Statistics for People Who (Think They) Hate Statistics

by Neil J. Salkind

X1 is the value of the first independent variable, X2 is the value of the second independent variable, b is the regression weight for that particular variable, and a is the intercept of the regression line, or where the regression line crosses the y-axis. As you may have guessed, this model is called multiple regression (multiple predictors, right?). So, in theory anyway, you are predicting an outcome from two independent variables rather than one. But you want to add additional predictor variables only under certain conditions. Read on. Any variable you add has to make a unique contribution to understanding the dependent variable. Otherwise, why use it? What do we mean by unique? The additional variable needs to explain differences in the predicted variable that the first predictor does not. That is, the two variables in combination should predict Y better than any one of the variables would do alone. In our example, level of participation in extracurricular activities could make a unique contribution. But should we add a variable such as the number of hours each student studied in high school as a third independent variable or predictor? Because number of hours of study is probably highly related to high school GPA (another of our predictor variables, remember?), study time probably would not add very much to the overall prediction of college GPA. We might be better off looking for another variable (such as ratings on letters of recommendation) rather than collecting the...