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NAG Toolbox

NAG Toolbox: nag_correg_coeffs_pearson_subset (g02bg)

Purpose

nag_correg_coeffs_pearson_subset (g02bg) computes means and standard deviations, sums of squares and cross-products of deviations from means, and Pearson product-moment correlation coefficients for selected variables.

Syntax

[xbar, std, ssp, r, ifail] = g02bg(x, kvar, 'n', n, 'm', m, 'nvars', nvars)
[xbar, std, ssp, r, ifail] = nag_correg_coeffs_pearson_subset(x, kvar, 'n', n, 'm', m, 'nvars', nvars)
Note: the interface to this routine has changed since earlier releases of the toolbox:
Mark 22: n has been made optional
.

Description

The input data consist of nn observations for each of mm variables, given as an array
[xij],  i = 1,2,,n(n2),j = 1,2,,m(m2),
[xij],  i=1,2,,n(n2),j=1,2,,m(m2),
where xijxij is the iith observation on the jjth variable, together with the subset of these variables, v1,v2,,vpv1,v2,,vp, for which information is required.
The quantities calculated are:
(a) Means:
n
xj = 1/nxij,  j = v1,v2,,vp.
i = 1
x-j=1ni=1nxij,  j=v1,v2,,vp.
(b) Standard deviations:
sj = sqrt(1/(n 1)i = 1n(xijxj)2),   j = v1,v2,,vp.
sj=1n- 1 i= 1n (xij-x-j) 2,   j=v1,v2,,vp.
(c) Sums of squares and cross-products of deviations from zero:
n
Sjk = (xijxj)(xikxk),  j,k = v1,v2,,vp.
i = 1
Sjk=i=1n(xij-x-j)(xik-x-k),  j,k=v1,v2,,vp.
(d) Pearson product-moment correlation coefficients:
Rjk = (Sjk)/(sqrt(SjjSkk)),   j,k = v1,v2,vp.
Rjk=SjkSjjSkk ,   j,k=v1,v2,vp.
If SjjSjj or SkkSkk is zero, RjkRjk is set to zero.

References

None.

Parameters

Compulsory Input Parameters

1:     x(ldx,m) – double array
ldx, the first dimension of the array, must satisfy the constraint ldxnldxn.
x(i,j)xij must be set to xijxij, the value of the iith observation on the jjth variable, for i = 1,2,,ni=1,2,,n and j = 1,2,,mj=1,2,,m.
2:     kvar(nvars) – int64int32nag_int array
nvars, the dimension of the array, must satisfy the constraint 2nvarsm2nvarsm.
kvar(j)kvarj must be set to the column number in x of the jjth variable for which information is required, for j = 1,2,,pj=1,2,,p.
Constraint: 1kvar(j)m1kvarjm, for j = 1,2,,pj=1,2,,p.

Optional Input Parameters

1:     n – int64int32nag_int scalar
Default: The first dimension of the array x.
nn, the number of observations or cases.
Constraint: n2n2.
2:     m – int64int32nag_int scalar
Default: The second dimension of the array x.
mm, the number of variables.
Constraint: m2m2.
3:     nvars – int64int32nag_int scalar
Default: The dimension of the array kvar.
pp, the number of variables for which information is required.
Constraint: 2nvarsm2nvarsm.

Input Parameters Omitted from the MATLAB Interface

ldx ldssp ldr

Output Parameters

1:     xbar(nvars) – double array
The mean value, xjx-j, of the variable specified in kvar(j)kvarj, for j = 1,2,,pj=1,2,,p.
2:     std(nvars) – double array
The standard deviation, sjsj, of the variable specified in kvar(j)kvarj, for j = 1,2,,pj=1,2,,p.
3:     ssp(ldssp,nvars) – double array
ldsspnvarsldsspnvars.
ssp(j,k)sspjk is the cross-product of deviations, SjkSjk, for the variables specified in kvar(j)kvarj and kvar(k)kvark, for j = 1,2,,pj=1,2,,p and k = 1,2,,pk=1,2,,p.
4:     r(ldr,nvars) – double array
ldrnvarsldrnvars.
r(j,k)rjk is the product-moment correlation coefficient, RjkRjk, between the variables specified in kvar(j)kvarj and kvar(k)kvark, for j = 1,2,,pj=1,2,,p and k = 1,2,,pk=1,2,,p.
5:     ifail – int64int32nag_int scalar
ifail = 0ifail=0 unless the function detects an error (see [Error Indicators and Warnings]).

Error Indicators and Warnings

Errors or warnings detected by the function:
  ifail = 1ifail=1
On entry,n < 2n<2.
  ifail = 2ifail=2
On entry,nvars < 2nvars<2,
ornvars > mnvars>m.
  ifail = 3ifail=3
On entry,ldx < nldx<n,
orldssp < nvarsldssp<nvars,
orldr < nvarsldr<nvars.
  ifail = 4ifail=4
On entry,kvar(j) < 1kvarj<1,
orkvar(j) > mkvarj>m for some j = 1,2,,nvarsj=1,2,,nvars.

Accuracy

nag_correg_coeffs_pearson_subset (g02bg) does not use additional precision arithmetic for the accumulation of scalar products, so there may be a loss of significant figures for large nn.

Further Comments

The time taken by nag_correg_coeffs_pearson_subset (g02bg) depends on nn and pp.
The function uses a two pass algorithm.

Example

function nag_correg_coeffs_pearson_subset_example
x = [3, 3, 1, 2;
     6, 4, -1, 4;
     9, 0, 5, 9;
     12, 2, 0, 0;
     -1, 5, 4, 12];
kvar = [int64(4);1;2];
[xbar, std, ssp, r, ifail] = nag_correg_coeffs_pearson_subset(x, kvar)
 

xbar =

    5.4000
    5.8000
    2.8000


std =

    4.9800
    5.0695
    1.9235


ssp =

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


r =

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


ifail =

                    0


function g02bg_example
x = [3, 3, 1, 2;
     6, 4, -1, 4;
     9, 0, 5, 9;
     12, 2, 0, 0;
     -1, 5, 4, 12];
kvar = [int64(4);1;2];
[xbar, std, ssp, r, ifail] = g02bg(x, kvar)
 

xbar =

    5.4000
    5.8000
    2.8000


std =

    4.9800
    5.0695
    1.9235


ssp =

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


r =

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


ifail =

                    0



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