The F-test is a statistical test used primarily in regression analysis and ANOVA (Analysis of Variance) to compare two competing models. It assesses whether the variance explained by a model is significantly greater than the variance not explained by the model. In the context of regression, the F-test helps determine if adding more variables to a model improves its ability to explain the dependent variable’s variance.

In regression analysis, the F-test can answer two main questions: whether a more complex model (with additional variables) is better than a simpler model, and whether a simple intercept-only model is sufficient. The simpler model is referred to as the restricted model, while the more complex one is the unrestricted model. The F-statistic is calculated based on the ratio of the explained variance to the unexplained variance, and it follows an F-distribution under the null hypothesis that the simpler model is adequate ¹².

However, the F-test has limitations, particularly with large sample sizes or many explanatory variables, as it may not accurately reflect the goodness-of-fit of the model ².