ASSESSING ANNUAL VALUE BY RIDGE REGRESSION

Abstract

ln the ordinary least square (OLS) approach to regression the coefficient estimates are often inflated unstable, especially if the predictor variables are not orthogonal. This dissertation explores the use of ridge regression as a method of producing more stable and less inflated regression coefficients than those of the conventional OLS. In ridge regression, the benefits of stability are purchased at the cost of some small bias in the regression coefficients, but on the whole this may be a better and preferable situation. To achieve this the computations of beta and regression coefficients are based on a modified correlation matrix in which the principal diagonal is augmented by a factor 'k' which may range from zero to one. The selection of 'k' is one of the controversial aspects of the ridge concept, but with a suitable value of k, it can be shown that the coefficient estimates are closer to the true coefficients than those chosen by OLS regression. This study attempts to select 'k' via the ridge and vif ³ traces and one other method. The ridge trace is a plot of beta coefficients against different values of k while the vif trace is - 1. Orthogonal means complete absence of multicollinearity. 2. b = ( x' x + kI ⁻¹) x' y as opposed to OLS estimate where b = (x' x)⁻¹ x' y. 3. Variance inflation factor. A plot of the variance inflation factors against different values of k. The ridge trace is also used for variables selection by dropping those predictor variables which are shown to be unstable as well as those which have small values. The result tends to move towards an orthogonal set of variables which can be processed by the OLS method. In addition, ridge regression can be used as a means of analysis by creating additional data with values of k increasing from zero to one.