To determine the appropriateness of the linear model based on the provided residuals, we need to analyze what residuals represent. Residuals are the differences between the observed values and the values predicted by the model. A good linear model will generally have residuals that are relatively small and randomly distributed around zero.
Here are the residuals given: 0.26, 0.93, 0.5489, and 0.659.
- The fact that the residuals are all positive indicates that the predicted values are consistently below the observed values. However, the magnitude of these residuals matters as well.
- All of the residuals being less than 1 suggests that while the model may not perfectly fit the data, the discrepancies between the predicted and observed values are not excessively large.
However, having all positive residuals does not necessarily indicate a lack of accuracy or appropriateness. Instead, it just indicates that the model consistently under-predicts the observed values.
Considering these points, the best conclusion Jes can make based on the residuals is:
The linear model accurately represents the data since all residuals are less than 1.
This option reflects the understanding that while the residuals are positive, they are within a reasonable range.