Collinearity and numerical instabilities in numerical solution of linear models

In this paper we give the expression of the multiple correlation coefficient in a linear model according to the coefficients of correlation. This expression makes it possible to analyze from a numerical point of view the instability of estimates in the case of collinear explanatory variables in the linear model or in the autoregressive model. This numerical approach, that we show on two examples, thus supplements the usual approach of the quasi collinearity, founded on the statistical properties of the estimators.