There is no single formula.
It is necessary to calculate the total sum of squares and the regression sum of squares. These are used to calculate the residual sum of squares. The next step is to use the appropriate degrees of freedom to calculate the mean regression sum of squares and the mean residual sum of squares.

The ratio of these two is distributed as Fisher's F statistics with the degrees of freedom which were used to obtain the average sums of squares. The ratio is compared with published values of the F-statistic since there is no simple analytical form for the integral.

In estimating a linear relationship using ordinary least squares (OLS), the regression estimates are such that the sums of squares of the residuals are minimised. This method treats all residuals as being as important as others.

There may be reasons why the treatment of all residuals in the same way may not be appropriate. One possibility is that there is reason to believe that there is a systematic trend in the size of the error term (residual). One way to compensate for such heteroscedasticity is to give less weight to the residual when the residual is expected to be larger. So, in the regression calculations, rather than minimise the sum of squares of the residuals, what is minimised is their weighted sum of squares.