After confirming that the fitted model meets the assumptions necessary for linear regression, the next step of a regression analysis is usually to evaluate how well the model is performing in terms of fit and accuracy. The Global F-Test is one such measure.
Global F test is the most high-level model significance measure, which simply reports if any component of the model is significant. The null hypothesis is that nothing is significant, and the alternative is that at least one coefficient is. The test statistic represents a signal to noise ratio and is found by:
MSR: Mean Squared due to regression
MSE: Mean Squared Error
MSR is the component that measures the signal the model captures above simply using the overall mean to predict each observation, and MSE is the residual component that measures how far the predictions are from the actual values. This test is often not very informative from a practical standpoint, especially if there are many predictors in the model.
