Categories → Statistics , Validation
The F-statistic in regression analysis measures the ratio of explained variance to unexplained variance in the model, assessing the overall significance of the regression equation.
The F-statistic is a measure used to assess the overall significance of the regression model as a whole. It essentially tests whether there is any relationship between the independent variables (Treatment and any other input features) and the dependent (Outcome) variable in the population. The F-statistic is calculated by taking the ratio of two measures of variability: the explained variability and the unexplained variability.
Explained variability is captured by the difference between the total sum of squares (SST) and the residual sum of squares (SSE). SST measures the total variation in the dependent (Outcome) variable, while SSE measures the variation that is not explained by the regression model. Hence, the difference between SST and SSE represents the variability explained by the regression model.
Unexplained variability, on the other hand, is represented solely by the residual sum of squares (SSE), which measures the discrepancy between the observed values of the dependent variable and the values predicted by the regression equation.
Correction factors based on the degrees of freedom of the regression and the error are applied to both numerator and denominator of the F-statistic ratio, respectively.
The ratio follows an F-distribution under the null hypothesis that all regression coefficients are equal to zero, implying that the model has no explanatory power.
In regression analysis, the F-statistic is used to determine whether the overall regression model is statistically significant. If the F-statistic is greater than a critical value at a chosen significance level (e.g., 0.05), then the null hypothesis is rejected, indicating that at least one of the independent variables has a statistically significant relationship with the dependent variable. In other words, the regression model as a whole provides a better explanation of the variation in the dependent variable than a model with no independent variables. This helps researchers ascertain the overall effectiveness and relevance of the regression model in explaining the variability observed in the data. Additionally, the F-test can also be used to compare the overall fit of two or more regression models, such as nested models or models with different sets of predictors, by comparing their F-statistics.
A good example of the F-statistic in linear regression analysis can be found here, with Python code.
If you generate a Result for a Fixed-Effects model, the F-statistic will be included in your Result. The purpose of this feature is to help you assess significance of the overall model and result, as described above.