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 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.
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 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 half of the residuals are positive and half of the residuals are negative.
, 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 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.
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 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 half of the residuals are positive and half of the residuals are negative.
Answers
GPT-4o mini
To evaluate the accuracy of the linear model based on the residuals Jade found, we need to consider the significance of those residuals. Residuals are the differences between the observed values and the predicted values from the linear model.
Here are the residuals Jade found:
- 2.6 (positive)
- 9.3 (positive)
- −5.489 (negative)
- −6.59 (negative)
Here's how to analyze those residuals:
1. **Magnitude of Residuals**: The residuals of 2.6 and 9.3 indicate that for one of the points, the predicted value is 9.3 units lower than the actual value, which suggests a significant discrepancy between the predicted and actual values. Larger residuals suggest that the model does not fit the data well.
2. **Direction of Residuals**: The positive residuals indicate that for those points, the model underestimates the values, while the negative residuals mean the model overestimates them.
3. **Balance of Residuals**: Although having both positive and negative residuals might indicate that the model captures some aspects of the trend, the presence of significant values (like 9.3) suggests that it may not accurately represent the data overall.
Given this analysis, the best conclusion for Jade to make from the available options 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 reflects the model's inability to accurately predict the observed values, especially given the substantial residual value.
Here are the residuals Jade found:
- 2.6 (positive)
- 9.3 (positive)
- −5.489 (negative)
- −6.59 (negative)
Here's how to analyze those residuals:
1. **Magnitude of Residuals**: The residuals of 2.6 and 9.3 indicate that for one of the points, the predicted value is 9.3 units lower than the actual value, which suggests a significant discrepancy between the predicted and actual values. Larger residuals suggest that the model does not fit the data well.
2. **Direction of Residuals**: The positive residuals indicate that for those points, the model underestimates the values, while the negative residuals mean the model overestimates them.
3. **Balance of Residuals**: Although having both positive and negative residuals might indicate that the model captures some aspects of the trend, the presence of significant values (like 9.3) suggests that it may not accurately represent the data overall.
Given this analysis, the best conclusion for Jade to make from the available options 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 reflects the model's inability to accurately predict the observed values, especially given the substantial residual value.