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

Question

, 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 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.
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.

Answer 1

To evaluate how well the linear model represents the data based on the residuals, we must consider the size and sign of the residuals.

1. A residual is the difference between the actual value and the predicted value, indicating how far off the prediction is.
2. A residual close to zero indicates that the model's prediction is close to the actual value.
3. Large residuals (in absolute terms) indicate a poor fit of the model.

The residuals provided are: 2.6, 9.3, -5.489, and -6.59.

• The residual of 2.6 indicates that the actual value is 2.6 units above the predicted value.
• The residual of 9.3 is quite large and indicates that this point is far above the predicted value, suggesting a significant error in the model's prediction for that data point.
• The negative residuals (-5.489 and -6.59) indicate that the actual values are below the predicted values, but their magnitudes are less important than the fact that a residual of 9.3 is relatively large.

Considering the size of the residuals, particularly the large positive residual (9.3), it supports the conclusion that the linear model does not accurately represent the data because at least one residual is significantly far from zero.

Therefore, the most appropriate 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.