Some thoughts on regression and prediction. Part I

Abstract

The paper reviews some of the applications of the regression technique and points out possible pitfalls associated with them. Examples are given to show that the regression method can lead to misleading results in the disaggregation problem. Multicollinearity has been defined with special reference to the precision of prediction in the domain of interest of explanatory variables rather than high interdependence among them. Precision of prediction in certain directions of the vector of explanatory variables may be extremely good although the variables are highly correlated among themselves. The effects of multicollinearity have been studied in detail, including the case where the explanatory variables are subject to errors of observations. Estimation of the regression function has been considered when both the dependent and explanatory variable by inverse regression is more useful than that by direct regression.