Reading Wooldridge's book on introductory econometrics I observe that the F test allows us to see if, in a group, at least one of the coefficients is statistically significant. However, in my model I have that, individually, one of the variables of the group I want to test is already statistically significant (measured by the t-test). So, if that is the case I expect that, no matter with which variable I test for, if I include the one that is already individually significant, the F test will also be significant. Is there any useful usage I can make with the F test in this case?
Hello Santiago and Calleagues,
A t -test for one variable is identical to an F-test, in a simple regression model (with one explanatory variable); as a matter of fact in this case the square of the t-statistic value is exactly equal to the F statistic value (t^2 =F).
Once you include additional independent variables the F-test is the one that you rely to report the results. If you have significant F- test then you report the regression results and you look which explanatory variables are significant using the t-test. However if the F-test is insignificant you stop there and you do not report the regression.You need to find another model that at the minimum passes the F-test.This is a specification issue.
Kind regards,
George K Zestos
Hi, I am not totally convinced that including one statistically significant variable according to a t test, will imply a significant F test. It sounds reasonable, but I would like to see the proof of that. I have in mind the following: you can express the F test in terms of the R2. If you have a variable that is statistically significant, but explains very little of the variance of the dependent variable, maybe you end up with an insignificant F test. I will think about it. Great question!!!
Hi, with respect to Pablo's argument, the F test is kind of a "gate" to deciding if you your e.g. regression equation is statistically significant. If it is not, results of t-tests significance for variables in the equation can be not very informative. So you should start with F test. It means that it is possible, to get statistically significant t-tests for the seperate variables and not significant F test.
Unless there is one variable equation...
Hello Santiago and Calleagues,
A t -test for one variable is identical to an F-test, in a simple regression model (with one explanatory variable); as a matter of fact in this case the square of the t-statistic value is exactly equal to the F statistic value (t^2 =F).
Once you include additional independent variables the F-test is the one that you rely to report the results. If you have significant F- test then you report the regression results and you look which explanatory variables are significant using the t-test. However if the F-test is insignificant you stop there and you do not report the regression.You need to find another model that at the minimum passes the F-test.This is a specification issue.
Kind regards,
George K Zestos
Technically if a regression coeff is signif with a p-value of 0.05 this means you are 95% sure that the regression coeff is n.e. 0. This is not the same as knowing the coeff is 0 with 100% confidence. Hence the F test has value. See eg Devore and Berk, Mathematical Statistics. D. Booth
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