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 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.
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 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.
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Answer 1

To assess how well the linear model represents the data based on the residuals, we can analyze the provided residuals: 2.6, 9.3, −5.489, and −6.59.

Residuals indicate the difference between the actual values and the predicted values from the linear model.

1. A positive residual (like 2.6 or 9.3) means the actual value was higher than the predicted value.
2. A negative residual (like -5.489 or -6.59) means the actual value was lower than the predicted value.

The fact that one of the residuals (9.3) is significantly larger than the others indicates that at least one of the actual data points is quite far from its predicted value. This suggests that there is poor accuracy in the linear model for at least some points.

Therefore, the best conclusion for Jade to make about the linear model based on the given 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.