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Determine the reliability of the linear model given the residual plot.

(1 point)
Responses

The residual plot is equally and randomly distributed around the line where residual=0. Therefore, the linear regression model is not a good choice for these data and will not provide accurate results when making predictions.
The residual plot is equally and randomly distributed around the line where residual=0. Therefore, the linear regression model is not a good choice for these data and will not provide accurate results when making predictions.

The given residual plot clearly has a pattern. Therefore, the linear model is not reliable and will not provide accurate predictions for the original data.

The residual plot is equally and randomly distributed around the line where residual=0. Therefore, the linear regression model is a good choice for these data and will provide accurate results when making predictions.
The residual plot is equally and randomly distributed around the line where residual=0. Therefore, the linear regression model is a good choice for these data and will provide accurate results when making predictions.

The given residual plot clearly has a pattern. Therefore, the linear model is reliable and will provide accurate predictions for the original data.

1 answer

To determine the reliability of the linear model based on the residual plot, we need to analyze the characteristics of the residuals.

  1. If the residuals are equally and randomly distributed around the line where residuals equal 0, it indicates that the linear model is a good fit for the data, and thus, predictions made by this model are likely to be reliable.

  2. Conversely, if the residual plot shows a discernible pattern (e.g., a curve), this suggests that a linear model may not adequately capture the relationship between the variables, leading to unreliable predictions.

Given these points, the responses can be evaluated as follows:

  • Response A: Suggests the model is not a good choice because the residuals are randomly distributed. (Incorrect interpretation)
  • Response B: Incorrectly states the model is not reliable based on an observed pattern (assumed to be present) in residuals.
  • Response C: Correctly asserts that a pattern in residuals implies unreliability of the linear model.
  • Response D: Correctly denotes that random distribution of residuals indicates the model is a good fit.
  • Response E: Incorrectly claims the linear model is reliable when there is a pattern in the residuals.

Based on the information provided, if the residual plot shows a random distribution, then the third response ("The residual plot is equally and randomly distributed...") is correct. If it shows a pattern, then the second response is correct.

However, since I don't have a visual of the residual plot to make a definitive statement, the conclusion about reliability would need to be drawn from the specific characteristics of the actual plot.