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 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 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 residuals are positive.

Answer 1

To evaluate the appropriateness of the linear model based on the residuals, Jes should consider the characteristics of the residuals:

1. Residuals measure the difference between observed values and values predicted by the model.
2. An ideal residual plot should show residuals that are randomly distributed around zero, without any apparent pattern.

In this case, Jes has calculated the residuals to be 0.26, 0.93, 0.5489, and 0.659. All of these residuals are positive, indicating that the model is consistently underestimating the observed values. However, the significance of their size is also important.

While the fact that the residuals are less than 1 could suggest that the model is reasonably accurate in terms of prediction error magnitude, simply being less than 1 does not guarantee a good fit. The positivity of all residuals does indicate some systematic bias in the model—it tends to underestimate the data points.

Therefore, the most appropriate conclusion Jes can make based on the current residuals is:

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

This suggests a systematic error in the model predictions.