To analyze the residuals, we need to consider what they represent. A residual is the difference between the actual value and the predicted value from the trend line. Positive residuals indicate that the predicted value is lower than the actual value, and negative residuals indicate that the predicted value is higher than the actual value.
Jade's residuals are: 2.6, 9.3, -5.489, and -6.59.
Here are a few points to consider:
- The residuals 2.6 and 9.3 are both positive, indicating that the actual values for those points are higher than the predicted values from the model.
- The residuals -5.489 and -6.59 are negative, indicating that the actual values for those points are lower than the predicted values.
- The presence of both positive and negative residuals suggests that the predictions from the linear model are sometimes underestimating and sometimes overestimating the actual values.
Based on this information, let's evaluate the provided response options:
- The first option implies that the small positive residual (2.6) shows the model is accurate, which only reflects on that specific point.
- The second option is valid because the large positive residual (9.3) indicates that this data point is relatively far from the predicted value.
- The third option could be misinterpreted; while having both positive and negative residuals suggests variability, it doesn't necessarily indicate that the model is inaccurate on its own.
- The fourth option, like the third, is misleading since presence of both types of residuals isn’t inherently indicative of model accuracy.
Among the choices, the most conclusive and accurate response is:
The linear model does not accurately represent the data since the residual 9.3 means that the actual point is far from the estimate.
This option specifically highlights a significant deviation in one of the residuals, which is a strong indicator that the linear model may not adequately fit the data overall.