Abstract
Multiple Linear Regression is a classic example of the regression analysis.
When sample size is large enough and when there are no multi-collinearity among independent variables, Multiple Linear Regression is the excellent method. When data do not meet the condition mentioned above, Multiple Linear Regression does not provide a solution or may not give a stable solution. Several methods have been proposed to overcome the deficiency of Multiple Linear Regression. T-method（ 1） is one of them. Since T-method uses single regression, it is free from multi-collinearity problem, but the performance is not necessarily better than Multiple Linear Regression.
This paper describes a new method based on the idea of T-method（ 1） to improve the performance. The new method uses single regression and repeats it until the estimation settles the best. Thus this method is named Multiple Single Regression. The numerical simulation revealed that Multiple Single Regression is superior to Multiple Linear Regression, T-Method（ 1）, Principal Component Regression, and Partial Least Squares.
