Solving the minimisation problemUse calculus: take the first order derivative w.r.t. eachˆβkand set them tozero
Solving the minimisation problemUse calculus: take the first order derivative w.r.t. eachˆβkand set them tozero (i.e.first order conditions)n∑i=1(yi−ˆβ0−ˆβ1x1i−ˆβ2x2i)=0n∑i=1x1i(yi−ˆβ0−ˆβ1x1i−ˆβ2x2i)=0n∑i=1x2i(yi−ˆβ0−ˆβ1x1i−ˆβ2x2i)=0Solving these equations simultaneously yieldsˆβ0,ˆβ1,ˆβ2One can solve these equations only if the regressors are not perfectly linearlyrelatedAlgebraic properties: FOC]1→∑ni=1ˆui= 0 and FOC]2→∑ni=1ˆuix1i= 0and FOC]3→∑ni=1ˆuix2i=