NAG Library Function Document

nag_cov_to_corr (g02bwc)

+− Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

+− 10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

1 Purpose

nag_cov_to_corr (g02bwc) calculates a matrix of Pearson product-moment correlation coefficients from sums of squares and cross-products of deviations about the mean.

2 Specification

#include <nag.h>

#include <nagg02.h>

void	nag_cov_to_corr (Integer m, double r[], NagError *fail)

3 Description

nag_cov_to_corr (g02bwc) calculates a matrix of Pearson product-moment correlation coefficients from sums of squares and cross-products about the mean for observations on

m

variables which can be computed by a single call to nag_sum_sqs (g02buc) or a series of calls to nag_sum_sqs_update (g02btc). The sums of squares and cross-products are stored in an array packed by column and are overwritten by the correlation coefficients.

Let

c_{j k}

be the cross-product of deviations from the mean, for

j = 1, 2, \dots, m

and

k = j, \dots, m

, then the product-moment correlation coefficient,

r_{j k}

is given by

r_{j k} = \frac{c_{j k}}{\sqrt{c_{j j} c_{k k}}} .

4 References

None.

5 Arguments

1: m – IntegerInput: On entry: $m$ , the number of variables.

Constraint: $m \geq 1$ .
2: r[ $(m \times m + m) / 2$ ] – doubleInput/Output: On entry: contains the upper triangular part of the sums of squares and cross-products matrix of deviations from the mean. These are stored packed by column, i.e., the cross-product between variable $j$ and $k$ , $k \geq j$ , is stored in $r [(k \times (k - 1) / 2 + j) - 1]$ .

On exit: Pearson product-moment correlation coefficients.
These are stored packed by column corresponding to the input cross-products.
3: fail – NagError *Input/Output: The NAG error argument (see Section 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

NE_BAD_PARAM: On entry, argument $⟨value⟩$ had an illegal value.
NE_INT: On entry, $m = ⟨value⟩$ .
Constraint: $m \geq 1$ .
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
NE_ZERO_VARIANCE: On entry, a variable has zero variance.

7 Accuracy

The accuracy of nag_cov_to_corr (g02bwc) is entirely dependent upon the accuracy of the elements of array r.

8 Parallelism and Performance

Not applicable.

9 Further Comments

nag_cov_to_corr (g02bwc) may also be used to calculate the correlations between parameter estimates from the variance-covariance matrix of the parameter estimates as is given by several functions in this chapter.

10 Example

A program to calculate the correlation matrix from raw data. The sum of squares and cross-products about the mean are calculated from the raw data by a call to nag_sum_sqs (g02buc). The correlation matrix is then calculated from these values.

NAG Library Function Documentnag_cov_to_corr (g02bwc)