consider to model:Yi=βo+β1Xi+εi
Given some observed data y1, x1, y2, x2,..., y n, xn
Show that the estimated sample covariance Cov(εi,Xi) MUST equal 0 in an OLS regression, where εi=Yi+β0-β1Xi is the estimated residual from the model. In other words, show that the sample correlation between the estimated errors and the X variable is always equal to 0 in OLS regression.
thx for help!