How to do Linear Regression in R Using Principal Component Regression

# ---------------------------------------------------------------------------
# How to do Linear Regression in R Using Principal Component 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 Principal Component Regression
# -----------------------------

# fit model
fit <- pcr(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)

# visualise regression
plot(longley$Employed, predictions)

1. 16
2. 7

	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

Data: 	X dimension: 16 6 
	Y dimension: 16 1
Fit method: svdpc
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    1.812    1.294   0.4934   0.5823   0.5596   0.4197
adjCV        3.627    1.771    1.280   0.4881   0.5705   0.5470   0.4085

TRAINING: % variance explained
          1 comps  2 comps  3 comps  4 comps  5 comps  6 comps
X           64.96    94.90    99.99   100.00   100.00   100.00
Employed    78.42    89.73    98.51    98.56    98.83    99.55
[1] 0.0522765