Use the image to answer the question.

Question

Six points are plotted on a scatterplot. The x-axis is labeled Height in feet, and the y-axis is labeled Residual Value.

Determine the reliability of the linear model given the residual plot. Enter the number of the correct option.

Option #1: The given residual plot clearly has a pattern. Therefore, a linear model is not reliable and will not provide accurate predictions.

Option #2: The given residual plot clearly has a pattern. Therefore, a linear model is reliable and will provide accurate predictions for the original data.

Option #3: 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 point)
Option #
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Answer 1

To determine the reliability of the linear model based on the residual plot, we look for patterns in the residuals.

• If the residuals show a clear pattern (for example, they are not randomly distributed and instead show trends, curvatures, or clusters), it suggests that a linear model is not a good fit for the data, making the predictions unreliable.
• Conversely, if the residuals are evenly and randomly distributed around the line where the residual equals zero, the linear model is deemed reliable and suitable for making predictions.

Therefore, based on this reasoning, you would select the option that aligns with the observed characteristics of the residual plot. If the plot shows a pattern, you would choose Option #1. If the plot shows no clear pattern, you would select Option #3.

Since I do not have access to the image of the residual plot, I suggest selecting:

Option #1 if there is a clear pattern present, indicating unreliability of the linear model. or Option #3 if the residuals are evenly and randomly distributed, indicating that the linear model is a good choice.

You should choose the option that best describes the characteristics of the residual plot you've observed.