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 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.
, 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 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.
Answers
GPT-4o mini
The most appropriate 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 response highlights that a large residual (in this case, 9.3) indicates that the actual value is significantly different from the predicted value, suggesting that the linear model may not be the best fit for the data. While having both positive and negative residuals might indicate variability, the presence of a particularly large residual suggests a lack of fit in the model.
**"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 response highlights that a large residual (in this case, 9.3) indicates that the actual value is significantly different from the predicted value, suggesting that the linear model may not be the best fit for the data. While having both positive and negative residuals might indicate variability, the presence of a particularly large residual suggests a lack of fit in the model.