CHOOSING THE DEPENDENT VARIABLE

When we are computing correlation coefficients it does not matter which variable we plot on the horizontal axis and which we plot on the vertical. The correlation coefficient is exactly the same. That is not usually true for regression. The slope and the intercept will differ depending on which variable is the Y variable in the equation and which is the X variable. Since regression analysis is used to predict values of a dependent variable from values of an independent variable, Y is taken to be the dependent variable and X the independent.

In this example, X is the independent variable and Y is the dependent variable. Although the regression line is a useful summary of the relationship between two variables , the values of the slope and intercept alone do not indicate how well the line actually fits the data. We need some measure of goodness of fit. We know that if the regression line fits the data perfectly , the observed values for the dependent variable equal the predicted values. They all fall exactly on the line. The more poorly the line fits, the more discrepancy we would expect between the line and the actual values.