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In regression analysis, there are several metrics that can be used to evaluate the goodness of the model. Here are some common methods:
Measure of Determination (R²): R² indicates how well the dependent variable is explained by the independent variables in the model. It ranges from 0 to 1. A value of 1 indicates that the model perfectly explains the observed data. A lower value indicates a lower fit of the model to the data. Note, however, that R² is not always a reliable metric, especially when the number of independent variables is high.
Adjusted coefficient of determination (adjusted R²): Unlike R², adjusted R² takes into account the number of independent variables in the model. It is therefore useful if you want to compare models that have different numbers of independent variables. A higher value of adjusted R² indicates a better fit of the model to the data.
Residual analysis: analysis of the residuals (or prediction errors) can also provide information about model performance. You can look at the distribution of the residuals to make sure they are normally distributed and have no systematic patterns. Systematic patterns in the residuals might indicate that the model is not capturing certain aspects of the data.
Standard error of the estimators: The standard error of the estimators indicates how precisely the coefficients are estimated in the model. A low standard error indicates a more precise estimate.
F-test and t-test: The F-test can be used to test whether the included independent variables have an overall statistically significant effect on the dependent variable. The t-test can be used to test the statistical significance of individual coefficients.
It is important to use multiple evaluation metrics and critically interpret the results to gain a comprehensive understanding of model performance.