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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 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 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 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.

1 answer

To evaluate whether the linear model accurately represents the data based on the given residuals, we can consider both the positive and negative values of the residuals as well as their magnitudes.

The residual values given are:

  • 2.6 (a small positive residual)
  • 9.3 (a larger positive residual)
  • -5.489 (a small negative residual)
  • -6.59 (a larger negative residual)
  1. Positive residuals indicate that the actual value is greater than the predicted value.
  2. Negative residuals indicate that the actual value is less than the predicted value.

Since there are both positive and negative residuals, this suggests that the model may fit the data better in some areas than others. However, the presence of large residuals (like 9.3) implies that there are points significantly far from the predicted values, indicating potential issues with the model's accuracy.

Conclusion

Given these points, the best choice from the responses 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 conclusion addresses the larger residual, which suggests a significant deviation from the model's predictions.