A new approach to finding relevant components in linear regression

This paper contains some remarks on the so-called “relevant subspaces” useful when data reduction, near-collinearity of prediction problems are to be dealt with. The presentation is mainly based on a geometrical point of view. The consequences of relevant subspaces on the most common linear regression methods are analysed and a new method is developed to extract relevant subspaces. An experiment based on simulations is proposed to verify if the forecasting ability of some regression methods is influenced by relevant components.