Regression with Robust Standard Errors

Regression with robust standard errors keeps the ordinary least squares coefficients but computes sandwich (heteroskedasticity-consistent or cluster-robust) standard errors that remain valid when error variances differ or errors are correlated within clusters.

강건 표준오차 회귀는 OLS 계수는 그대로 두고 이분산이나 군집 내 상관에도 타당한 샌드위치 표준오차로 추론하는 방법입니다.

The Breusch-Pagan test says my residuals are heteroskedastic, or my data are clustered in schools; how do I get valid standard errors?

잔차가 이분산이거나 자료가 학교별로 묶여 있을 때 타당한 표준오차는 어떻게 구하나요?

Robust standard errors replace the usual variance formula with a sandwich estimator that uses the observed squared residuals, so inference stays valid under heteroskedasticity of unknown form. With a cluster variable, residuals are summed within clusters first, which allows arbitrary correlation inside each cluster.

When to use Regression with Robust Standard Errors

• Residual variance changes across observations
• Observations are grouped in clusters such as schools, firms or regions
• You want to keep OLS coefficients but report defensible inference

When to use something else

• The variance pattern is known and you want efficient estimates; use weighted least squares regression instead
• You need to model between-cluster variation explicitly; use hierarchical linear modeling (HLM) instead

Assumptions and requirements

• The mean model is correctly specified
• Observations (or clusters) are independent
• The number of observations or clusters is large enough, ideally 30 to 50 clusters or more

What the analysis reports

• OLS coefficients with robust standard errors, t, p and confidence intervals
• Classical standard errors and their ratio to robust ones
• Robust overall F test
• Breusch-Pagan test result

How to report it

An OLS regression with [HC3 / cluster-robust] standard errors showed that [predictor] predicted [outcome], b = [value], robust SE = [value], t([df]) = [value], p = [value].

Related methods

• Weighted Least Squares Regression
• Multiple Linear Regression
• Hierarchical Linear Modeling (HLM)

Run Regression with Robust Standard Errors on Quorant