It is well known that OLS estimates of parameters are unstable when the vectors of the
explanatory variables are multicollinear. Multicollinearity refers to the situation where the
explanatory variables are not orthogonal. In addition to the problem of estimation, multicollinearity
makes misleading or erroneous inferences on: identifying the relative effects
of the explanatory variables; prediction; and selection of an appropriate set of variables for
the model, etc.
Hoerl & Kennard (1970) have demonstrated that some of these undesirable effects of
multicollinearity can be reduced by using ‘ridge’ estimates in place of the least squares
estimates. The ridge estimates depend on a parameter, k that is determined by the data
in practice. Several mechanical rules and a graphical procedure, known as the ridge
trace, have been proposed for the selection of k.