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Univariate partial least squares (PLS) is a method of modeling relationships between a Y variable and other explanatory variables. It may be used with any number of explanatory variables, even far more than the number of observations. A simple interpretation is given that shows the method to be a straightforward and reasonable way of forming prediction equations. Its relationship to multivariate PLS, in which there are two or more Y variables, is examined, and an example is given in which it is compared by simulation with other methods of forming prediction equations. With univariate PLS, linear combinations of the explanatory variables are formed sequentially and related to Y by ordinary least squares regression. It is shown that these linear combinations, here called components, may be viewed as weighted averages of predictors, where each predictor holds the residual information in an explanatory variable …