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!

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- May 30th 2009, 08:34 PMStillRussianCentroid 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! - May 30th 2009, 09:48 PMmatheagle
Just plug in in for the x and see if you get .

You saw my other proof earlier today, use that post. - May 31st 2009, 10:10 AMStillRussian
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 (Smile) - May 31st 2009, 08:38 PMmatheagle
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. - Jun 1st 2009, 04:50 AMStillRussian
Matheagle,

thank you very very much for all your help!