Correlation, Variance and Covariance (Matrices)

var, cov and cor compute the variance of x and the covariance or correlation of x and y if these are vectors.
cov2cor scales a covariance matrix into the corresponding correlation matrix efficiently.
var(x, y = NULL, na.rm = FALSE, use)
cov(x, y = NULL, use = 'everything', method = c('pearson', 'kendall', 'spearman'))
cor(x, y = NULL, use = 'everything', method = c('pearson', 'kendall', 'spearman'))
cov2cor(V)

Examples
----------
var(1:10) # 9.166667
var(1:5, 1:5) # 2.5

## Two simple vectors
cor(1:10, 2:11) # == 1

## Correlation Matrix of Multivariate sample:
(Cl <- cor(longley))

## Graphical Correlation Matrix:
symnum(Cl) # highly correlated

## Spearman's rho and Kendall's tau
symnum(clS <- cor(longley, method = 'spearman'))
symnum(clK <- cor(longley, method = 'kendall'))

## How much do they differ?
i <- lower.tri(Cl)
cor(cbind(P = Cl[i], S = clS[i], K = clK[i]))

## cov2cor() scales a covariance matrix by its diagonal to become the correlation matrix.
cov2cor # see the function definition {and learn ..}
stopifnot(all.equal(Cl, cov2cor(cov(longley))), all.equal(cor(longley, method = 'kendall'), cov2cor(cov(longley, method = 'kendall'))))

##--- Missing value treatment:

C1 <- cov(swiss)
range(eigen(C1, only.values = TRUE)$values) # 6.19 1921

## swM := 'swiss' with 3 'missing's :
swM <- swiss
colnames(swM) <- abbreviate(colnames(swiss), min=6)
swM[1,2] <- swM[7,3] <- swM[25,5] <- NA # create 3 'missing'

## Consider all 5 'use' cases :
(C. <- cov(swM)) # use='everything' quite a few NA's in cov.matrix

try(cov(swM, use = 'all')) # Error: missing obs...
C2 <- cov(swM, use = 'complete')

stopifnot(identical(C2, cov(swM, use = 'na.or.complete')))

range(eigen(C2, only.values = TRUE)$values) # 6.46 1930

C3 <- cov(swM, use = 'pairwise')

range(eigen(C3, only.values = TRUE)$values) # 6.19 1938

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