compares the unique variation of one variable to the unique variation of the other. The semipartial correlation can be viewed as more practically relevant "because it is scaled to (i.e., relative to) the total variability in the dependent (response) variable." Conversely, it is less theoretically useful because it is less precise about the role of the unique contribution of the independent variable. The absolute value of the semipartial correlation of X with Y is always less than or equal to that of the partial correlation of X with Y. The reason is this: Suppose the correlation of X with Z has been removed from X, giving the residual vector ex . In computing the semipartial correlation, Y still contains both unique variance and variance due to its association with Z. But ex , being uncorrelated with Z, can only explain some of the unique part of the variance of Y and not the part related to Z. In contrast, with the partial correlation, only ey (the part of the variance of Y that is unrelated to Z) is to be explained, so there is less variance of the type that ex cannot explain. Use in time series analysis In time series analysis, the partial autocorrelation function (sometimes "partial correlation function") of a time series is defined, for lag , as This function is used to determine the appropriate lag length for an autoregression. See also Linear regression Conditional independence Multiple correlation References External links Mathematical formulae in the "Description" section of the IMSL Numerical Library PCORR routine A three-variable example Covariance and correlation Autocorrelation Articles with example R code