How to do Linear Regression in R Using Partial Least Squared Regression¶

# load data longley data for Econometrics
library(pls)
data(longley)
Data <- as.matrix(longley)

dim(Data)
head(Data)

x <- Data[,1:6]
y <- Data[,7]

# ----------------------------------------
# Using Partial Least Squared Regression
# ----------------------------------------

# fit model
fit <- plsr(Employed~., data=longley, validation="CV")

# summarize the fit
summary(fit)

# make predictions
predictions <- predict(fit, longley, ncomp=6)

# summarize accuracy
mse <- mean((longley$Employed - predictions)^2)
print(mse)

# plot
plot(longley$Employed, predictions)

Data: 	X dimension: 16 6 
	Y dimension: 16 1
Fit method: kernelpls
Number of components considered: 6

VALIDATION: RMSEP
Cross-validated using 10 random segments.
       (Intercept)  1 comps  2 comps  3 comps  4 comps  5 comps  6 comps
CV           3.627    1.455    1.040   0.4751   0.5486   0.5269   0.4641
adjCV        3.627    1.420    1.037   0.4713   0.5382   0.5166   0.4507

TRAINING: % variance explained
          1 comps  2 comps  3 comps  4 comps  5 comps  6 comps
X           63.88    93.35    99.99   100.00   100.00   100.00
Employed    87.91    93.70    98.51    98.65    99.16    99.55
[1] 0.0522765

	GNP.deflator	GNP	Unemployed	Armed.Forces	Population	Year	Employed
1947	83.0	234.289	235.6	159.0	107.608	1947	60.323
1948	88.5	259.426	232.5	145.6	108.632	1948	61.122
1949	88.2	258.054	368.2	161.6	109.773	1949	60.171
1950	89.5	284.599	335.1	165.0	110.929	1950	61.187
1951	96.2	328.975	209.9	309.9	112.075	1951	63.221
1952	98.1	346.999	193.2	359.4	113.270	1952	63.639