Behavior of the coefficients of ordinary least squares (OLS) regression with the coefficients regularized by the one-parameter ridge (Ridge-1) and two-parameter ridge (Ridge-2) regressions are compared. The ridge models are not prone to multicollinearity. The fit quality of Ridge-2 does not decrease with the profile parameter increase, but the Ridge-2 model converges to a solution proportional to the coefficients of pair correlation between the dependent variable and predictors. The Correlation-Regression (CORE) model suggests meaningful coefficients and net effects for the individual impact of the predictors, high quality model fit, and convenient analysis and interpretation of the regression. Simulation with three correlations show in which areas the OLS regression coefficients have the same signs with pair correlations, and where the signs are opposite. The CORE technique should be used to keep the expected direction of the predictor’s impact on the dependent variable.
"Multiple Regression in Pair Correlation Solution,"
Journal of Modern Applied Statistical Methods:
1, Article 11.
Available at: http://digitalcommons.wayne.edu/jmasm/vol8/iss1/11