STUDY OF REGRESSION MODELS WITHOUT A FREE TERM

Abstract

Purpose. The aim of the article is to use the analogue of the coefficient of determination of multiple regression for a classical regression model without a free term and constructing the appropriate Fisher and Student statistics for econometric analysis. Methodology of research. Methods of general scientific and empirical techniques based on a systemic approach were used in the process of research. In addition, the following methods of scientific knowledge were used to solve the tasks: methods of analysis and observation - to identify the main social factors influencing the level of crime; methods of matrix theory, theory of probabilities and mathematical statistics - for checking the laws of distribution of random variables, building criteria for the significance of the regression equation and its coefficients. Findings. It was studied how the absence of a free term in multiple linear regression affects the Student and Fisher statistics when studying the significance of regression coefficients and the regression equation as a whole, respectively. The obtained results indicate that the introduced definitions affect the adjusted coefficient of multiple regression and the F-statistic, but do not change the standard error of the regression, including the Student's statistics. The need to calculate qualitative indicators of regression models in accordance with derived formulas and algorithms, and to be critical of the final numerical results obtained when using computer statistical packages, is substantiated. Originality. A comprehensive study of linear regression models was conducted, which takes into account the effect of the absence of a free term when evaluating the quality of empirical models. Practical value. The obtained research results allow avoiding calculation errors and acceptance of implausible conclusions, which occur in the practice of qualitative analysis of linear regression models without a free term. Key words: multiple regression model, free term, method of least squares, Student's test, Fisher's test.