How do you test if a model is a good fit?

If the residuals from a model exhibit randomness, it is a strong indication that the model has captured the essence of the relationship between the explanatory variables and the response variable. This randomness suggests that the model's predictions are not systematically biased and that it is able to account for the variability in the data.

Conversely, if the residuals show discernible patterns, such as clustering or systematic deviations, it implies that the model may be missing some important factors or relationships. This could indicate that the model needs to be refined or that a different model might be more appropriate.

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The accuracy of a model's fit to data is crucial in assessing its predictive power. When a model aligns with the observed data, it indicates that the model effectively captures the underlying patterns and relationships.

In statistical modeling, residuals play a pivotal role in evaluating the goodness of fit. Residuals represent the differences between the observed data points and the values predicted by the model. Ideally, these differences should resemble random errors, without any discernible patterns.