A regression model has all coefficients with significant $p-$values, but the model has high error. Is this model useful?
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When evaluating a regression model with significant coefficients but high error, you should consider the context and purpose of the model. Look at the size of the regression coefficients and their practical significance, assess model assumptions, consider overfitting, and evaluate if the model is likely to be generalizable to new data. Additionally, examine other performance metrics beyond $p$-values and errors, such as $R^2$, adjusted $R^2$, and AIC/BIC criteria to get a comprehensive understanding of the model's validity and usefulness.
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