NAG Library Function Document

nag_all_regsn (g02eac)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     order – Nag_OrderTypeInput

On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by $\mathbf{order}=\mathrm{Nag\_RowMajor}$. See Section 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.

Constraint: $\mathbf{order}=\mathrm{Nag\_RowMajor}$ or Nag_ColMajor.

2:     mean – Nag_IncludeMeanInput

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

$\mathbf{mean}=\mathrm{Nag\_MeanInclude}$

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

$\mathbf{mean}=\mathrm{Nag\_MeanZero}$

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

Constraint: $\mathbf{mean}=\mathrm{Nag\_MeanInclude}$ or $\mathrm{Nag\_MeanZero}$.

3:     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 sx.

4:     m – IntegerInput

On entry: the number of variables contained in x.

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

5:     x[$\mathit{dim}$] – const doubleInput

Note: the dimension, dim, of the array x must be at least

• $\max \left(1,\mathbf{pdx}\times \mathbf{m}\right)$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\max \left(1,\mathbf{n}\times \mathbf{pdx}\right)$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

Where $\mathbf{X}\left(i,j\right)$ appears in this document, it refers to the array element

• $\mathbf{x}\left[\left(j-1\right)\times \mathbf{pdx}+i-1\right]$ when $\mathbf{order}=\mathrm{Nag\_ColMajor}$;
• $\mathbf{x}\left[\left(i-1\right)\times \mathbf{pdx}+j-1\right]$ when $\mathbf{order}=\mathrm{Nag\_RowMajor}$.

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:     pdx – IntegerInput

On entry: the stride separating row or column elements (depending on the value of order) in the array x.

Constraints:

• if $\mathbf{order}=\mathrm{Nag\_ColMajor}$, $\mathbf{pdx}\ge \mathbf{n}$;
• if $\mathbf{order}=\mathrm{Nag\_RowMajor}$, $\mathbf{pdx}\ge \mathbf{m}$.

7:     var_names[m] – const char *Input

On entry: $\mathbf{var\_names}\left[\mathit{i}-1\right]$ must contain the name of the independent variable in row $\mathit{i}$ of x, for $\mathit{i}=1,2,\dots ,\mathbf{m}$.

8:     sx[m] – const IntegerInput

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

$\mathbf{sx}\left[j-1\right]\ge 2$

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

$\mathbf{sx}\left[j-1\right]=1$

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.

$\mathbf{sx}\left[j-1\right]=0$

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

Constraints:

• $\mathbf{sx}\left[\mathit{j}-1\right]\ge 0$, for $\mathit{j}=1,2,\dots ,\mathbf{m}$;
• at least one value of $\mathbf{sx}=1$.

9:     y[n] – const doubleInput

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

10:   wt[$n$] – const doubleInput

On entry: optionally, the weights to be used in the weighted regression.

If $\mathbf{wt}\left[i-1\right]=0.0$, then 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 weights are not provided then wt must be set to the null pointer, i.e., (double *)0, and the effective number of observations is n.

Constraint: if $\mathbf{wt}\text{ is not }\mathbf{NULL}$, $\mathbf{wt}\left[\mathit{i}\right]\ge 0.0$, for $\mathit{i}=0,1,\dots ,n-1$.

11:   nmod – Integer *Output

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

12:   model[$\mathit{dim}$] – const char *Output

Note: the dimension, dim, of the array model must be at least big enough to hold the names of all the free independent variables which appear in all the models. This will never exceed $2^{\mathit{k}}\times \mathbf{m}$, where $\mathit{k}$ is the number of free variables in the model.

On exit: the names of the independent variables in each model, represented as pointers to the names provided by you in var_names. The model names are stored as follows:

• if the first model has three names, i.e., $\mathbf{nterms}\left[0\right]=3$; then $\mathbf{model}\left[0\right]$, $\mathbf{model}\left[1\right]$ and $\mathbf{model}\left[2\right]$ will contain these three names;
• if the second model has two names, i.e., $\mathbf{nterms}\left[1\right]=2$; then $\mathbf{model}\left[3\right]$, $\mathbf{model}\left[4\right]$ will contain these two names.

13:   rss[$\max \left(2^{\mathit{k}},\mathbf{m}\right)$] – doubleOutput

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

14:   nterms[$\max \left(2^{\mathit{k}},\mathbf{m}\right)$] – IntegerOutput

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

15:   mrank[$\max \left(2^{\mathit{k}},\mathbf{m}\right)$] – IntegerOutput

On exit: $\mathbf{mrank}\left[i-1\right]$ contains the rank of the residual sum of squares for the $i$th model.

16:   fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_FREE_VARS

There are no free x variables.

NE_FULL_RANK

Full model is not of full rank.

NE_INDEP_VARS_OBS

Number of requested $x$-variables $\ge$ number of observations.

NE_INT

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

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

On entry, $\mathbf{pdx}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{pdx}>0$.

NE_INT_2

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

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

NE_INT_ARRAY_ELEM_CONS

On entry, $\mathbf{sx}\left[〈\mathit{\text{value}}〉\right]<0$.

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_REAL_ARRAY_ELEM_CONS

On entry, $\mathbf{wt}\left[〈\mathit{\text{value}}〉\right]<0.0$.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (g02eace.c)

9.2  Program Data

Program Data (g02eace.d)

9.3  Program Results

Program Results (g02eace.r)