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Zbl 0555.62057
Jahn, W.; Riedel, M.
Reduction of the dimension in the linear model with stochastic regressors. (English)
[J] Commentat. Math. Univ. Carol. 25, 747-761 (1984). ISSN 0010-2628

First of all we introduce the linear model with stochastic regressors. The estimates of the parmater ${\bbfB}$ and $\sigma\sp 2\sb{Y/X}$ of this model are influenced by multicollinearity. As one of the possibilities to reduce the degree of multicollinearity subset regression is proposed. As a criterion for the selection of a model for the best extrapolation we use the mean square error of extrapolation. Some important properties of the estimates of the selected model will be shown.

MSC 2000:: *62J05 Linear regression
62J99 Linear statistical inference

Keywords: dimension reduction; linear model; stochastic regressors; multicollinearity; subset regression; mean square error of extrapolation

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