- Consider the standard linear model
for multiple regression, in which a single variable (Y)
is a function of multiple independent variables
(xi):
- Y =
b1*x1 +
b2*x2 + ... +
bqxq
Suppose that the dependent variable, Y,
is an attitudinal variable such as "Satisfaction with
Life."
- Why are some people are more
satisfied with their lives than others?
You theorize that one's happiness depends on one's
socioeconomic status, usually measured by
- income
education
occupational prestige
Normally, these three variables do not
incorrelate sufficiently to form a reliable
scale.
- So you treat them as independent
variables predicting to Life Satisfaction in a regression
equation.
Research, however, shows that
"satisfied" people often lead "dull" not "exciting"
lives.
- You could treat "Excitement in Life"
as a dependent variable and run another regression
equation.
Then you would compare the equations and the
coefficients.
-
- Alternatively, you could seek to
explain "Happiness in Life" measured by both
variables:
- satisfaction
excitement
This reconceptualization of the research
fits canonical analysis, which computes the maximum
correlation between two sets of variables:
a1*y1
+ a2*y2 + ... +
apyp = b1*x1 +
b2*x2 + ... +
bqxq
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