Quadratic regression (source code)

= Quadratic regression
{title2=$E(Y\mid x)=\beta_0+\beta_1x+\beta_2x^2$}

A <polynomial regression> of degree two is linear in its unknown <regression coefficients> despite being curved in the predictor. Its <design matrix> has columns $1,x,x^2$; three distinct predictor values give full column <matrix rank>.