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JMP 12 Multivariate Methods by SAS Institute

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Chapter 7 
Partial Least Squares Models
Develop Models Using Correlations between Ys and Xs
The Partial Least Squares (PLS) platform fits linear models based on factors, namely, linear combinations of the explanatory variables (Xs). These factors are obtained in a way that attempts to maximize the covariance between the Xs and the response or responses (Ys). PLS exploits the correlations between the Xs and the Ys to reveal underlying latent structures.
Partial least squares performs well in situations such as the following, where the use of ordinary least squares does not produce satisfactory results: More X variables than observations; highly correlated X variables; a large number of X variables; several Y variables and many X variables.
Figure 7.1 ...

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