Question

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 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 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 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.
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Answer 1

To analyze the residuals, we need to understand what they represent. Residuals are the differences between the actual values and the values predicted by the model. A positive residual indicates that the actual value is higher than the predicted value, while a negative residual indicates that the actual value is lower than the predicted value.

Given Jade's residuals: 2.6, 9.3, −5.489, and −6.59:

• The positive residuals (2.6 and 9.3) indicate instances where the actual values were higher than expected by the model.
• The negative residuals (−5.489 and −6.59) indicate instances where the actual values were lower than expected.

Since the residuals include both positive and negative values, this suggests that the model may not consistently predict the data well across all observations. The presence of a relatively large residual like 9.3 suggests a significant discrepancy for at least one observation.

Taking all this information into account, the best conclusion Jade can draw 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 indicates that there are specific points where the model's predictions are substantially off, which would generally lead to the conclusion that the linear model is not a good fit for the data.