Russel-Research-Method-in-Anthropology

628 Chapter 20
TABLE 20.16
Regression Predictions for the Dependent Variable in Table 20.14
where the infant
and compare that
For the mortality rate in predict that the to the actual TFR
country of 2000 was TFR will be in table 19.8
Armenia 26 1.018.051(26)2.344 1.70
Chad 112 1.018.051(112)6.730 6.07
El Salvador 32 1.018.051(32)2.650 3.17
Ghana 66 1.018.051(66)4.384 5.15
Iran 35 1.018.051(35)2.803 2.80
Latvia 18 1.018.051(18)1.936 1.25
Namibia 65 1.018.051(65)4.333 4.90
Panama 21 1.018.051(21)2.089 2.63
Slovenia 7 1.018.051(7)1.375 1.26
Suriname 29 1.018.051(29)2.497 2.21
which is the difference between the predicted number for the dependent variable
and the actual measurement. This is also called the residual—that is,
what’s left over after making your prediction using the regression equation.
(To anticipate the discussion of multiple regression in chapter 21: The idea in
multiple regression is to use two or more independent variables in order to
reduce the size of the residuals.)
You’ll recall from chapter 19, in the section on variance and the standard
deviation, that in the case of the mean, the total variance is the average of the
2
squared deviations of the observations from the mean,xx/n. In the
case of the regression line predictors, the variance is the sum of the squared
deviations from the regression line. Table 20.17 compares these two sets of
errors, or variances, for the data in table 20.14.
We now have all the information we need for a true PRE measure of association
between two interval variables. Recall the formula for a PRE measure:
the old error minus the new error, divided by the old error. For our example
in table 20.14:
PRE 26.1362.890
26.136
.889
In other words: The proportionate reduction of error in guessing the TFR
in table 20.14—given that you know the distribution of informant mortality
rates and can apply a regression equation—compared to just guessing the
mean of TFR is .889, or about 89%.