Statistics

Linear Regression

Also known as: OLS, Ordinary Least Squares

Fitting a linear relationship by minimising the sum of squared residuals.

For a simple regression, the slope is Cov(x,y)/Var(x). Under the standard assumptions OLS estimates the conditional expectation E[y|x].

The trap asked most often. Regressing y on x is not the same as regressing x on y. The two slopes multiply to R-squared, so they coincide only in a perfect fit.

The assumption that bites in finance. Autocorrelated errors leave coefficients unbiased but make standard errors far too small, so things look significant that are not. Use robust or Newey-West standard errors.

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Linear Regression for Quant Interviews

What the coefficients mean, what the assumptions are, and the questions interviewers actually ask about it.

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