# Non-significant intercept in regression with a two level factor in R

I have a linear regression with two explanatory variables. One of them is a two level categorical variable. When I perform the fit, R tells me that the intercept is highly non significant. When I force the intercept to be zero in the regression, it tells me that the coefficient for the 0-level of the categorical variable is highly non significant. What should I do?

I suggest you don't remove the intercept. In this context it doesn't make much sense to do that (and generally doesn't; there are a few rare exceptions where you want a no-intercept model, but then $R^2$ doesn't mean what you might think it does.)