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re:st: Insignificant coefficient in prediction

From   Christopher F Baum <>
To   <>
Subject   re:st: Insignificant coefficient in prediction
Date   Wed, 1 Dec 2010 14:27:10 -0500

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 Baum   |   Boston College Economics and DIW Berlin   |
An Introduction to Stata Programming   |
An Introduction to Modern Econometrics Using Stata   |

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