To evaluate the appropriateness of the linear model based on the provided residuals, we can analyze the nature and size of the residuals.
Residuals represent the difference between the observed values and the predicted values from the linear model. Generally, a good linear model should have residuals that are randomly distributed around zero, without any systematic patterns.
Let's review the provided responses:
- The linear model does not accurately represent the data since all data points are less than 1.
- The linear model accurately represents the data since all residuals are less than 1.
- The linear model does not accurately represent the data since all residuals are positive.
- The linear model accurately represents the data since all residuals are positive.
Out of these options, the appropriate conclusion to draw from the provided residuals depends on their values:
- While the fact that the residuals are all less than 1 might suggest that the model has a relatively small error, it does not guarantee that the model is good.
- The fact that all residuals are positive suggests that the linear model consistently underestimates the actual values, which could indicate a systematic deviation.
Considering these points, the most accurate conclusion Jes can make is:
The linear model does not accurately represent the data since all residuals are positive.
This indicates that the model consistently underpredicts the actual values, which is a sign that it may not fit the data well. Thus, the best response is option 3.