The Problem of Underestimating the Residual Error Variance in Forward Stepwise Regression. Freedman, L. S., Pee, D., & Midthune, D. N. *JRSSD*, 41(4):405-412, [Royal Statistical Society, Wiley], 1992. abstract bibtex Under the global null hypothesis that all covariates are unrelated to the outcome variables, forward stepwise regression procedures should have the property that the probability of selecting a given variable and finding it significant at the $\alpha$ level is equal to $\alpha$. Because of the problem of underestimating the residual error variance the actual probability can be very different from $\alpha$. This problem becomes of practical concern when the ratio of the number of variables to the number of observations becomes greater than 0.25, and is more serious for logistic than for linear regression.

@article{fre92pro,
title = {The {{Problem}} of {{Underestimating}} the {{Residual Error Variance}} in {{Forward Stepwise Regression}}},
volume = {41},
abstract = {Under the global null hypothesis that all covariates are unrelated to the outcome variables, forward stepwise regression procedures should have the property that the probability of selecting a given variable and finding it significant at the {$\alpha$} level is equal to {$\alpha$}. Because of the problem of underestimating the residual error variance the actual probability can be very different from {$\alpha$}. This problem becomes of practical concern when the ratio of the number of variables to the number of observations becomes greater than 0.25, and is more serious for logistic than for linear regression.},
number = {4},
journal = {JRSSD},
author = {Freedman, L. S. and Pee, D. and Midthune, D. N.},
year = {1992},
keywords = {variable-selection,bias,stepwise,effective-degrees-of-freedom},
pages = {405-412},
publisher = {[Royal Statistical Society, Wiley]},
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citeulike-linkout-0 = {http://www.jstor.org/stable/2349005},
posted-at = {2016-07-04 18:07:56},
priority = {0}
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