NAG Library Routine Document

g02eaf (linregm_rssq)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:     $\mathbf{mean}$ – Character(1)Input

On entry: indicates if a mean term is to be included.

$\mathbf{mean}=\text{'M'}$

A mean term, intercept, will be included in the model.

$\mathbf{mean}=\text{'Z'}$

The model will pass through the origin, zero-point.

Constraint: $\mathbf{mean}=\text{'M'}$ or $\text{'Z'}$.

2:     $\mathbf{weight}$ – Character(1)Input

On entry: indicates if weights are to be used.

$\mathbf{weight}=\text{'U'}$

Least squares estimation is used.

$\mathbf{weight}=\text{'W'}$

Weighted least squares is used and weights must be supplied in array wt.

Constraint: $\mathbf{weight}=\text{'U'}$ or $\text{'W'}$.

3:     $\mathbf{n}$ – IntegerInput

On entry: $n$, the number of observations.

Constraints:

• $\mathbf{n}\ge 2$;
• $\mathbf{n}\ge m$, is the number of independent variables to be considered (forced plus free plus mean if included), as specified by mean and isx.

4:     $\mathbf{m}$ – IntegerInput

On entry: the number of variables contained in x.

Constraint: $\mathbf{m}\ge 2$.

5:     $\mathbf{x}\left(\mathbf{ldx},\mathbf{m}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: $\mathbf{x}\left(\mathit{i},\mathit{j}\right)$ must contain the $\mathit{i}$th observation for the $\mathit{j}$th independent variable, for $\mathit{i}=1,2,\dots ,\mathbf{n}$ and $\mathit{j}=1,2,\dots ,\mathbf{m}$.

6:     $\mathbf{ldx}$ – IntegerInput

On entry: the first dimension of the array x as declared in the (sub)program from which g02eaf is called.

Constraint: $\mathbf{ldx}\ge \mathbf{n}$.

7:     $\mathbf{vname}\left(\mathbf{m}\right)$ – Character(*) arrayInput

On entry: $\mathbf{vname}\left(\mathit{j}\right)$ must contain the name of the variable in column $\mathit{j}$ of x, for $\mathit{j}=1,2,\dots ,\mathbf{m}$.

8:     $\mathbf{isx}\left(\mathbf{m}\right)$ – Integer arrayInput

On entry: indicates which independent variables are to be considered in the model.

$\mathbf{isx}\left(j\right)\ge 2$

The variable contained in the $j$th column of x is included in all regression models, i.e., is a forced variable.

$\mathbf{isx}\left(j\right)=1$

The variable contained in the $j$th column of x is included in the set from which the regression models are chosen, i.e., is a free variable.

$\mathbf{isx}\left(j\right)=0$

The variable contained in the $j$th column of x is not included in the models.

Constraints:

• $\mathbf{isx}\left(\mathit{j}\right)\ge 0$, for $\mathit{j}=1,2,\dots ,\mathbf{m}$;
• at least one value of $\mathbf{isx}=1$.

9:     $\mathbf{y}\left(\mathbf{n}\right)$ – Real (Kind=nag_wp) arrayInput

On entry: $\mathbf{y}\left(\mathit{i}\right)$ must contain the $\mathit{i}$th observation on the dependent variable, $y_{\mathit{i}}$, for $\mathit{i}=1,2,\dots ,n$.

10:   $\mathbf{wt}\left(*\right)$ – Real (Kind=nag_wp) arrayInput

Note: the dimension of the array wt must be at least $\mathbf{n}$ if $\mathbf{weight}=\text{'W'}$.

On entry: if $\mathbf{weight}=\text{'W'}$, wt must contain the weights to be used in the weighted regression.

If $\mathbf{wt}\left(i\right)=0.0$, the $i$th observation is not included in the model, in which case the effective number of observations is the number of observations with nonzero weights.

If $\mathbf{weight}=\text{'U'}$, wt is not referenced and the effective number of observations is n.

Constraint: if $\mathbf{weight}=\text{'W'}$, $\mathbf{wt}\left(\mathit{i}\right)\ge 0.0$, for $\mathit{i}=1,2,\dots ,n$.

11:   $\mathbf{nmod}$ – IntegerOutput

On exit: the total number of models for which residual sums of squares have been calculated.

12:   $\mathbf{modl}\left(\mathbf{ldmodl},\mathbf{m}\right)$ – Character(*) arrayOutput

On exit: the first $\mathbf{nterms}\left(i\right)$ elements of the $i$th row of modl contain the names of the independent variables, as given in vname, that are included in the $i$th model.

Constraint: the length of modl should be greater or equal to the length of vname.

13:   $\mathbf{ldmodl}$ – IntegerInput

On entry: the first dimension of the array modl and the dimension of the arrays rss, nterms and mrank as declared in the (sub)program from which g02eaf is called.

Constraints:

• $\mathbf{ldmodl}\ge \mathbf{m}$;
• $\mathbf{ldmodl}\ge 2^{\mathit{k}}$, $\mathit{k}$ is the number of free variables in the model as specified in isx, and hence $2^{\mathit{k}}$ is the total number of models to be generated.

14:   $\mathbf{rss}\left(\mathbf{ldmodl}\right)$ – Real (Kind=nag_wp) arrayOutput

On exit: $\mathbf{rss}\left(\mathit{i}\right)$ contains the residual sum of squares for the $\mathit{i}$th model, for $\mathit{i}=1,2,\dots ,\mathbf{nmod}$.

15:   $\mathbf{nterms}\left(\mathbf{ldmodl}\right)$ – Integer arrayOutput

On exit: $\mathbf{nterms}\left(\mathit{i}\right)$ contains the number of independent variables in the $\mathit{i}$th model, not including the mean if one is fitted, for $\mathit{i}=1,2,\dots ,\mathbf{nmod}$.

16:   $\mathbf{mrank}\left(\mathbf{ldmodl}\right)$ – Integer arrayOutput

On exit: $\mathbf{mrank}\left(i\right)$ contains the rank of the residual sum of squares for the $i$th model.

17:   $\mathbf{wk}\left(\mathbf{n}\times \left(\mathbf{m}+1\right)\right)$ – Real (Kind=nag_wp) arrayWorkspace

18:   $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this argument, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6

Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, $\mathbf{ldmodl}=〈\mathit{\text{value}}〉$ and $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldmodl}\ge \mathbf{m}$.

On entry, $\mathbf{ldx}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldx}\ge \mathbf{n}$.

On entry, $\mathbf{m}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{m}\ge 2$.

On entry, $\mathbf{mean}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{mean}=\text{'M'}$ or $\text{'Z'}$.

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 2$.

On entry, $\mathbf{weight}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{weight}=\text{'W'}$ or $\text{'U'}$.

$\mathbf{ifail}=2$

On entry, $\mathbf{wt}\left(〈\mathit{\text{value}}〉\right)<0.0$.
Constraint: $\mathbf{wt}\left(i\right)\ge 0.0$, for $i=1,2,\dots ,n$.

$\mathbf{ifail}=3$

On entry, $\mathbf{isx}\left(〈\mathit{\text{value}}〉\right)<0$.
Constraint: $\mathbf{isx}\left(i\right)\ge 0$, for $i=1,2,\dots ,\mathbf{m}$.

There are no free variables, i.e., no element of $\mathbf{isx}=1$.

$\mathbf{ifail}=4$

On entry, $\mathbf{ldmodl}=〈\mathit{\text{value}}〉$ and number of possible models is $〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{ldmodl}\ge$ the number of possible models.

$\mathbf{ifail}=5$

On entry, the number of independent variables to be considered (forced plus free plus mean if included) is greater or equal to the effective number of observations.

$\mathbf{ifail}=6$

The full model is not of full rank, i.e., some of the independent variables may be linear combinations of other independent variables. Variables must be excluded from the model in order to give full rank.

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g02eafe.f90)

10.2

Program Data

Program Data (g02eafe.d)

10.3

Program Results

Program Results (g02eafe.r)