es used GeoGebra to find a linear model (trend line) of the data collected for their science project. They calculated the following residuals for their data 0.26, 0.93, 0.5489, and 0.659. What conclusion can Jes make about the appropriateness of the linear model based on the residuals?(1 point)

Question

Responses

The linear model does not accurately represent the data since all residuals are positive.
The linear model does not accurately represent the data since all residuals are positive.

The linear model accurately represents the data since all residuals are less than 1.
The linear model accurately represents the data since all residuals are less than 1.

The linear model accurately represents the data since all residuals are positive.
The linear model accurately represents the data since all residuals are positive.

The linear model does not accurately represent the data since all data points are less than 1.

Answer 1

To evaluate the appropriateness of the linear model based on the residuals, we need to understand what residuals represent. Residuals are the differences between the observed values and the predicted values from the linear model.

The residuals provided are: 0.26, 0.93, 0.5489, and 0.659. Here:

1. All residuals are positive, indicating that the predicted values are underestimating the observed values.
2. The magnitude of the residuals is generally small (all less than 1), suggesting that the model predictions are relatively close to the actual data points.

Given these observations, the best conclusion Jes can make is:

The linear model accurately represents the data since all residuals are less than 1.

This indicates that the model fits the data reasonably well, even though the fact that all residuals are positive suggests some consistent underestimation. However, because the residuals are not large, it can be inferred that the linear model is still a good approximation of the relationship in the data.