In model evaluation, which criterion is most commonly used to assess the goodness of fit?

The R-squared value is widely recognized as a standard criterion for assessing the goodness of fit in regression models, particularly in the context of linear regression. It indicates the proportion of the variance in the dependent variable that can be explained by the independent variables in the model. Essentially, R-squared provides insights into how well the model's predictions align with the actual data.

When R-squared is calculated, it ranges from 0 to 1: an R-squared of 0 suggests that the model explains none of the variance, while an R-squared of 1 indicates that the model perfectly explains the variance. This intuitive interpretation allows practitioners to evaluate models easily in terms of their explanatory power.

While other measures like Akaike Information Criterion (AIC), Standard Error of Estimate (SEE), and Mean Squared Error (MSE) also provide insights into model performance, they serve different purposes. AIC is primarily used for model selection, balancing goodness of fit with complexity, and is more concerned with predictive capability than goodness of fit. SEE quantifies the average distance that the observed values fall from the regression line, but it doesn't provide the same direct assessment of explained variance as R-squared. MSE measures the average of the squares of the errors