To analyze the appropriateness of the linear model based on the given residuals (0.26, 0.93, 0.5489, and 0.659), we need to consider what residuals represent. Residuals are the differences between the observed values and the values predicted by the model.
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All Residuals are Positive: If all residuals are positive, it suggests that the model consistently underestimates the observed values. While this indicates that the model is not perfectly accurate, it doesn't necessarily mean that the model is entirely inappropriate—it may still capture a general trend in the data.
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Magnitude of Residuals: The magnitude of residuals being less than 1 indicates that the errors in predictions are relatively small, which is a good sign. However, we generally want to assess whether these residuals display a pattern or randomness. If they show a consistent trend (e.g., increasing or decreasing), it might indicate that a linear model is not the best fit.
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Conclusion About the Linear Model: Based on the information provided about the residuals, you could conclude that the linear model does not accurately represent the data since the residuals are consistently positive. This suggests that the linear model is not capturing the behavior of the data well.
Given this reasoning, the best conclusion from your options would be:
"The linear model does not accurately represent the data since all residuals are positive."
In a broader sense, further analysis would typically involve checking for patterns in the residuals (e.g., plotting them) and possibly exploring more complex models if necessary.