Question
Jade was working on her statistics homework. One of the questions gave her a trend line and asked her to find the residuals. She found the following residuals 2.6, 9.3, −5.489
, and −6.59
. What conclusion can Jade make about the linear model based on the residuals?(1 point)
Responses
The linear model seems to accurately represent the data since the residual 2.6 means that the actual point is not far from the estimate.
The linear model seems to accurately represent the data since the residual 2.6 means that the actual point is not far from the estimate.
The linear model does not accurately represent the data since half of the residuals are positive and half of the residuals are negative.
The linear model does not accurately represent the data since half of the residuals are positive and half of the residuals are negative.
The linear model seems to accurately represent the data since half of the residuals are positive and half of the residuals are negative.
The linear model seems to accurately represent the data since half of the residuals are positive and half of the residuals are negative.
The linear model does not accurately represent the data since the residual 9.3 means that the actual point is far from the estimate.
, and −6.59
. What conclusion can Jade make about the linear model based on the residuals?(1 point)
Responses
The linear model seems to accurately represent the data since the residual 2.6 means that the actual point is not far from the estimate.
The linear model seems to accurately represent the data since the residual 2.6 means that the actual point is not far from the estimate.
The linear model does not accurately represent the data since half of the residuals are positive and half of the residuals are negative.
The linear model does not accurately represent the data since half of the residuals are positive and half of the residuals are negative.
The linear model seems to accurately represent the data since half of the residuals are positive and half of the residuals are negative.
The linear model seems to accurately represent the data since half of the residuals are positive and half of the residuals are negative.
The linear model does not accurately represent the data since the residual 9.3 means that the actual point is far from the estimate.
Answers
GPT-4o mini
To assess the accuracy of the linear model based on the residuals, we need to consider what the residuals signify. Residuals are the differences between the observed values and the predicted values from the model. Positive residuals indicate that the model underestimated the actual value, while negative residuals indicate it overestimated.
Jade found the residuals: 2.6, 9.3, −5.489, and −6.59. The key points are:
- The positive residuals (2.6 and 9.3) suggest that the model's predictions are lower than the actual data points.
- The negative residuals (−5.489 and −6.59) indicate that the model's predictions are higher than the actual data points.
- The presence of both positive and negative residuals doesn't inherently mean the model is accurate or inaccurate.
However, the magnitudes of the residuals also matter. The residual \(9.3\) suggests a significant discrepancy between the predicted and observed values, implying potential issues with the model's fit.
Given this information, the most accurate conclusion is:
**The linear model does not accurately represent the data since the residual \(9.3\) means that the actual point is far from the estimate.**
This response is supported by the presence of a large residual, indicating poor fit for at least one data point, which can affect the overall reliability of the linear model.
Jade found the residuals: 2.6, 9.3, −5.489, and −6.59. The key points are:
- The positive residuals (2.6 and 9.3) suggest that the model's predictions are lower than the actual data points.
- The negative residuals (−5.489 and −6.59) indicate that the model's predictions are higher than the actual data points.
- The presence of both positive and negative residuals doesn't inherently mean the model is accurate or inaccurate.
However, the magnitudes of the residuals also matter. The residual \(9.3\) suggests a significant discrepancy between the predicted and observed values, implying potential issues with the model's fit.
Given this information, the most accurate conclusion is:
**The linear model does not accurately represent the data since the residual \(9.3\) means that the actual point is far from the estimate.**
This response is supported by the presence of a large residual, indicating poor fit for at least one data point, which can affect the overall reliability of the linear model.