FEATURES OF THE ORDINARY LEAST SQUARE (OLS) METHOD. IMPLICATIONS FOR THE ESTIMATION METHODOLOGY

The ordinary least square method (OLS) is frequently used for the parameters estimation of different functional relationships. Having in view a series of properties revealed by the author, this paper presents the factors that determine the size of the estimated parameters and coefficients of determination, and also the calculated values of the Fisher test, used for validation and of the Student test, used for assessing the relevance of each estimated parameter. The cases of unifactorial linear regression and that of multifactorial linear regression are presented. A special attention is paid to bifactorial linear regression, because in this way one may emphasize, with a small volume of computations, the correlations between the parameters’ estimated values and some indicators that test the relevance of the obtained results can be emphasized. Also, the impact of multicolinearity on values of estimated parameters is revealed with the help of alignment coefficient. In the end, a methodology for the acceptation of a new explanatory variable in a linear regression model is proposed.