Linear regression model ($Y=X\beta +\epsilon$)

A statistical model specifying a response as a linear combination of known regressor columns and an error. Common assumptions are $\mathbb{E}[\epsilon ]=0$ and $\mathrm{Cov}(\epsilon )={\sigma }^{2}I$, although a normal distribution is an additional assumption, not part of the displayed equation alone. Full column rank of the design matrix makes the coefficients identifiable. Statistical association does not by itself give a causal effect.