I often hear that in a regression model (of any type), it is bad for slope(s) and intercept to be (highly) correlated. In R, this correlation is gotten by cov2cor(vcov(fitted_model)).

My understanding is that after fitting a regression model, we get a single estimate for each slope and the intercept from our model.

Question: So, what correlations are we talking about given some few estimates at hand? And how high degrees of such correlations could affect our inference about our estimated slopes and intercept?

I highly appreciate an R demonstration.

I often hear (e.g., p. 99 of this book) that in a regression model (of any type), it is bad for slope(s) and intercept to be (highly) correlated. In R, this correlation is gotten by cov2cor(vcov(fitted_model)).

My understanding is that after fitting a regression model, we get a single estimate for each slope and the intercept from our model.

Question: So, what correlations are we talking about given some few estimates at hand? And how high degrees of such correlations could affect our inference about our estimated slopes and intercept?

I highly appreciate an R demonstration.