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IMPACT OF COLLINEARITY ON THE ESTIMATED PARAMETERS AND CLASSICAL STATISTICAL TESTS VALUES OF MULTIFACTORIAL LINEAR REGRESSIONS IN CONDITIONS OF O.L.S

Florin Pavelescu ()

Journal for Economic Forecasting, 2005, vol. 2, issue 2, 50-71

Abstract: This paper demonstrates the fact that collinearity between the explanatory variables has an important influence on the estimated parameters values and, also, on the Fisher and Student tests if the Ordinary Least Squares (OLS) Method is used. The impact of collinearity in linear regressions is revealed with the help of the size of alignment coefficients (an indicator proposed by the author). It is emphasized that a negative alignment coefficient shows that a critical point of collinearity is surpassed. Consequently, the conditions when all the alignment coefficients are positive in the case of linear regressions with two, three and n ( ) explanatory variables are established. Having in view the O.L.S. properties, a revision of the calculus formula for the Student test and an improvement of the estimation methodology are proposed.

Keywords: coefficient of determination; alignment coefficient; coefficient of (direct) correlation between the explanatory variables; coefficient of mediated correlation by resultative variable between the explanatory variables collinearity; chaos and order in multifactorial linear regression; Fisher test; Student test; corrected Student test (search for similar items in EconPapers)
JEL-codes: C51 C52 (search for similar items in EconPapers)
Date: 2005
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