Russel-Research-Method-in-Anthropology

Multivariate Analysis 663
which means that we need to find a separate constant—one called b 1 and one
called b 2 —by which to multiply each of the two independent variables. The
general formula for multiple regression is:
y a b 1 x 1 b 2 x 2 ... b n x n Formula 21.4
Recall that simple regression yields a PRE measure, r 2 . It tells you how much
better you can predict a series of measures of a dependent variable than you
could by just guessing the mean for every measurement. Multiple regression
is also a PRE measure. It, too, tells you how much better you can predict measures
of a dependent variable than you could if you guessed the mean—but
using all the information available in a series of independent variables.
The key to regression are those b coefficients, orweights, in Formula 21.4.
We want coefficients that, when multiplied by the independent variables, produce
the best possible prediction of the dependent variable—that is, we want
predictions that result in the smallest possible residuals. Those coefficients,
by the way, are not existential constants. Remember that samples yield statistics,
which only estimate parameters. Your statistics change with every sample
you take and with the number of independent variables in the equation.
The MVD-TEENBIRTH Puzzle
Let’s try to solve the puzzle of the relation between teenage births and the
rate of motor vehicle deaths. We can take a stab at this using multiple regression
by trying to predict the rate of teenage births without the data from motor
vehicle deaths.
From our previous analyses with elaboration tables and with partial correlation,
we already had an idea that income might have something to do with the
rate of teen births. We know from the literature (Handwerker 1998) that poverty
is associated with violence and with teenage pregnancy, and that this is
true across ethnic groups, so I’ve added a variable on violent crimes that I
think might be a proxy for the amount of violence against persons in each of
the states.
Table 21.16 shows the correlation matrix for four variables: TEENBIRTH
(the percentage of births to teenagers in the 50 U.S. states during 1996);
INCOME (the mean per capita income for each of the 50 states during 1996);
VIOLRATE (the rate of violent crime—rape, murder, assault, and robbery—
per 100,000 population in the 50 states in 1995); and MVD (the number of
motor vehicle deaths per 100 million vehicle miles in each of the 50 states in
1995).
We see right away that the mean per capita income predicts the rate of births
to teenagers (r .700) almost as well as does the rate of motor vehicle