Question
Jade was working on her statistics homework. One of the questions gave her a trend line and asked her to find the residuals. She found the following residuals 2.6, 9.3,−5.489 − 5.489 , and −6.59 − 6.59 . What conclusion can Jade make about the linear model based on the residuals?(1 point) Responses The linear model does not accurately represent the data since the residual 9.3 means that the actual point is far from the estimate. The linear model does not accurately represent the data since the residual 9.3 means that the actual point is far from the estimate. The linear model seems to accurately represent the data since the residual 2.6 means that the actual point is not far from the estimate. The linear model seems to accurately represent the data since the residual 2.6 means that the actual point is not far from the estimate. The linear model does not accurately represent the data since half of the residuals are positive and half of the residuals are negative.
Answers
GPT-4o mini
To evaluate the performance of the linear model based on the residuals, Jade should consider both the size and the sign of the residuals.
1. **Residuals Overview**: The residuals given are 2.6, 9.3, -5.489, and -6.59.
- Positive residuals (2.6 and 9.3) indicate that the actual values are above the predicted values (the model underestimated these points).
- Negative residuals (-5.489 and -6.59) indicate that the actual values are below the predicted values (the model overestimated these points).
2. **Values of Residuals**:
- A larger positive residual (like 9.3) suggests a significant underestimation by the model, which indicates a poor fit for that particular data point.
- Both negative residuals are relatively large in absolute value (-5.489 and -6.59), implying that the model also overestimates other points considerably.
3. **Conclusion**: The presence of a large positive residual (9.3) and significant negative residuals suggests that the linear model does not fit the data well overall, as there is notable error for multiple data points.
### Therefore, the most accurate conclusion Jade can make 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.**
1. **Residuals Overview**: The residuals given are 2.6, 9.3, -5.489, and -6.59.
- Positive residuals (2.6 and 9.3) indicate that the actual values are above the predicted values (the model underestimated these points).
- Negative residuals (-5.489 and -6.59) indicate that the actual values are below the predicted values (the model overestimated these points).
2. **Values of Residuals**:
- A larger positive residual (like 9.3) suggests a significant underestimation by the model, which indicates a poor fit for that particular data point.
- Both negative residuals are relatively large in absolute value (-5.489 and -6.59), implying that the model also overestimates other points considerably.
3. **Conclusion**: The presence of a large positive residual (9.3) and significant negative residuals suggests that the linear model does not fit the data well overall, as there is notable error for multiple data points.
### Therefore, the most accurate conclusion Jade can make 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.**