Sample Size in Multiple Regression Models: A simulation study

Abstract

The aim of the research is to study the efficiency of the following indicators of the multiple regression model, i.e., the value of "F", R2, Adj., R2, Standard Beta B, Unstandard Beta B, and EMS, in the light of different sample sizes using three methods of multiple regression (standard – gradual – hierarchical). The descriptive method was used. The research community consisted of a virtual community that simulates reality, and it was obtained through the simulation method. It consists of 500 items, created using Mics. Excel program, which are observations that represent one dependent variable denoted by the symbol (Y), and five independent variables, coded (X1, X2, X3, X4, X5), with the aim of evaluating the efficiency of the indicators of multiple regression models (standard - progressive - hierarchical), in light of the different number of samples, range from (10 ≤ n ≥ 500). It was noticed that the conditions of multiple regression were not available in samples less than 50, so the indicators of regression models were studied with sample numbers ranging from (50 to 500). The results indicated that all the multiple regression models indicators increase and improve with increasing the number of the sample, and the best estimate for the regression models was when (n = 225), at a rate of (45) for each independent variable, as the value of R2 was (43%), and was equal to the value of the modified R2, and it was All indicators are good, and by increasing the sample from that, and until reaching the entire population (n=500), the percentage of improvement in the indicators was small, and the value of R2 was (45%). The results also indicated that there is no reliance on only one indicator to judge the quality of the multiple regression models, as well as the difference in the efficiency of the indicators according to the number of the sample, and the statistical method used, especially in the number of small samples. The study recommended using large samples in multiple regression studies, relying on more than one indicator to know the efficiency of regression models, and taking into account the regression method used according to the importance of the researcher's variables.