Russel-Research-Method-in-Anthropology

Bivariate Analysis: Testing Relations 627
ues that are farthest apart to maximize the accuracy of the line. For table
20.16, choose Slovenia and Chad:
and
1. For Slovenia, the expected TFR is:
y 1.018 .051(7) 1.375
2. For Chad, the expected TFR is:
y 1.018 .051(112) 6.730
Put a dot on figure 20.4 at the intersection of
x 7, y 1.375
x 112, y 6.730
and connect the dots. That’s the regression line.
The squared deviations (the distances from any dot to the line, squared) add
up to less than they would for any other line we could draw through that graph.
That’s why the regression line is also called the best fitting or the least
squares line.
Suppose we want to predict the dependent variable y (TFR) when the independent
variable x (INFMORT) is 4, as it is in the Czech Republic. In that
case,
y 1.018 .051(4) 1.22
or 1.22 total births during the lifetime of women born between 1995 and 2000
in Czech Republic (the current TFR for the Czech Republic is, in fact, about
1.2). In other words, the regression equation lets us estimate the TFR for infant
mortality levels that are not represented in our sample.
How Regression Works
To give you an absolutely clear idea of how the regression formula works,
table 20.16 shows all the predictions along the regression line for the data in
table 20.14.
We now have two predictors of TFR: (1) the mean TFR, which is our best
guess when we have no data about some independent variable like infant mortality
and (2) the values produced by the regression equation when we do have
information about something like infant mortality.
Each of these predictors produces a certain amount of error, or variance,