Question: A forest management agency collects measurements from beech trees in a public park. The age of many…

A forest management agency collects measurements from beech trees in a public park. The age of many of the trees is known, and the basal area—the area of land occupied by the trunks of the trees—is also measured. A least-squares equation that compares the basal area to the age of each tree is given by area = 0.439(age) + 6.226.

Residuals vs. Age (Years)

Based on the residual plot shown, is a linear model appropriate for comparing tree age to basal area?

• Because the residuals are centered about zero, a linear model is appropriate.
• Because the residual plot does not show a clear pattern, a linear model is appropriate.
• Because the residual plot shows a random scatter of points, a linear model is not appropriate.
• Because the residual plot does not appear linear, it is likely that tree age and basal area do not have a linear relationship.

Solution

The image shows a homework problem about assessing the appropriateness of a linear model based on a residual plot. The problem asks whether a linear model is appropriate for comparing tree age to basal area, with options to choose from based on the given residual plot. Looking at the plot, the residuals seem to be randomly scattered around zero without a discernible pattern. This indicates that a linear model is appropriate. Therefore, the correct option is: - Because the residuals are centered around zero, a linear model is appropriate.