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 , and −6.59 . What conclusion can Jade make about the linear model based on the residuals?(1 point) Responses The linear model seems to accurately represent the data since half of the residuals are positive and half of the residuals are negative. The linear model seems to accurately represent the data since half of the residuals are positive and half of the residuals are negative. The linear model does not accurately represent the data since half of the residuals are positive and half of the residuals are negative. The linear model does not accurately represent the data since half of the residuals are positive and half of the residuals are negative. 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 the residual 9.3 means that the actual point is far from the estimate.
Answers
GPT-4o mini
To evaluate the accuracy of the linear model based on the provided residuals (2.6, 9.3, -5.489, and -6.59), we need to consider the following points:
1. **Positive and Negative Residuals**: The presence of both positive and negative residuals shows that the model is making errors in both directions (overestimating and underestimating). However, simply having both types does not necessarily indicate that the model is accurate or inaccurate.
2. **Magnitude of Residuals**: The magnitude of the residuals indicates how far the predicted values are from the actual values. A large residual (such as 9.3) suggests a substantial difference between the predicted value and the actual data point. This can indicate that the linear model is not accurately capturing the trend for that specific point.
Considering these points, the most relevant conclusion based on the residuals provided 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 the issue with the large residual value, which signifies a significant prediction error by the model.
1. **Positive and Negative Residuals**: The presence of both positive and negative residuals shows that the model is making errors in both directions (overestimating and underestimating). However, simply having both types does not necessarily indicate that the model is accurate or inaccurate.
2. **Magnitude of Residuals**: The magnitude of the residuals indicates how far the predicted values are from the actual values. A large residual (such as 9.3) suggests a substantial difference between the predicted value and the actual data point. This can indicate that the linear model is not accurately capturing the trend for that specific point.
Considering these points, the most relevant conclusion based on the residuals provided 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 the issue with the large residual value, which signifies a significant prediction error by the model.