Monday, November 10, 2008

Semi-partial correlation

The semi-partial correlation measures the additional information of an independent variable (X), compared with one or several control variables (Z1,..., Zp), that we can used for the explanation of a dependent variable (Y).

We can compute the semi-partial correlation in various ways. The square of the semi-partial correlation can be obtained with the difference between the square of the multiple correlation coefficient of regression Y / X, Z1...,Zp (including X) and the same quantity for the regression Y / Z,...,Zp (without X).

We can also obtain the semi-partial correlation by computing the residuals of the regression X/Z1,...,Zp; then, we compute the correlation between Y and these residuals. In other words, we seek to quantify the relationship between X and Y, by removing the effect of Z on the latter. The semi-partial correlation is an asymmetrical measure.

In this tutorial, we show the different ways for computing the semi-partial correlation.

Keywords: correlation, Pearson's correlation, semi-partial correlation, multiple linear regression
Tutorial: en_Tanagra_Semi_Partial_Correlation.pdf
Dataset: cars_semi_partial_correlation.xls
Reference: M. Brannick, « Partial and Semipartial Correlation », University of South Florida.