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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 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 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 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.

1 answer

To assess the linear model using the residuals she calculated (2.6, 9.3, −5.489, and −6.59), it is important to note a few points:

  1. Understanding Residuals: A residual is the difference between the actual value and the predicted value from the model. Positive residuals indicate that the actual value is above the predicted value, while negative residuals indicate that the actual value is below the predicted value.

  2. Magnitude of Residuals: The size of the residuals is also important. A large residual (like 9.3) suggests that the prediction is far from the actual value, which could indicate that the linear model is not a good fit for that data point.

  3. Distribution of Residuals: While the distribution of residuals (positive vs. negative) can provide some insights, simply having half positive and half negative does not guarantee that the model is good. What matters more is the magnitude of the residuals and whether they exhibit a consistent pattern.

Given these points, the most appropriate conclusion from the provided options 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 reflects the fact that the large residual value indicates a significant discrepancy between the model's predictions and the actual data, suggesting that the linear model may not fit the data well.