cor {base}

R Documentation

Correlation, Variance and Covariance (Matrices)

Description

var, cov and cor compute the variance of x and the covariance or correlation of x and y if these are vectors. If x and y are matrices then the covariances (or correlations) between the columns of x and the columns of y are computed.

Usage

var(x, y = NULL, na.rm = FALSE, use)
cor(x, y = NULL, use = "all.obs")
cov(x, y = NULL, use = "all.obs")

Arguments

x	a numeric vector, matrix or data frame.
y	NULL (default) or a vector, matrix or data frame with compatible dimensions to x. The default is equivalent to y = x (but more efficient).
use	an optional character string giving a method for computing covariances in the presence of missing values. This must be (an abbreviation of) one of the strings "all.obs", "complete.obs" or "pairwise.complete.obs".
na.rm	logical. Should missing values be removed?

Details

For cov and cor one must either give a matrix or data frame for x or give both x and y.

var just another interface to cov, where na.rm is used to determine the default for use when that is unspecified. If na.rm is TRUE then the complete observations (rows) are used (use = "complete") to compute the variance. Otherwise (use = "all"), var will give an error if there are missing values.

If use is "all.obs", then the presence of missing observations will produce an error. If use is "complete.obs" then missing values are handled by casewise deletion. Finally, if use has the value "pairwise.complete.obs" then the correlation between each pair of variables is computed using all complete pairs of observations on those variables. This can result in covariance or correlation matrices which are not positive semidefinite.

The denominator n - 1 is used which gives an unbiased estimator of the (co)variance for i.i.d. observations. These functions return NA when there is only one observation, and from R 1.2.3 fail if x has length zero.

Value

For r <- cor(*, use = "all.obs"), it is now guaranteed that all(r <= 1).

See Also

cov.wt for weighted covariance computation, sd for standard deviation (vectors).

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:
data(longley)
(Cl <- cor(longley))
## Graphical Correlation Matrix:
symnum(Cl) # highly correlated

##--- Missing value treatment:
data(swiss)
C1 <- cov(swiss)
range(eigen(C1, only=TRUE)$val) # 6.19  1921
swiss[1,2] <- swiss[7,3] <- swiss[25,5] <- NA # create 3 "missing"
## Not run: 
 C2 <- cov(swiss) # Error: missing obs...

## End(Not run)
C2 <- cov(swiss, use = "complete")
range(eigen(C2, only=TRUE)$val) # 6.46  1930
C3 <- cov(swiss, use = "pairwise")
range(eigen(C3, only=TRUE)$val) # 6.19  1938

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