To determine the appropriateness of the linear model based on the residuals, we need to analyze the residuals themselves. Residuals represent the difference between the observed values and the values predicted by the model. In this case, the residuals provided are:
- 0.26
- 0.93
- 0.5489
- 0.659
Here's what can be interpreted from these residuals:
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All residuals are positive: This indicates that the model underestimates the observed values. However, having all positive residuals does not necessarily indicate that the model is inappropriate; it merely shows a tendency in the errors.
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All residuals are less than 1: This may suggest that the model's predictions are relatively close to the actual data, which could indicate a reasonable fit.
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Overall assessment: A good linear model should have residuals that are randomly distributed around 0 with no systematic patterns. It is also important for residuals to be small in magnitude.
Considering the options provided, the most appropriate conclusion from the residuals given is:
The linear model accurately represents the data since all residuals are less than 1.
This suggests that, while there may be some systematic error (as indicated by all positive residuals), the magnitude of the errors is fairly small, indicating a generally good fit.