To evaluate the linear model based on the residuals given (2.6, 9.3, -5.489, and -6.59), we should consider the following points:
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Residuals Definition: Residuals are the differences between the actual values and the predicted values from a model. A smaller residual indicates a better model fit for that particular data point.
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Sign of Residuals: Positive residuals indicate that the actual value is above the predicted value, while negative residuals imply that the actual value is below the predicted value.
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Magnitude of Residuals: Large residuals (like 9.3) suggest that the model is not accurately predicting that particular data point.
Based on these points, let's analyze the options:
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The first option suggests that the model is accurate because half the residuals are positive and half are negative. This isn't a sufficient reason because having both signs does not imply accuracy; it could just mean the model consistently underestimates or overestimates values.
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The second option highlights that the large residual (9.3) indicates a poor fit for the corresponding data point, which is a valid conclusion about the model's limitations.
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The third option states that the model is inaccurate for having half of the residuals positive and half negative, which again is not a strong enough basis for assessing model fit.
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The fourth option mentions that a small residual (2.6) means the actual point is not far from the estimate, but this doesn't take the large residuals into account which are more significant.
Given this analysis, the best conclusion Jade can draw from the residuals 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.