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

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

Answer 1

To assess the appropriateness of the linear model based on the provided residuals (0.26, 0.93, 0.5489, and 0.659), it's important to consider what residuals indicate. Residuals are the differences between the observed values and the values predicted by the linear model.

1. The fact that all residuals are positive indicates that the model is consistently underestimating the actual data points, suggesting that the linear model may not fit the data well.

2. The residuals being less than 1 does not imply that the model is appropriate; rather, they should be considered along with their signs and the overall pattern.

Given these points, the most accurate conclusion would be:

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

This suggests that the linear model consistently underestimates the data points, indicating potential inadequacy in the linear fit.