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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

Author

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  • Pavelescu, Florin Marius

    (Institute of National Economy)

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.

Suggested Citation

  • Pavelescu, Florin Marius, 2005. "Impact Of Collinearity On The Estimated Parameters And Classical Statistical Tests Values Of Multifactorial Linear Regressions In Conditions Of O.L.S," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 2(2), pages 50-71.
    • Handle: RePEc:rjr:romjef:v:2:y:2005:i:2:p:50-71
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    Citations

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    Cited by:

    1. Pavelescu, Florin Marius, 2009. "A Review Of Student Test Properties In Condition Of Multifactorial Linear Regression," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 6(1), pages 63-75, March.
    2. Pavelescu, Florin Marius, 2010. "An Analysis Model for the Disturbances Generated by Collinearity in the Context of the OLS Method," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(2), pages 245-264, July.
    3. Florin Marius Pavelescu, 2010. "An Extensive Study on the Disturbances Generated by Collinearity in a Linear Regression Model with Three Explanatory Variables," Romanian Journal of Economics, Institute of National Economy, vol. 31(2(40)), pages 65-93, December.
    4. Florin-Marius PAVELESCU, 2011. "Some aspects of the translog production function estimation," Romanian Journal of Economics, Institute of National Economy, vol. 32(1(41)), pages 131-150, June.
    5. Gertrude Sebunya Muwanga, 2017. "Estimation Of Cob-Douglas And Translog Production Functions With Capital And Gender Disaggregated Labor Inputs In The Usa," Journal of Smart Economic Growth, , vol. 2(3), pages 55-105, December.

    More about this item

    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;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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