R: Correlation, Variance and Covariance (Matrices)

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"

     C2 <- cov(swiss) # Error: missing obs...

    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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