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Partial least squares (pls) regression

Partial least squares regression does dimensionality reduction like principal component analysis (see later) and performs regression using these components: 

Code:

> library(pls)
> res = plsr(bwt~., data=bwdf)
> res
Partial least squares regression , fitted with the kernel algorithm.
Call:
plsr(formula = bwt ~ ., data = bwdf)

> summary(res)
Data:   X dimension: 189 9 
        Y dimension: 189 1
Fit method: kernelpls
Number of components considered: 9
TRAINING: % variance explained
     1 comps  2 comps  3 comps  4 comps  5 comps  6 comps  7 comps  8 comps  9 comps
X     96.965    99.78    99.82    99.91    99.94    99.96    99.98    99.99   100.00
bwt    3.487     4.03    17.12    20.15    23.65    24.10    24.26    24.27    24.27

It shows that all the predictors can be combined into 9 components, the first one of which alone explains 97% of variance. However, this component explains only 3.5% of variance of outcome variable bwt. Even all components combined explain only 24% of variance. 


References:
Bjørn-Helge Mevik, Ron Wehrens and Kristian Hovde Liland (2013). pls: Partial Least Squares and Principal Component regression. R package version 2.4-3. http://CRAN.R-project.org/package=pls
 


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