Thread: Centroid point proof

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!

Just plug in in for the x and see if you get .
You saw my other proof earlier today, use that post.

Right, so I have

β0_hat + β1x_bar = y_bar – β1_hat*x_bar + β1_hat*x_bar =y_bar
It just seemed too good to be true

It looks right.
But again I do need to know the model.
However I think this is true for any model.



is the fitted line, with

giving us

.

NOW setting in the line completes this.

Matheagle,

thank you very very much for all your help!