# Partial Correlation

Partial correlation is the measure of association between two variables, while controlling or adjusting the effect of one or more additional variables.  Partial correlations can be used in many cases that assess for relationship, like whether or not the sale value of a particular commodity is related to the expenditure on advertising when the effect of price is controlled. What is the relationship between test scores and GPA scores after controlling for hours spent studying?

After controlling for age, what is the relationship between Z drugs with XY symptoms?

In SPSS, this test can be computed by selecting “correlate” from the analyze menu, and then selecting “partial” from the correlate.

The control variables are the variables which extract the variance which is obtained from the initial correlated variables.

The order of correlation refers to the correlation with control variables.  For example, first order is the one which has a single control variable.

The spurious correlation refers to that type of correlation that is false or the correlation that actually didn’t exist.

Similarly related, semi partial correlations  measure the association between the dependent variable (Y) and independent variable (X),after controlling for one aspect on only one variable (X or Y, but not both).

For small models like models with one control variable or sometimes with two or three, partial correlation is useful and is quite common, it is generally helpful in detecting a false relationship model.

Assumptions

Useful in only small models like the models which involve three or four variables.

Used in only those models which assume a linear relationship.

The data is supposed to be interval in nature.

The residual variables or unmeasured variables are not correlated with any of the variables in the model, except for the one for which these residuals have occurred.