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Chapter Contents
Chapter Introduction
NAG Toolbox

# NAG Toolbox: nag_correg_linregm_service_select (g02ce)

## Purpose

nag_correg_linregm_service_select (g02ce) takes selected elements from two vectors (typically vectors of means and standard deviations) to form two smaller vectors, and selected rows and columns from two matrices (typically either matrices of sums of squares and cross-products of deviations from means and Pearson product-moment correlation coefficients, or matrices of sums of squares and cross-products about zero and correlation-like coefficients) to form two smaller matrices, allowing reordering of elements in the process.

## Syntax

[xbar2, std2, ssp2, r2, ifail] = g02ce(xbar, std, ssp, r, korder, 'n', n, 'm', m)
[xbar2, std2, ssp2, r2, ifail] = nag_correg_linregm_service_select(xbar, std, ssp, r, korder, 'n', n, 'm', m)

## Description

Input to the function consists of:
(a) A vector of means:
 (x1,x2,x3, … ,xn), $(x-1,x-2,x-3,…,x-n),$
where n$n$ is the number of input variables.
(b) A vector of standard deviations:
 (s1,s2,s3, … ,sn). $(s1,s2,s3,…,sn).$
(c) A matrix of sums of squares and cross-products of deviations from means:
 S11 S12 S13 . . . S1n S21 S22 S2n S31 . . . . . . . Sn1 Sn2 . . . . Snn
.
$S11 S12 S13 . . . S1n S21 S22 S2n S31 . . . . . . . Sn1 Sn2 . . . . Snn .$
(d) A matrix of correlation coefficients:
 R11 R12 R13 . . . R1n R21 R22 R2n R31 . . . . . . . Rn1 Rn2 . . . . Rnn
.
$R11 R12 R13 . . . R1n R21 R22 R2n R31 . . . . . . . Rn1 Rn2 . . . . Rnn .$
(e) The number of variables, m$m$, in the required subset, and their row/column numbers in the input data, i1,i2,i3,,im${i}_{1},{i}_{2},{i}_{3},\dots ,{i}_{m}$,
 i ≤ ik ≤ n  for k = 1,2, … ,m (n ≥ 2,m ≥ 1  and  m ≤ n).
New vectors and matrices are output containing the following information:
(i) A vector of means:
 (xi1,xi2,xi3, … ,xim). $(x-i1,x-i2,x-i3,…,x-im).$
(ii) A vector of standard deviations:
 (si1,si2,si3, … ,sim). $(si1,si2,si3,…,sim).$
(iii) A matrix of sums of squares and cross-products of deviations from means:
 Si_1i_1 Si_1i_2 Si_1i_3 . . . Si_1i_m Si_2i_1 Si_2i_2 . Si_3i_1 . . . . . . . Si_mi_1 Si_mi_2 . . . . Si_mi_m
.
$Si1i1 Si1i2 Si1i3 . . . Si1im Si2i1 Si2i2 . Si3i1 . . . . . . . Simi1 Simi2 . . . . Simim .$
(iv) A matrix of correlation coefficients:
 Ri_1i_1 Ri_1i_2 Ri_1i_3 . . . Ri_1i_m Ri_2i_1 Ri_2i_2 . Ri_3i_1 . . . . . . . Ri_mi_1 Ri_mi_2 . . . . Ri_mi_m
.
$Ri1i1 Ri1i2 Ri1i3 . . . Ri1im Ri2i1 Ri2i2 . Ri3i1 . . . . . . . Rimi1 Rimi2 . . . . Rimim .$
Note:  for sums of squares of cross-products of deviations about zero and correlation-like coefficients Sij${S}_{ij}$ and Rij${R}_{ij}$ should be replaced by ij${\stackrel{~}{S}}_{ij}$ and ij${\stackrel{~}{R}}_{ij}$ in the description of the input and output above.

None.

## Parameters

### Compulsory Input Parameters

1:     xbar(n) – double array
n, the dimension of the array, must satisfy the constraint n2${\mathbf{n}}\ge 2$.
xbar(i)${\mathbf{xbar}}\left(\mathit{i}\right)$ must be set to xi${\stackrel{-}{x}}_{\mathit{i}}$, the mean of variable i$\mathit{i}$, for i = 1,2,,n$\mathit{i}=1,2,\dots ,n$.
2:     std(n) – double array
n, the dimension of the array, must satisfy the constraint n2${\mathbf{n}}\ge 2$.
std(i)${\mathbf{std}}\left(\mathit{i}\right)$ must be set to si${s}_{\mathit{i}}$, the standard deviation of variable i$\mathit{i}$, for i = 1,2,,n$\mathit{i}=1,2,\dots ,n$.
3:     ssp(ldssp,n) – double array
ldssp, the first dimension of the array, must satisfy the constraint ldsspn$\mathit{ldssp}\ge {\mathbf{n}}$.
ssp(i,j)${\mathbf{ssp}}\left(\mathit{i},\mathit{j}\right)$ must be set to the sum of cross-products of deviations from means Sij${S}_{\mathit{i}\mathit{j}}$ (or about zero, ij${\stackrel{~}{S}}_{\mathit{i}\mathit{j}}$) for variables i$\mathit{i}$ and j$\mathit{j}$, for i = 1,2,,n$\mathit{i}=1,2,\dots ,n$ and j = 1,2,,n$\mathit{j}=1,2,\dots ,n$.
4:     r(ldr,n) – double array
ldr, the first dimension of the array, must satisfy the constraint ldrn$\mathit{ldr}\ge {\mathbf{n}}$.
r(i,j)${\mathbf{r}}\left(\mathit{i},\mathit{j}\right)$ must be set to the Pearson product-moment correlation coefficient Rij${R}_{\mathit{i}\mathit{j}}$ (or the correlation-like coefficient, ij${\stackrel{~}{R}}_{\mathit{i}\mathit{j}}$) for variables i$\mathit{i}$ and j$\mathit{j}$, for i = 1,2,,n$\mathit{i}=1,2,\dots ,n$ and j = 1,2,,n$\mathit{j}=1,2,\dots ,n$.
5:     korder(m) – int64int32nag_int array
m, the dimension of the array, must satisfy the constraint 1mn$1\le {\mathbf{m}}\le {\mathbf{n}}$.
korder(i)${\mathbf{korder}}\left(\mathit{i}\right)$ must be set to the number of the original variable which is to be the i$\mathit{i}$th variable in the output vectors and matrices, for i = 1,2,,m$\mathit{i}=1,2,\dots ,m$.
Constraint: 1korder(i)n$1\le {\mathbf{korder}}\left(\mathit{i}\right)\le {\mathbf{n}}$, for i = 1,2,,m$\mathit{i}=1,2,\dots ,m$.

### Optional Input Parameters

1:     n – int64int32nag_int scalar
Default: The dimension of the arrays xbar, std and the first dimension of the arrays ssp, r and the second dimension of the arrays ssp, r. (An error is raised if these dimensions are not equal.)
n$n$, the number of variables in the input data.
Constraint: n2${\mathbf{n}}\ge 2$.
2:     m – int64int32nag_int scalar
Default: The dimension of the array korder.
The number of variables m$m$, required in the reduced vectors and matrices.
Constraint: 1mn$1\le {\mathbf{m}}\le {\mathbf{n}}$.

### Input Parameters Omitted from the MATLAB Interface

ldssp ldr ldssp2 ldr2

### Output Parameters

1:     xbar2(m) – double array
The mean of variable i$i$, xbar(i)${\mathbf{xbar}}\left(i\right)$, where i = korder(k)$i={\mathbf{korder}}\left(\mathit{k}\right)$, for k = 1,2,,m$\mathit{k}=1,2,\dots ,m$. (The array xbar2 must differ from xbar and std.)
2:     std2(m) – double array
The standard deviation of variable i$i$, std(i)${\mathbf{std}}\left(i\right)$, where i = korder(k)$i={\mathbf{korder}}\left(\mathit{k}\right)$, for k = 1,2,,m$\mathit{k}=1,2,\dots ,m$. (The array std2 must differ from both xbar and std.)
3:     ssp2(ldssp2,m) – double array
ldssp2m$\mathit{ldssp2}\ge {\mathbf{m}}$.
ssp2(k,l)${\mathbf{ssp2}}\left(\mathit{k},\mathit{l}\right)$ contains the value of ssp(i,j)${\mathbf{ssp}}\left(i,j\right)$, where i = korder(k)$i={\mathbf{korder}}\left(\mathit{k}\right)$ and j = korder(l)$j={\mathbf{korder}}\left(\mathit{l}\right)$, for k = 1,2,,m$\mathit{k}=1,2,\dots ,m$ and l = 1,2,,m$\mathit{l}=1,2,\dots ,m$. (The array ssp2 must differ from both ssp and r.)
That is to say: on exit, ssp2(k,l)${\mathbf{ssp2}}\left(k,l\right)$ contains the sum of cross-products of deviations from means Sij${S}_{ij}$ (or about zero, ij${\stackrel{~}{S}}_{ij}$).
4:     r2(ldr2,m) – double array
ldr2m$\mathit{ldr2}\ge {\mathbf{m}}$.
r2(k,l)${\mathbf{r2}}\left(\mathit{k},\mathit{l}\right)$ contains the value of r(i,j)${\mathbf{r}}\left(i,j\right)$, where i = korder(k)$i={\mathbf{korder}}\left(\mathit{k}\right)$ and j = korder(l)$j={\mathbf{korder}}\left(\mathit{l}\right)$, for k = 1,2,,m$\mathit{k}=1,2,\dots ,m$ and l = 1,2,,m$\mathit{l}=1,2,\dots ,m$. (The array r2 must differ from both ssp and r.)
That is to say: on exit, r2(k,l)${\mathbf{r2}}\left(k,l\right)$ contains the Pearson product-moment coefficient Rij${R}_{ij}$ (or the correlation-like coefficient, ij${\stackrel{~}{R}}_{ij}$).
5:     ifail – int64int32nag_int scalar
${\mathrm{ifail}}={\mathbf{0}}$ unless the function detects an error (see [Error Indicators and Warnings]).

## Error Indicators and Warnings

Errors or warnings detected by the function:
ifail = 1${\mathbf{ifail}}=1$
 On entry, n < 2${\mathbf{n}}<2$, or m < 1${\mathbf{m}}<1$.
ifail = 2${\mathbf{ifail}}=2$
 On entry, n < m${\mathbf{n}}<{\mathbf{m}}$.
ifail = 3${\mathbf{ifail}}=3$
 On entry, ldssp < n$\mathit{ldssp}<{\mathbf{n}}$, or ldr < n$\mathit{ldr}<{\mathbf{n}}$, or ldssp < m$\mathit{ldssp}<{\mathbf{m}}$, or ldr2 < m$\mathit{ldr2}<{\mathbf{m}}$.
ifail = 4${\mathbf{ifail}}=4$
 On entry, korder(i) < 1${\mathbf{korder}}\left(i\right)<1$, or korder(i) > n${\mathbf{korder}}\left(i\right)>{\mathbf{n}}$ for some i = 1,2, … ,m$i=1,2,\dots ,m$.

## Accuracy

Not applicable.

The time taken by nag_correg_linregm_service_select (g02ce) depends on n$n$ and m$m$.
The function is intended primarily for use when a subset of variables from a larger set of variables is to be used in a regression, and is described accordingly. There is however no reason why the function should not also be used to select specific rows and columns from vectors and arrays which contain any other non-statistical information; the matrices need not be symmetric.
The function may be used either with sums of squares and cross-products of deviations from means and Pearson product-moment correlation coefficients in connection with a regression involving a constant, or with sums of squares and cross-products about zero and correlation-like coefficients in connection with a regression with no constant.

## Example

```function nag_correg_linregm_service_select_example
xbar = [5.8;
2.8;
1.8;
5.4];
std = [5.0695;
1.924;
2.5884;
4.98];
ssp = [102.8, -29.2, -14.2, -57.6;
-29.2, 14.8, -6.2, 6.4;
-14.2, -6.2, 28.6, 42.4;
-57.6, 6.4, 42.4, 99.2];
r = [1, -0.7486, -0.2619, -0.5704;
-0.7486, 1, -0.3014, 0.167;
-0.2619, -0.3014, 1, 0.796;
-0.5704, 0.167, 0.796, 1];
korder = [int64(4);1;2];
[xbar2, std2, ssp2, r2, ifail] = nag_correg_linregm_service_select(xbar, std, ssp, r, korder)
```
```

xbar2 =

5.4000
5.8000
2.8000

std2 =

4.9800
5.0695
1.9240

ssp2 =

99.2000  -57.6000    6.4000
-57.6000  102.8000  -29.2000
6.4000  -29.2000   14.8000

r2 =

1.0000   -0.5704    0.1670
-0.5704    1.0000   -0.7486
0.1670   -0.7486    1.0000

ifail =

0

```
```function g02ce_example
xbar = [5.8;
2.8;
1.8;
5.4];
std = [5.0695;
1.924;
2.5884;
4.98];
ssp = [102.8, -29.2, -14.2, -57.6;
-29.2, 14.8, -6.2, 6.4;
-14.2, -6.2, 28.6, 42.4;
-57.6, 6.4, 42.4, 99.2];
r = [1, -0.7486, -0.2619, -0.5704;
-0.7486, 1, -0.3014, 0.167;
-0.2619, -0.3014, 1, 0.796;
-0.5704, 0.167, 0.796, 1];
korder = [int64(4);1;2];
[xbar2, std2, ssp2, r2, ifail] = g02ce(xbar, std, ssp, r, korder)
```
```

xbar2 =

5.4000
5.8000
2.8000

std2 =

4.9800
5.0695
1.9240

ssp2 =

99.2000  -57.6000    6.4000
-57.6000  102.8000  -29.2000
6.4000  -29.2000   14.8000

r2 =

1.0000   -0.5704    0.1670
-0.5704    1.0000   -0.7486
0.1670   -0.7486    1.0000

ifail =

0

```