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Regression equation

The correlation coefficient is a single number that summarizes the association between two variables. If two variables are so related, it means that when one changes by a unit amount, the other changes on average by that certain amount.

For instance, a $1 increase in compensatory damage awards might on average lead to a $1 increase in punitive awards (or to a 50 cent increase or to a $2 increase). If Y represents the variable being explained (usually called the dependent variable) and X represents the variable that is believed to influence Y (usually called the independent variable), this relationship is described as the regression of Y on X. In this context, regression implies that the average value of Y relates to, or is a function of, X.

The relationship can be represented by an equation called the regression equation:

Y = bX + c

Equation (2)

or, in our example,

punitive damages = (b times compensatory damages) + c.

The regression equation can then be graphed, using b as the slope of the line and c as the intercept. Many computer programs, spreadsheets, and even hand calculators can compute the regression equation for a given data set.