Multiple
Regression v. Canonical Correlation |

- Consider the standard linear model
for multiple regression, in which a single variable (Y)
is a function of multiple independent variables
(x
_{i}):- Y =
b
_{1}*x_{1}+ b_{2}*x_{2 }+ ... + b_{q}x_{q}
- Y =
b
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: _{1}*y_{1
}+ a_{2}*y_{2 }+ ... +
a_{p}y_{p } = b_{1}*x_{1} +
b_{2}*x_{2 }+ ... +
b_{q}x_{q} |