Russel-Research-Method-in-Anthropology

624 Chapter 20
TABLE 20.14
Infant Mortality by TFR for 10 Countries from Table 19.8
INFMORT
TFR
State x y
Armenia 26 1.70
Chad 112 6.07
El Salvador 32 3.17
Ghana 66 5.15
Iran 35 2.80
Latvia 18 1.25
Namibia 65 4.90
Panama 21 2.63
Slovenia 7 1.26
Suriname 29 2.21
Mean of x 41.10 Mean of y 3.114
countries. Your best guess—your lowest prediction error—would be the mean,
3.114 children per woman. You can see this in figure 20.4 where I’ve plotted
the distribution of TFR and INFMORT for the 10 countries in table 20.14.
The Sums of the Squared Distances to the Mean
Each dot in figure 20.4 is physically distant from the dotted mean line by a
certain amount. The sum of the squares of these distances to the mean line is
the smallest sum possible (that is, the smallest cumulative prediction error you
could make), given that you only know the mean of the dependent variable.
The distances from the dots above the line to the mean are positive; the distances
from the dots below the line to the mean are negative. The sum of the
actual distances is zero. Squaring the distances gets rid of the negative numbers.
But suppose you do know the data in table 20.14 regarding the infant mortality
rate for each of those 10 countries. Can you reduce the prediction error
in guessing the TFR for those countries? Could you draw another line through
figure 20.4 that ‘‘fits’’ the dots better and reduces the sum of the distances
from the dots to the line?
You bet you can. The solid line that runs diagonally through the graph in
figure 20.4 minimizes the prediction error for these data. This line is called
the best fitting line, or the least squares line, or the regression line. When
you understand how this regression line is derived, you’ll understand how correlation
works.