To determine the appropriateness of the linear model based on the provided residuals (0.26, 0.93, 0.5489, and 0.659), we need to consider the characteristics of residuals in the context of linear regression.
Residuals are the differences between the observed values and the predicted values from the model. Here are some points to consider:
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Residually Positive or Negative: If all residuals are positive, it indicates that the model consistently underestimates the observed values.
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Magnitude of Residuals: The scale of the residuals matters too. Although some may be less than 1, we cannot solely conclude the accuracy of the model based on this criterion.
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Independence and Distribution: Ideally, residuals should be randomly distributed around zero (both positive and negative) and not form any discernible patterns.
Based on the provided options:
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"The linear model does not accurately represent the data since all data points are less than 1" - This is not necessarily true; the magnitude alone does not determine appropriateness.
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"It does not accurately represent the data since all residuals are positive" - This is a valid point; if all residuals are positive, it suggests the model consistently underestimates the data.
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"It accurately represents the data since all residuals are positive" - This statement contradicts the previous one and is incorrect.
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"The linear model accurately represents the data since all residuals are less than 1" - This is also not correct since having residuals under a certain value does not imply accuracy.
The most appropriate conclusion based on the given residuals would be:
It does not accurately represent the data since all residuals are positive.
This indicates that the model underestimates the actual values, which is a sign of a potentially poor fit.