Question

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

Answer 1

To evaluate the appropriateness of the linear model based on the given residuals (0.26, 0.93, 0.5489, and 0.659), it's essential to understand what residuals represent. Residuals are the differences between the observed values and the values predicted by the model.

The residuals are as follows:

• 0.26
• 0.93
• 0.5489
• 0.659

1. Magnitude of Residuals: While it is true that all the residuals are less than 1, this alone does not confirm that the model is appropriate, as they could still be significant enough to indicate a poor fit depending on the scale of the data.

2. Sign of Residuals: All the residuals are positive, which suggests that the model is consistently underestimating the actual values.

Given this information, the best conclusion Jes can make is:

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

This statement reflects that the model consistently under-predicts the observed values, indicating that a better-fitting model may be necessary.