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 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 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.

Answer 1

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

In this case, Jes calculated residuals of 0.26, 0.93, 0.5489, and 0.659, all of which are positive and all less than 1. Here's what a conclusion can be drawn from this:

1. All residuals are positive: This indicates that the model consistently underestimates the actual data points, but it doesn't inherently mean that the linear model is inappropriate.

2. All residuals are less than 1: This suggests that the predictions are relatively close to the actual values, which can indicate a reasonable fit, depending on the context and scale of the data.

Considering these observations, the best conclusion Jes can make is: "The linear model accurately represents the data since all residuals are less than 1."

This implies that while there is an underestimation (indicated by positive residuals), the size of the residuals indicates a fairly good fit for a linear model.