Russel-Research-Method-in-Anthropology

664 Chapter 21
TABLE 21.16
Correlation Matrix for Variables Associated with the Percentage of
Teenage Births in the United States
TEENBIRTH INCOME VIOLRATE MVD
TEENBIRTH 1.00
INCOME .700 1.00
VIOLRATE .340 .190 1.00
MVD .778 .662 .245 1.00
deaths (r .778), and that mean income also predicts the rate of motor
vehicle deaths rather well (r .662).
This is a clue about what might be going on: An antecedent variable, the
level of income, might be responsible for the rate of motor vehicle deaths and
the rate of teenage births. (By the way, did you notice that the strong correlations
above were negative? The greater the mean income in the state, the lower
the rate of teenage births and the lower the rate of motor vehicle deaths.
Remember, correlations can vary from 1.0 to 1.0 and the strength of the
correlation has nothing to do with its direction.)
And one more thing: The rate of violent crimes against people is moderately
correlated with the rate of teenage births (r .340), but is only weakly correlated
with the mean income (r .190) and with the rate of motor vehicle
deaths (r .245).
The task for multiple regression is to see how the independent variables
predict the dependent variable together. If the correlation between mean per
capita income and the rate of births to teenagers is .700, that means that the
independent variable accounts for 49% (.700 2 ) of the variance in the dependent
variable. And if the correlation between the rate of violent crimes and the
rate of births to teenagers is .340, then the independent variable accounts for
11.56% (.340 2 ) of the variance in the dependent variable.
We can’t just add these variances-accounted-for together, though, because
the two independent variables are related to each other—each of the independent
variables accounts for some variance in the other.
Table 21.17 shows what the output looks like from SYSTAT when I asked
the program to calculate the multiple correlation, called R, for INCOME and
VIOLRATE with TEENBIRTH as the dependent variable.
Table 21.17 tells us that the regression equation is:
TEENBIRTH 28.096(.006VIOLRATE)(.001INCOME)
For example, the violence rate for Wisconsin was 281 crimes per 100,000
residents in 1995 and the average income in Wisconsin was $21,184 in 1996.