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 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 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 given residual plot clearly has a pattern. Therefore, a linear model is reliable and will 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.
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Answer 1

To determine the reliability of the linear model based on the residual plot, we need to understand how residuals behave in a well-fitted linear model.

If the residuals are equally and randomly distributed around the line where the residual equals zero (the horizontal line at zero), it indicates that the linear model provides a good fit for the data and can make accurate predictions.

Conversely, if there is a recognizable pattern in the residuals (such as curvature or clustering), it suggests that the linear model is not appropriate for the data and may lead to inaccurate predictions.

Given this understanding, the correct response would depend on the specific characteristics of the residual plot you have. Generally, if there is no pattern and the residuals are randomly distributed, you would conclude that the linear model is a good choice. If there is a pattern, you would conclude that the linear model is not a good choice.

1. **If the residual plot is equally and randomly distributed around the line where residual=0:** This indicates that the linear regression model is a good choice for this data and will provide accurate results when making predictions.

2. **If the residual plot shows a clear pattern:** This suggests that a linear model is not reliable and will not provide accurate predictions for the original data.

Without the image of the residual plot, I can't provide a definitive answer, but you can apply this reasoning to choose the correct response based on what you see in the plot.