g02bw calculates a matrix of Pearson product-moment correlation coefficients from sums of squares and cross-products of deviations about the mean.

# Syntax

C# |
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public static void g02bw( int m, double[] r, out int ifail ) |

Visual Basic |
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Public Shared Sub g02bw ( _ m As Integer, _ r As Double(), _ <OutAttribute> ByRef ifail As Integer _ ) |

Visual C++ |
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public: static void g02bw( int m, array<double>^ r, [OutAttribute] int% ifail ) |

F# |
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static member g02bw : m : int * r : float[] * ifail : int byref -> unit |

#### Parameters

- m
- Type: System..::..Int32
*On entry*: $m$, the number of variables.*Constraint*: ${\mathbf{m}}\ge 1$.

- r
- Type: array<System..::..Double>[]()[][]An array of size [$\left({\mathbf{m}}\times {\mathbf{m}}+{\mathbf{m}}\right)/2$]
*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 $k$, $k\ge j$, is stored in ${\mathbf{r}}\left[\left(k\times \left(k-1\right)/2+j\right)-1\right]$.*On exit*: Pearson product-moment correlation coefficients.These are stored packed by column corresponding to the input cross-products.

- ifail
- Type: System..::..Int32%
*On exit*: ${\mathbf{ifail}}={0}$ unless the method detects an error or a warning has been flagged (see [Error Indicators and Warnings]).

# Description

g02bw 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 g02bu or a series of calls to g02bt. The sums of squares and cross-products are stored in an array packed by column and are overwritten by the correlation coefficients.

Let ${c}_{jk}$ be the cross-product of deviations from the mean, for $\mathit{j}=1,2,\dots ,m$ and $\mathit{k}=j,\dots ,m$, then the product-moment correlation coefficient, ${r}_{jk}$ is given by

$${r}_{jk}=\frac{{c}_{jk}}{\sqrt{{c}_{jj}{c}_{kk}}}\text{.}$$ |

# References

None.

# Error Indicators and Warnings

**Note:**g02bw may return useful information for one or more of the following detected errors or warnings.

Errors or warnings detected by the method:

- ${\mathbf{ifail}}=1$
On entry, ${\mathbf{m}}<1$.

- ${\mathbf{ifail}}=2$
- A variable has a zero variance. All correlations involving the variable with zero variance will be returned as zero.

# Accuracy

# Parallelism and Performance

None.

# Further Comments

g02bw 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 methods in this chapter.