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RE: re:st: Insignificant coefficient in prediction


From   DE SOUZA Eric <eric.de_souza@coleurope.eu>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   RE: re:st: Insignificant coefficient in prediction
Date   Wed, 1 Dec 2010 20:32:47 +0100

The example I give my students is a regression of y on x1 and x2 where the corelation between x1 and x2 in 0.99... Both coefficients (on x1 and x2) are insignificantly different from zero. But the R2 is very high. 


Eric de Souza
BE-8000 Brugge (Bruges)
Belgium

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Christopher F Baum
Sent: 01 December 2010 20:27
To: statalist@hsphsun2.harvard.edu
Subject: re:st: Insignificant coefficient in prediction

<>
Mike said

sysuse auto, clear
reg mpg weight length  // length is not significant predict mpgh, xb

The predicted values use all coefficients including the coefficient of 'length' even if it is not significant.

Well, of course. yhat is the linear combination X*b. If you arbitrarily leave out one or more of the terms in that linear combination, you are not going to get predictions of the regression surface. For in-sample predictions, the mean error will not be zero in that instance, as it will be for regression with a constant term. So if you want a point prediction, you use all of the estimated coefficients, whether or not you can precisely estimate them...

Consider regressing y on x and (x + epsilon), where x is highly correlated with y. The predictions of that model, for small epsilon, will have a very high R^2, but the individual standard errors will be huge due to near-perfect collinearity. That does not suggest that you should use the naive model y = b0 (constant), though.

KIt

Kit Baum   |   Boston College Economics and DIW Berlin   |   http://ideas.repec.org/e/pba1.html
An Introduction to Stata Programming   |   http://www.stata-press.com/books/isp.html
An Introduction to Modern Econometrics Using Stata   |   http://www.stata-press.com/books/imeus.html


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