Partial least squares regression is an extension of the multiple linear regression model (see, e.g., Multiple Regression or General Stepwise Regression). In its simplest form, a linear model specifies the (linear) relationship between a dependent (response) variable Y, and a set of predictor variables, the X's, so that
Y = b0 + b1X1 + b2X2 + ... + bpXp
In this equation b0 is the regression coefficient for the intercept and the bi values are the regression coefficients (for variables 1 through p) computed from the data.
ARTICLE: de Jong, S. (1993). SIMPLS: An alternative approach to partial least squares regression. Chemometrics and Intelligent Laboratory Systems, 18: 251-263.