I have performed a simple linear regression which consists of an intercept and 20 variables in R. The variables can be seen as two groups, call the parameters for the first group the alpha group and for the second group the beta group. I now wish to test if the beta group as a whole is insignificant, and if the reduced model (only containing the alpha parameters) is not significantly worse than the full model. If I would look at the parameter's p-values alone, I might discard too many parameters. On the other hand, I could look at the F statistic alone, but then that would determine if the full model as a whole is significant.
How would one go about doing this in R?