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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

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.

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.

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.
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.

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.

1 answer

To determine the reliability of a linear model based on a residual plot, we look for patterns in the residuals. If the residuals are randomly distributed around the zero line, it indicates that the linear model is a good fit. Conversely, if there is a discernible pattern (for example, a curve or systematic changes), it suggests that the linear model may not adequately capture the underlying relationship in the data.

Since the question states that the given residual plot has a pattern, we can conclude that:

"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 is the correct response.