Bootstrap Regression

Bootstrap regression estimates the sampling variability of least-squares coefficients by refitting the model on resampled cases, resampled residuals or randomly sign-flipped residuals.

부트스트랩 회귀는 사례·잔차를 다시 뽑거나 잔차의 부호를 무작위로 바꿔 최소제곱 회귀를 반복 적합해 계수의 표본 변동을 추정하는 방법입니다.

My regression residuals are not normal and possibly heteroskedastic; how can I get trustworthy confidence intervals for the coefficients?

회귀 잔차가 정규분포가 아니고 이분산 같아요. 계수의 신뢰구간을 믿을 만하게 구하려면 어떻게 하나요?

Bootstrap regression refits the model many times on resampled data so that standard errors, confidence intervals and p-values come from the empirical distribution of the coefficients rather than from normal-theory formulas. Case resampling and the wild bootstrap remain valid under heteroskedasticity, and the wild cluster bootstrap handles clustered data with few clusters.

When to use Bootstrap Regression

• Residuals are skewed or heteroskedastic and the sample is moderate.
• Observations are clustered and the number of clusters is small (wild cluster bootstrap).
• BCa or studentized intervals are wanted for regression coefficients.

When to use something else

• The outcome is binary or a count; use a logistic or Poisson model with robust or bootstrap standard errors.
• Observations are serially dependent in time; use a block bootstrap or HAC standard errors.

Assumptions and requirements

• Cases (or clusters) are independent draws.
• The linear mean model is correctly specified.
• The residual bootstrap additionally assumes homoskedastic, exchangeable errors.

What the analysis reports

• Coefficients with OLS and bootstrap standard errors and bootstrap bias
• Percentile, BCa or studentized confidence intervals
• Bootstrap-t p-values (symmetric, unrestricted)
• Number of clusters for the wild cluster scheme

How to report it

With [number] pairs bootstrap resamples, the coefficient of [X] was b = [value], bootstrap SE = [value], 95% BCa CI [[value], [value]], p = [value].

Related methods

• Multiple Linear Regression
• Robust (Sandwich) Standard Errors
• Bootstrap Confidence Intervals (BCa)

Run Bootstrap Regression on Quorant