cancor {stats} R Documentation

## Canonical Correlations

### Description

Compute the canonical correlations between two data matrices.

### Usage

```cancor(x, y, xcenter = TRUE, ycenter = TRUE)
```

### Arguments

 `x` numeric matrix (n * p1), containing the x coordinates. `y` numeric matrix (n * p2), containing the y coordinates. `xcenter` logical or numeric vector of length p1, describing any centering to be done on the x values before the analysis. If `TRUE` (default), subtract the column means. If `FALSE`, do not adjust the columns. Otherwise, a vector of values to be subtracted from the columns. `ycenter` analogous to `xcenter`, but for the y values.

### Details

The canonical correlation analysis seeks linear combinations of the `y` variables which are well explained by linear combinations of the `x` variables. The relationship is symmetric as ‘well explained’ is measured by correlations.

### Value

A list containing the following components:

 `cor` correlations. `xcoef` estimated coefficients for the `x` variables. `ycoef` estimated coefficients for the `y` variables. `xcenter` the values used to adjust the `x` variables. `ycenter` the values used to adjust the `x` variables.

### References

Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole.

Hotelling H. (1936). Relations between two sets of variables. Biometrika, 28, 321–327.

Seber, G. A. F. (1984). Multivariate Observations. New York: Wiley, p. 506f.

`qr`, `svd`.

### Examples

```pop <- LifeCycleSavings[, 2:3]
oec <- LifeCycleSavings[, -(2:3)]
cancor(pop, oec)

x <- matrix(rnorm(150), 50, 3)
y <- matrix(rnorm(250), 50, 5)
(cxy <- cancor(x, y))
all(abs(cor(x %*% cxy\$xcoef,
y %*% cxy\$ycoef)[,1:3] - diag(cxy \$ cor)) < 1e-15)
all(abs(cor(x %*% cxy\$xcoef) - diag(3)) < 1e-15)
all(abs(cor(y %*% cxy\$ycoef) - diag(5)) < 1e-15)
```

[Package stats version 2.5.0 Index]