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