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A scatterplot with six plotted points.

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 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 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 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 reliable and will provide accurate predictions for the original data.

1 answer

To determine the reliability of the linear model based on the description of the residual plot, we need to follow these guidelines:

  1. If the residuals are evenly and randomly distributed around zero, it indicates that the linear model fits the data well and is a good choice for making predictions. In this case, the residual plot does not display any discernible pattern.

  2. If there is a pattern in the residuals (like a curve or a systematic distribution), it suggests that the linear model is not a good fit for the data, as it indicates that there are trends not captured by the model.

Given the options you provided, the appropriate response would be:

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 indicates that the linear model may not adequately describe the relationship in the data based on the patterns observed in the residuals.