To assess the appropriateness of the linear model based on the residuals provided (0.26, 0.93, 0.5489, and 0.659), we need to consider what the residuals represent. Residuals are the differences between the observed values and the values predicted by the model.
In this case:
- The residuals are all positive, which indicates that the observed values are higher than the predicted values for those data points.
- The fact that the residuals are all less than 1 suggests that the errors are relatively small.
However, the positivity of the residuals alone does not necessarily indicate that the model is appropriate, nor does the fact that they are all less than 1. Instead, we typically assess the overall pattern of residuals (if they are randomly distributed around zero) to determine if a linear model is appropriate.
Given the choices provided, the best conclusion based on the residuals would be:
The linear model accurately represents the data since all residuals are less than 1.
This suggests that while the model is not perfect (since the residuals are positive), the remaining size of the residuals indicates that the model is providing reasonably close predictions.