WinCross' Regression starts by selecting the independent variable that is most correlated with y as its initial independent dependent variable. It then uses the adjusted-R2 as its metric and, at each step of the process, selects the independent variable that, when added to those already selected, produces the largest adjusted-R2. It halts when an independent variable is selected whose coefficient is not significantly different from 0 using the appropriate t statistic.
Sometimes these regressions are called “driver analysis,” in that all the independent variables are positively correlated with the dependent variables and the analysts wants to know which of the independent variables “drives” the dependent variable. Multiple regression may produce negative coefficients for some of these variables, even though they are positively correlated with the dependent variable. The reason that happens is that use of some of the independent variables will produce an overestimate of the dependent variable, which can be reduced by including an additional independent variable with a negative coefficient in the regression. WinCross has added the facility to allow the stepwise regression to terminate when an independent variable is introduced and its coefficient is negative.
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