As might be expected, the number and type of possible relation-
ships among variables becomes quite complex when questions
are asked about a dependent variable and two or more independent
variables. There are, however, four basic issues which apply to
many analytical situations:

1. Can the values of two or more variables be used to predict the
likely values of another variable? For instance, in trying to explain
the overwhelming success of the Republican party in southern New
England during the 1860 presidential election, a historian would
systematically examine which of the chief social and economic
characteristics of the region, such as urbanization or industrializa-
tion, were associated with the Lincoln vote. Therefore, this first
query simply restates the problem of whether or not two variables
are related in the sense discussed in the previous chapter. When
more than one variable may be used to forecast a dependent vari-
able, it is possible to improve predictions of the values of the de-
pendent variable by merely adding the predictive power of all the
independent variables together rather than using just one of them.
Statistics that accomplish this task are often called linear additive
models. In most situations additional independent variables must
be reasonably well correlated with the dependent variable in order
to improve prediction significantly. Moreover, they should not be
highly intercorrelated among themselves so as not to be redundant.
Otherwise, using any one of them would provide about as much
unique information for predicting the dependent variable as em-
ploying all of them. The sole exception to this general rule involves
so-called suppressor variables which actually improve the overall
accuracy of the prediction. They are independent variables, unre-

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