Abstract
Multiple Regression is a form of model for prediction purposes. With large number of predictor variables, the multiple regression becomes complex. It may underfit on higher number of dimension (variables) reduction. Most of the regression techniques are either correlation based or principal components based. The correlation based method becomes ineffective if the data contains a large amount of multicollinearity, and the principal component approach also becomes ineffective if response variables depends on variables with lesser variance. In this paper, we propose a Correlation Scaled Principal Component Regression (CSPCR) method which constructs orthogonal predictor variables having scaled by corresponding correlation with the response variable. That is, the construction of such predictors is done by multiplying the predictors with corresponding correlation with the response variable and then PCR is applied on a varying number of principal components. It allows higher reduction in the number of predictors, compared to other standard methods like Principal Component Regression (PCR) and Least Squares Regression (LSR). The computational results show that it gives a higher coefficient of determination than PCR, and simple correlation based regression (CBR).
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References
Armstrong, J.S.: Illusions in regression analysis. Int. J. Forecast. 28(3), 689 (2012). https://doi.org/10.1016/j.ijforecast.2012.02.001
Fisher, R.A.: The goodness of fit of regression formulae, and the distribution of regression coefficients. J. Roy. Stat. Soc. 85(4), 597–612 (1922). https://doi.org/10.2307/2341124. JSTOR 2341124
Kutner, M.H., Nachtsheim, C.J., Neter, J.: Applied Linear Regression Models, 4th edn., p. 25. McGraw-Hill/Irwin, Boston (2004)
Filzmoser, P., Croux, C.: Dimension reduction of the explanatory variables in multiple linear regression. Pliska Stud. Math. Bulgar. 14, 59–70 (2003)
Martens, H., Naes, T.: Multivariate Calibration. Wiley, London (1993)
Basilevsky, A.: Statistical Factor Analysis and Related Methods: Theory and Applications. Wiley & Sons, New York (1994)
Araújo, M.C.U., Saldanha, T.C.B., Galvão, R.K.H., Yoneyama, T., Chame, H.C., Visani, V.: The successive projections algorithm for variable selection in spectroscopic multicomponent analysis. Chemom. Intell. Lab. Syst. 57, 65–73 (2001)
Ng, K.S.: A Simple Explanation of Partial Least Squares, Draft, 27 April 2013
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Singh, K.K., Patel, A., Sadu, C. (2018). Correlation Scaled Principal Component Regression. In: Abraham, A., Muhuri, P., Muda, A., Gandhi, N. (eds) Intelligent Systems Design and Applications. ISDA 2017. Advances in Intelligent Systems and Computing, vol 736. Springer, Cham. https://doi.org/10.1007/978-3-319-76348-4_34
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DOI: https://doi.org/10.1007/978-3-319-76348-4_34
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