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I'm reading a handout on clustering here

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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?

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