Russel-Research-Method-in-Anthropology

Multivariate Analysis 661
You can also work out and test a model of how several independent variables
influence a dependent variable all at once. This is the task of multiple regression,
which we’ll take up next. (For more on partial correlation, see Gujarati
2003.)
Multiple Regression
Partial correlation tells us how much a third (or fourth . . .) variable contributes
to the relation between two variables. Multiple regression puts all the
information about a series of variables together into a single equation that
takes account of the interrelationships among independent variables. The
result of multiple regression is a statistic called multiple-R, which is the combined
correlation of a set of independent variables with the dependent variable,
taking into account the fact that each of the independent variables might be
correlated with each of the other independent variables.
What’s really interesting is R 2 . Recall from chapter 20 that r 2 —the square
of the Pearson product moment correlation coefficient—is the amount of variance
in the dependent variable accounted for by the independent variable in a
simple regression. R 2 ,ormultiple-R squared, is the amount of variance in
the dependent variable accounted for by two or more independent variables
simultaneously.
Now, if the predictors of a dependent variable were all uncorrelated with
each other, we could just add together the pieces of the variance in the dependent
variable accounted for by each of the independent variables. That is, it
would be nice if R 2 r 12 r 22 r 32 ...
It’s a real nuisance, but independent variables are correlated with one
another. (This interdependence among independent variables is called multicollinearity,
which we’ll discuss in depth later.) What we need is a method
for figuring out how much variance in a dependent variable is accounted for
by a series of independent variables after taking into account all of the overlap
in variances accounted for across the independent variables. That’s what multiple
regression does.
The Multiple Regression Equation
We covered basic regression in chapter 20, but just to bring you back up to
speed, remember that in simple regression we use an equation that expresses
how an independent variable is related to a dependent variable. On the lefthand
side of the equation, we have the unknown score for y, the dependent
variable. On the right-hand side, we have the y-intercept, called a. It’sthe