# Quant - F Stat

I understand that the F-test sets the independent variables, as a group, to explain the variabtion in the dependent variable But, what is the logic behind setting the values of the independent variables to zero (0)? i.e. H0: b1 = b2 = b3 = b4 = 0

First, it is not testing Independent Variables to 0, it is testing their coefficients to be 0. If all of these coefficients together come out to be statistically 0, then the regression model is not explaining anything. And we can reject the model there itself. So, the logic of using F-Stat is to determine, if regression model as a whole is statistically significant or not. IF model turns out to be significant, as explained by its F-stat, next, we can test individual independent variables for their individual significance by using t-test on their coefficients.

hi Rusbus, when you say “If all of these coefficients together come out to be statistically 0…” what do you mean exactly? the null is trying to prove that all the coefficients = 0. If they do, this means that the F-value will lie outside the critical F value?

gazhoo Wrote: ------------------------------------------------------- > hi Rusbus, > > when you say “If all of these coefficients > together come out to be statistically 0…” what > do you mean exactly? > > the null is trying to prove that all the > coefficients = 0. If they do, this means that the > F-value will lie outside the critical F value? F-test is a one sided test. Fstat is greater than or less than Fcrit = accept null hypothesis regression is insignificant.

aren/'t you supposed to reject the null if F-stat is greater or less than Fcritical?

You reject the null if the F stat is greater than the critical value determined from the F table. The null hypothesis is that the test parameters do NOT explain the model. Therefore if you reject the null, you are saying that the independant variables (as a group) do explain the dependant variable to some extent. If you fail to reject the null, it means that the independant variables do not explain the dependant one.