Hello everyone!
Does anybody know how to prove the fact that the centroid point (x_bar, y_bar) lies on the regression line?
Thank you!
It looks right.
But again I do need to know the model.
However I think this is true for any model.
$\displaystyle \hat y=\hat\beta_0+\hat\beta_1 x$
is the fitted line, with $\displaystyle \hat\beta_0=\bar y-\hat\beta_1 \bar x$
giving us
$\displaystyle \hat y =\bar y-\hat\beta_1 \bar x +\hat\beta_1 x =\bar y+\hat\beta_1(x- \bar x)$.
NOW setting $\displaystyle x=\bar x$ in the line $\displaystyle \hat y =\bar y+\hat\beta_1(x- \bar x)$ completes this.