Enhanced ridge regressions

With a simple transformation, the ordinary least squares objective can yield a family of modified ridge regressions which outperforms the regular ridge model. These models have more stable coefficients and a higher quality of fit with the growing profile parameter. With an additional adjustment based on minimization of the residual variance, all the characteristics become even better: the coefficients of these regressions do not shrink to zero when the ridge parameter increases, the coefficient of multiple determination stays high, while bias and generalized cross-validation are low. In contrast to regular ridge regression, the modified ridge models yield robust solutions with various values of the ridge parameter, encompass interpretable coefficients, and good quality characteristics.