# How to manually inflate standard errors to approximate clustered SEs

I'm reading a handout on clustering here

It's not clear to me how to compute $$\rho_x$$ or $$\rho_\epsilon$$. What is meant by within-cluster correlation of the regression, or within-cluster error correlation?

By way of example, let's say I have the following robust specification:

library(estimatr)
lm_robust(points ~ my_sex + partner_sex,
cluster = team_id,
se = "stata",
data = data)


Where I'm clustering at the "team" level and the average team size is 2. In this case, what is 𝜌𝑥 or 𝜌𝜖?