**Coefficient of Determination**

R^{2} is the __ coefficient
of determination__, or the squared value of the correlation coefficient or multiple
correlation coefficient. Simply, this is the proportion of the variation of the dependent
variable that is ‘explained’ by the total set of independent variables that are
used in the model (if the model is well built). Usually this explained proportion is not
as high as 30 or 40 percent (.3 to .4) in most models, for any set of variables.

Remember that the proportion of variation in the model explained by an independent variable may be reduced as other independent variables are added to the model. This might mean that the other factors are confounders for the model of interest, so that it is both influencing the outcome and the determining variable of interest. The new variable may also be an intermediate variable between the independent variable of interest and the outcome. This will be discussed later in this section on the topic of confounding.