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.

Answer 1

To determine the appropriateness of the linear model based on the residuals provided (2.6, 9.3, -5.489, and -6.59), we need to understand what residuals signify. A residual is the difference between the observed value and the predicted value by the model.

1. Positive residuals (like 2.6) indicate that the actual value is higher than what the model predicts.
2. Negative residuals (like -5.489 and -6.59) indicate that the actual values are lower than predicted.
3. A very large positive or negative residual (like 9.3) suggests a significant discrepancy between the predicted value and the actual value.

Given that one of the residuals (9.3) is quite large, it indicates that at least one of the actual points is far from the estimate produced by the linear model. This large residual suggests that the linear model may not accurately capture the relationship in the data for that particular data point.

Taking all this into account, the most appropriate conclusion 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."

Therefore, this response highlights a significant flaw in the model's predictions.