Pages: 201-212
Published: 30.04.2018
Abstract: The inverse model of multiple linear regression analysis (IM MLRA) is worked up in the article. Theorem is proved about of n z-variables of multidimensional (IM MLRA)-sample. The values of n z-variables located in the n columns of matrix Zmn The rank of this matrix is equal to n-1. The new inverse problem of multiple linear regression analysis (IP МLRА) is solved with the use of Inverse Model of Principal Component Analysis (IМ PCA[4]) statistical modeling of the n correlated z-variables satisfying IМ МLRА to all equations and mathematical relations. A new inverse problem of multiple linear regression analysis (IP MLRA) of statistical modeling of n correlated z-variables (n-1 independent, 1 dependent) that satisfy all the equations and relations of the IM MLRA is solved. The input parameter of the MZPM is the vector =(1,..., n-1) T of the regression coefficients for n-1 independent z-variables. A theorem on n z-variables of a multidimensional sample of IM MLRA is proved with values located in n columns of the matrix Zmn of rank n-1. Numerical algorithms have been tested using the example of modeling a multidimensional -sample of z-variables from OM MLRA (for n=4). The known vector =(1, 2, 3) T of the regression coefficients from the article [1] is used. The obtained model data are adequate for the values of given statistics of a real multidimensional sample.
Key words: inverse model of multiple linear regression analysis
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