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L. S. Freedman, D. Pee, D. N. Midthune, The Problem of Underestimating the Residual Error Variance in Forward Stepwise Regression, Journal of the Royal Statistical Society. Series D (The Statistician), Vol. 41, No. 4 (1992), pp. 405-412
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Freedman et al. (1992) studied this question.
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