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

**Components**: LINEAR CORRELATION, MULTIPLE LINEAR REGRESSION, SEMI-PARTIAL CORRELATION

**Tutorial**: en_Tanagra_Semi_Partial_Correlation.pdf

**Dataset**: cars_semi_partial_correlation.xls

**Reference**: M. Brannick, « Partial and Semipartial Correlation », University of South Florida.