Question

Question

Use the image to answer the question.

Ten points are plotted on a scatterplot. The x-axis is labeled Minutes Played, and the y-axis is labeled Residual Value.

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 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.

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

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

Answer 1

To determine the reliability of the linear model based on the residual plot, it is important to consider how the residuals are distributed.

If the residual plot shows a random scatter around the line where residuals equal zero, it indicates that the linear model is appropriate for the data and should provide accurate predictions. Conversely, if the residual plot shows a discernible pattern (such as a curve or clustering), it suggests that the linear model is not suitable and may not yield accurate predictions.

Given the options based on your description:

1. If the residual plot is equally and randomly distributed around the line where residual = 0, then the statement claiming the linear regression model is a good choice is correct.
2. If the residual plot shows a clear pattern, then the statement indicating the linear model is not reliable aligns with that observation.

Since I do not have access to the image in question, you will need to assess the pattern in the residual plot based on the criteria mentioned above. Thus, select the response that matches your observation of the residual plot:

• If it is random and evenly distributed: "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."

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