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A residual plot has an x-axis that ranges from 0 to 11 and is labeled 'Fitted Value.' The 1st increment on that axis is 5 and it continues by unit increments until 11. The y-axis ranges from negative 10 to 30 by increments of 10 and is labeled 'Residual.'

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

(1 point)
Responses

A.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 this 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 this data and will not provide accurate results when making predictions.

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

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

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

1 answer

To determine the reliability of the linear model based on the description of the residual plot, let's break down the information provided.

A good residual plot will generally have residuals that are randomly distributed around the horizontal line at zero. If the residuals show a pattern (such as a curve or systematic increases/decreases), this suggests that the linear model may not be the best fit for the data, and it indicates that the model may be unreliable for predictions.

Given that the response options include statements about how well the residuals are distributed, the correct choice among the provided responses is:

C. 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.

This choice reflects the conclusion that a pattern in the residuals indicates issues with the linear model, making it unreliable for accurate predictions.