Econometrics and statistical methods — from geometry to clustered standard errors.
Starting from scratch — the geometry of ℝⁿ, through OLS standard errors under homoskedasticity, heteroskedasticity, clustering, and finally multinomial logit. Each part builds on the last.
Two simulation exercises. Error in y: β̂ stays unbiased but SEs widen and R² collapses. Error in x: attenuation bias — the OLS slope shrinks toward zero, and more data doesn't fix it.
A point placed at x = x̄ contributes zero to both the numerator and denominator of the OLS slope formula. Its y-value is completely irrelevant to β̂. One enormous outlier — slope unchanged to machine precision.
