Russel-Research-Method-in-Anthropology

666 Chapter 21
The contribution of this correlation to the variance of TEENBIRTH is
.481776 2 , or .23211. INCOME accounts for 49% of the variance in TEEN-
BIRTH. Adding contributions, we get .49 .23211, or 72.2%, which is the
squared multiple-R in table 21.17.
There are three coefficients in the regression equation: a, b 1 , and b 2 . These
are the coefficients in formula 21.3. Each of the b coefficients is the product
of the standardized regression coefficient for each independent variable with
the ratio of the standard deviation of the independent variable to the standard
deviation of the dependent variable.
The standardized coefficient for the relation between (TEENBIRTH) and
(INCOME) is:
b(x 1 x 2 ) r 12 (r 13 )(r 23 )
1 (r 23 ) 2
for INCOME (x 2 ),b .793
for VIOLRATE (x 3 ),b .491
These figures are given in table 21.17 as the ‘‘Std. Coef,’’ or standardized
coefficients.
and:
The SD for the mean of INCOME is: 3,074,969
The SD for the mean of TEENBIRTH is: 3.399
The SD for the mean of VIOLRATE is: 269.225
Thus:
b 1 (.793)(3,074.969)/3.399 .001
b 2 (.491)(269.225)/3.399 .006
These figures, and b 1 and b 2 , are given in table 21.17 as the ‘‘Coefficients,’’
and are the unstandardized regression coefficients. The method for calculating
the value for a in the multiple regression equation is beyond the scope
of this book. (For more about deriving multiple regression equations, consult
Pedhazur [1997] or Gujarati [1995].)
But there’s more. If we add up the variances accounted for by the zeroorder
correlations of INCOME and VIOLRATE on TEENBIRTH, we get 49%
11.56% 60.56%. According to the results in table 21.17, however, the
income in a state and the rate of violent crimes together account for 72.2% of
the variance in teenage births. In other words, the two variables acting together
account for more than they do separately, and this is the case despite the fact
that the independent variables are moderately correlated (r .340) with each
other.