable is influencing the dependent variable?
d) How much is the variability in the dependent variable explained by the variability in the independent variable? Explain.
e) Is there any relationship between these two variables? Carry out a test on the significance of the slope.
f) Estimates the least-square regression equation to predict the model between the breast height diameters and the trees’ height.
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