Our contribution in this work is to set the directions for specialized econometric computations in a free computer algebra system, Xcas. We focus on the programming of a routine dedicated to correlation criteria for multiple regression models. We program several operations for detecting and evaluating collinearity by applying the diagnostic techniques of linear regression analysis. In order to illustrate the computational performance of our Xcas codes, we repeat most of the analysis carried out in widely used commercial software, along with some extra statistics. Xcas could constitute a supplemental tool in a collinear data study. Its use is proposed complementary to established econometric software or as substitute software.

Programming Correlation Criteria with free CAS Software

We have shown hot to treat consistently a set of rapidly mixing particles. It is possible to devise various dissipative transformations and then correct them to conserve the mass, centers of mass and velocity, and especially the total angular momentum. Furthermore, for simple linear friction laws it is possible to specify in advance the energy dissipation. In that case the conservation of the other integrals constraints the energy loss not exceed a maximum value.

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Mixing transformations of N particles conserving almost all classical integrals

Our contribution in this work is to set the directions for specialized econometric computations in a free computer algebra system, Xcas. We focus on the programming of a routine dedicated to correlation criteria for multiple regression models. We program several operations for detecting and evaluating collinearity by applying the diagnostic techniques of linear regression analysis. Xcas could constitute a supplemental tool in a collinear data study. Its use is proposed complementary to established econometric software or as substitute software.

Measures of correlation and computer algebra

Problems in data analysis, electrical networks, and finite element methods often involve linear models having singular, square matrices or matrices which are not square. The concept of generalized inverse extends the ranges of application of the notion of matrix inverse to such matrices and provides powerful mathematical tools for handling them. The use of symbolic generalized inverses during the analyses of these problems is equally powerful but requires more manipulation than can be reasonably performed by a human analyst. In this paper, the symbolic calculation of the Moore-Penrose generalized inverse, based on Albert’s limit formulation, will be expressed in Macsyma and examples of its use will be given. In particular, the computer derivation of a novel form of the generalized inverse of a covariance matrix typically used in statistical analysis will be shown.

W. J. Frawley

Papers

Computer Generation of Symbolic Generalized Inverses and Applications to Physics and Data Analysis