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The use of modern applied computer programs expands the possibility of multicomponent statistical analysis in materials science. The procedure for applying the method of multiple correlation and regression analysis for the study and modeling of multifactorial relationships of physical characteristics in crystalline structures is considered. The consideration is carried out using single crystals of undoped gallium arsenide as an example. The statistical analysis involved a complex of seven physical characteristics obtained by non-destructive methods for each of 32 points along the diameter of the crystal plate. The data array is investigated using multiple correlation analysis methods. A computational model of regression analysis is built. Based on it, using the programs Excel, STADIA and SPSS Statistics 17.0, statistical data processing and analytical study of the relationships of all characteristics are carried out. Regression relationships are obtained and analyzed in determining the concentration of the background carbon impurity, residual mechanical stresses, and the concentration of the background silicon impurity. The ability to correctly conduct multiple statistical analysis to model the properties of a GaAs crystal is established.  New relationships between the parameters of the GaAs crystal are revealed. It is found that the concentration of the background silicon impurity is related to the vacancy composition of the crystal and the concentration of cents EL2. It is also found that there is no relationship between the silicon concentration and the value of residual mechanical stresses. These facts and the thermal conditions for the formation of point defects during the growth of a single crystal indicate the absence of a redistribution of background impurities during cooling of an undoped GaAs crystal. The use of the multiple regression analysis method in materials science allows not only to model multifactor bonds in binary crystals, but also to carry out stochastic modeling of factor systems of variable composition

Application of multiple correlation analysis method to modeling the physical properties of crystals (on the example of gallium arsenide)