An Application of Proposed Ridge Regression Methods to Real Data Problem


  • N S M Shariff
  • H M B Duzan





Macroeconomic Variables, Multicollinearity, OLS, Ridge Regression.


The Ordinary Least Squares (OLS) is a common method to investigate the linear relationship among variable of interest. The presence of multicollinearity will produce unreliable result in the parameter estimates if OLS is applied to estimate the model. Due to such reason, this study aims to use the proposed ridge estimator as linear combinations of the coefficient of least squares regression of explanatory variables to the real application. The numerical example of stock market price and macroeconomic variables in Malaysia is employed using both methods with the aim of investigating the relationship of the variables in the presence of multicollinearity in the data set.  The variables on interest are Consumer Price Index (CPI), Gross Domestic Product (GDP), Base Lending Rate (BLR) and Money Supply (M1). The obtained findings show that the proposed procedure is able to estimate the model and produce reliable result by reducing the effect of multicollinearity in the data set.


[1] Hoerl AE & Kennard RW (1970), Ridge regression: applications to nonorthogonal problem. Technometrics, 12(1), 69-78.

[2] Hoerl AE & Kennard RW (1970), Ridge regression: biased estimation for nonorthogonal problems. Technometrics, 12(1), 55-67.

[3] Duzan H & Shariff NSM (2015), Ridge regression for solving the multicollinearity problem : review of methods and models. Journal of Applied Sciences, 15(3), 392-404.

[4] Kibria BMG (2003), Performance of some new ridge regression estimators. Communications in Statistics- Simulation and Computation, 32(2), 419-435.

[5] Mansson K, Shukur G & Kibria BMG (2010), A simulation study of some ridge regression estimators under different distributional assumptions. Communications in Statistics- Simulation and Computation, 39(8), 1639-1670.

[6] Duzan H & Shariff NSM (2016), Solution to the multicollinearity problem by adding some constant to the diagonal. Journal of Modern Appllied Statistical Methods, 15(1), 752-773.

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