Russel-Research-Method-in-Anthropology

662 Chapter 21
score for y if the dependent variable were zero. We have another coefficient,
called b, that tells by how much to multiply the score on the independent variable
for each unit change in that variable.
The general form of the equation (from chapter 20, formula 20.19) is:
y a bx
which means that the dependent variable, y, equals some constant plus another
constant times the independent variable, x. So, for example, a regression equation
like:
Starting Annual Income $22,000 ($4,000 Years of College)
predicts that, on average, people with a high school education will start out
earning $22,000 a year; people with a year of college will earn $26,000; and
so on. A person with nine years of university education (say, someone who
has a Ph.D.) would be predicted to start at $58,000:
Starting Annual Income $22,000 ($4,000 9) $58,000
Now suppose that the average starting salary for someone who has a Ph.D.
is $65,000. Several things could account for the discrepancy between our prediction
and the reality. Sampling problems, of course, could be the culprit. Or
it could be that there is just a lot of variability in starting salaries of people
who have the Ph.D. English teachers who go to work in small, liberal arts
colleges might start at $40,000, while people who have a Ph.D. in finance and
who go to work for major brokerage companies might start at $150,000.
No amount of fixing the sample will do anything to get rid of the variance
of starting salaries. In fact, the better the sample, the better it will reflect the
enormous variance in those salaries.
In simple regression, if starting salary and years of education are related
variables, we want to know ‘‘How accurately can we predict a person’s starting
salary if we know how many years of education they have beyond high
school?’’ In multiple regression, we build more complex equations that tell us
how much each of several independent variables contributes to predicting the
score of a single dependent variable.
A typical question for a multiple regression analysis might be ‘‘How well
can we predict a person’s starting salary if we know how many years of college
they have, and their major, and their gender, and their age, and their ethnic
background?’’ Each of those independent variables contributes something
to predicting a person’s starting salary after high school.
The regression equation for two independent variables, called x 1 and x 2 , and
one dependent variable, called y, is:
y a b 1 x 1 b 2 x 2 Formula 21.3