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 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 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.
−
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 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 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.
Answers
GPT-4o mini
To evaluate the linear model based on the given residuals, it's important to understand what residuals represent. Residuals indicate the difference between the observed values and the predicted values from the linear model.
In this case, Jade's residuals are:
- 2.6 (positive)
- 9.3 (positive)
- -5.489 (negative)
- -6.59 (negative)
From her findings, we can observe:
1. There are more positive residuals (2) than negative residuals (2), but this does not necessarily mean the linear model is accurate or inaccurate.
2. The residual of 9.3 indicates that there is a significant difference between the actual observed value and the predicted value; this could suggest that the model has areas where it does not predict well.
Given the options, the most accurate conclusion Jade can make based on the residuals 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 highlights the importance of the magnitude of residuals in assessing the accuracy of the model. Since one of the residuals (9.3) is quite large, it suggests that there may be an issue with the model's fit to the data.
In this case, Jade's residuals are:
- 2.6 (positive)
- 9.3 (positive)
- -5.489 (negative)
- -6.59 (negative)
From her findings, we can observe:
1. There are more positive residuals (2) than negative residuals (2), but this does not necessarily mean the linear model is accurate or inaccurate.
2. The residual of 9.3 indicates that there is a significant difference between the actual observed value and the predicted value; this could suggest that the model has areas where it does not predict well.
Given the options, the most accurate conclusion Jade can make based on the residuals 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 highlights the importance of the magnitude of residuals in assessing the accuracy of the model. Since one of the residuals (9.3) is quite large, it suggests that there may be an issue with the model's fit to the data.