Question

A biologist is studying the relationship between the mass of brains found in mammals taken from a forest and the body mass of the mammals. A sample of 14 such mammals was taken. The equation of the least-squares line for the relationship between brain mass and body mass is computed as body mass hat = 561.9 (brain mass) minus 16485.

1. A linear model is not appropriate, because the residuals are not centered about zero.
2. A linear model is appropriate, because there is a clear pattern shown in the residual plot.
3. A linear model is not appropriate, because there is a clear pattern shown in the residual plot.
4. A linear model is appropriate, because many of the residuals are close to zero for all brain weights.

Answer 1

The presence of a clear pattern in the residual plot suggests that the linear model does not adequately represent the relationship between the variables; thus, a linear model is not appropriate.

Step-by-step explanation:

When assessing the appropriateness of a linear model in statistics, we look at the plot of the residuals, which are the differences between the observed values and the values predicted by the linear model. If the residuals are centered about zero and randomly distributed without any discernible pattern, a linear model is usually considered appropriate. However, if there is a clear pattern in the residuals, it can indicate that the linear model is not suitable, perhaps because the relationship is not linear.

Therefore, the correct conclusion regarding the appropriateness of the linear model in the question is option 3: A linear model is not appropriate, because there is a clear pattern shown in the residual plot. A pattern indicates that the linear model does not capture all the nuances of the underlying relationship between the variables.