Finding F-statistics in R Original model:
ln(chnimpt) = β0 + β1 ln(chempit) + β2 ln(gast) + β3 ln(rtwext) + 
    β4bef ile6t + β5aff ile6t + β6af dec6t + ut

Problem Set:
Add monthly dummy variables (they are already in the data set) to the model  plus a linear time trend and test for seasonality by testing for the joint significance (using an F test) of the eleven seasonal dummy variables at the 5% level.

I added monthly dummies with the original equation and linear time trend("t")
mymodel <- lm(lchnimp ~ lchempi + lgas + lrtwex + befile6 + affile6 + 
     afdec6 + t + feb + mar + apr + may + jun + jul + aug +sep + 
     oct + nov + dec)

But how do I calculate the f-test for seasonality of the dummies?

An $F$-test compares nested models, testing if the coefficients in the additional features are zero.
Your full model contains all of the months, plus some other variables. Nested within that model is a reduced model that contains no months but does contain the other variables.
Test the nested models. I can’t remember which goes first, but if you get an $F$-stat below zero, reverse the order.
anova(full_model, reduced_model)

