SPURIOUS CORRELATION AND IT'S DETECTION
PARTIAL CORRELATION (DEFINED)
If we think we have a spurious correlation and we think
we know what extraneous variable is causing the problem, we
can control the extraneous variable and see what the "true"
relationship may be between the two variables.
The statistical procedure used for controlling the
extraneous variable is called partial correlation. Partial
correlation yields a single coefficient that can be
interpreted just like a Pearson's correlation coefficient.
The Partial correlation coefficient indicates the strength
and direction of the relationship between two variables when
an extraneous variable is controlled.
CONTROLLING MORE THAN ONE EXTRANEOUS VARIABLE:
In the social sciences, we often have situations where
there are several extraneous independent variables that are
having an effect on the relationship between two variables
that are the focus of our research. For example, if a
researcher was examining the relationship between divorce
rates and suicide rates, they must also consider and control
other extraneous variables such as church membership rates,
population growth, and alcohol use.
The task of controlling three extraneous variables while
examining the relationship between two focus variables can be
accomplished with a procedure called multiple regression.
Multiple regression coefficients indicate the strength
and direction of the relationship between the focus
independent variable and dependent variable while several
other extraneous variables are controlled.
If you have time
series data multiple regression is often inadequate as the
form of the identified relationship may be flawed as there may be a need to include lags. The
estimated parameters are usually biased by omitted noise structure both
in terms of ARIMA structure and Intervention Variables evidenced
by movements in the mean of the errors.
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