Fits a linear regression model by forward selection

はじめる前に
新機能一覧
Maple ワークシートの作成
Mapleワークシートを共有
Maple ウィンドウのカスタマイズ
Maple システムのカスタマイズ
コネクティビティ
Mathematics
数学
物理
プログラミング
グラフィックス
Student パッケージ
Science and Engineering
科学・エンジニアリング
アプリケーションと例題
リファレンス
システム
MapleSim
MapleSim ツールボックス
MapleSim ヘルプ
Tasks
Toolboxes
- BlockImporter
- Global Optimization
- Grid Computing
- Maple-NAG Connector
  - General information
  - Computational Routines
    - a02 (Complex Arithmetic)
    - c02 (Zeros of Polynomials)
    - c05 (Roots of One or More Transcendental Equations)
    - c06 (Fourier Transforms)
    - d01 (Quadrature)
    - d02 (Ordinary Differential Equations)
    - d03 (Partial Differential Equations)
    - d06 (Mesh Generation)
    - e01 (Interpolation)
    - e02 (Curve and Surface Fitting)
    - e04 (Minimizing or Maximizing a Function)
    - f01 (Matrix Factorizations)
    - f02 (Eigenvalues and Eigenvectors)
    - f03 (Determinants)
    - f04 (Simultaneous Linear Equations)
    - f06 (Linear Algebra Support Functions)
    - f07 (Linear Equations (LAPACK))
    - f08 (Least-squares and Eigenvalue Problems (LAPACK))
    - f11 (Large Scale Linear Systems)
    - f16 (NAG Interface to BLAS)
    - g01 (Simple Calculations on Statistical Data)
    - g02 (Correlation and Regression Analysis)
      - g02 Introduction
      - g02brc (nag_ken_spe_corr_coeff)
      - g02btc (nag_sum_sqs_update)
      - g02buc (nag_sum_sqs)
      - g02bwc (nag_cov_to_corr)
      - g02bxc (nag_corr_cov)
      - g02byc (nag_partial_corr)
      - g02cac (nag_simple_linear_regression)
      - g02cbc (nag_regress_confid_interval)
      - g02dac (nag_regsn_mult_linear)
      - g02dcc (nag_regsn_mult_linear_addrem_obs)
      - g02ddc (nag_regsn_mult_linear_upd_model)
      - g02dec (nag_regsn_mult_linear_add_var)
      - g02dfc (nag_regsn_mult_linear_delete_var)
      - g02dgc (nag_regsn_mult_linear_newyvar)
      - g02dkc (nag_regsn_mult_linear_tran_model)
      - g02dnc (nag_regsn_mult_linear_est_func)
      - g02eac (nag_all_regsn)
      - g02ecc (nag_cp_stat)
      - g02eec (nag_step_regsn)
      - g02fac (nag_regsn_std_resid_influence)
      - g02fcc (nag_durbin_watson_stat)
      - g02gac (nag_glm_normal)
      - g02gbc (nag_glm_binomial)
      - g02gcc (nag_glm_poisson)
      - g02gdc (nag_glm_gamma)
      - g02gkc (nag_glm_tran_model)
      - g02gnc (nag_glm_est_func)
      - g02hac (nag_robust_m_regsn_estim)
      - g02hbc (nag_robust_m_regsn_wts)
      - g02hdc (nag_robust_m_regsn_user_fn)
      - g02hfc (nag_robust_m_regsn_param_var)
      - g02hkc (nag_robust_corr_estim)
      - g02hlc (nag_robust_m_corr_user_fn)
      - g02hmc (nag_robust_m_corr_user_fn_no_derr)
    - g03 (Multivariate Methods)
    - g04 (Analysis of Variance)
    - g05 (Random Number Generators)
    - g07 (Univariate Estimation)
    - g08 (Nonparametric Statistics)
    - g10 (Smoothing in Statistics)
    - g11 (Contingency Table Analysis)
    - g12 (Survival Analysis)
    - g13 (Time Series Analysis)
    - h (Operations Research)
    - m01 (Sorting)
    - s (Approximations of Special Functions)
    - x01 (Mathematical Constants)
    - x02 (Machine Constants)
    - x04 (Input-Output Utilities)
  - Getting Started
  - Example Worksheet
エラーメッセージガイド
マニュアル
数学アプリ

NAG[g02eec] NAG[nag_step_regsn] - Fits a linear regression model by forward selection

Calling Sequence

g02eec(istep, mean, x, var_names, sx, y, addvar, newvar, chrss, f, model, nterm, rss, idf, ifr, free_vars, exss, q, p, 'n'=n, 'm'=m, 'maxip'=maxip, 'wt'=wt, 'fin'=fin, 'fail'=fail)

nag_step_regsn(. . .)

Parameters

istep - assignable;

Note: On exit the variable istep will have a value of type integer.

On entry: indicates which step in the forward selection process is to be carried out.

The process is initialized.

Constraint: . .

On exit: is incremented by 1.

mean - String;

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

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

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

Constraint: "Nag_MeanInclude" or "Nag_MeanZero". .

x - Matrix(1..dim1, 1..m, datatype=float[8], order=order);

Note: this array may be supplied in Fortran_order or C_order , as specified by order. All array parameters must use a consistent order.

On entry: must contain the th observation for the th independent variable, for ; .

var_names - Vector(1..m, datatype=REF(string[512]));

On entry: must contain the name of the independent variable in row of x, for .

sx - Vector(1..m, datatype=integer[kernelopts('wordsize')/8]);

On entry: indicates which independent variables could be considered for inclusion in the regression.

The variable contained in the th column of x is automatically included in the regression model, for .

The variable contained in the th column of x is considered for inclusion in the regression model, for .

The variable in the th column is not considered for inclusion in the model, for .

Constraint: and at least one value of , for . .

y - Vector(1..n, datatype=float[8]);

On entry: the dependent variable.

addvar - assignable;

Note: On exit the variable addvar will have a value of type boolean.

On exit: indicates if a variable has been added to the model.

A variable has been added to the model.

No variable had an value greater than and none were added to the model.

newvar - Vector(1.., datatype=REF(string[512]));

On exit: if , newvar contains the name of the variable added to the model.

chrss - assignable;

Note: On exit the variable chrss will have a value of type float.

On exit: if , chrss contains the change in the residual sum of squares due to adding variable newvar.

f - assignable;

Note: On exit the variable f will have a value of type float.

On exit: if , f contains the statistic for the inclusion of the variable in newvar.

model - Vector(1..maxip, datatype=REF(string[512]));

On entry: if , model need not be set.

If , model must contain the values returned by the previous call to nag_step_regsn (g02eec).

On exit: the names of the variables in the current model.

nterm - assignable;

Note: On exit the variable nterm will have a value of type integer.

On entry: if , nterm need not be set.

If , nterm must contain the value returned by the previous call to nag_step_regsn (g02eec).

On exit: the number of independent variables in the current model, not including the mean, if any.

rss - assignable;

Note: On exit the variable rss will have a value of type float.

On entry: if , rss need not be set.

If , rss must contain the value returned by the previous call to nag_step_regsn (g02eec).

On exit: the residual sums of squares for the current model.

idf - assignable;

Note: On exit the variable idf will have a value of type integer.

On entry: if , idf need not be set.

If , idf must contain the value returned by the previous call to nag_step_regsn (g02eec).

On exit: the degrees of freedom for the residual sum of squares for the current model.

ifr - assignable;

Note: On exit the variable ifr will have a value of type integer.

On entry: if , ifr need not be set.

If , ifr must contain the value returned by the previous call to nag_step_regsn (g02eec).

On exit: the number of free independent variables, i.e., the number of variables not in the model that are still being considered for selection.

free_vars - Vector(1..maxip, datatype=REF(string[512]));

On entry: if , free_vars need not be set.

If , free_vars must contain the values returned by the previous call to nag_step_regsn (g02eec).

On exit: the first ifr values of free_vars contain the names of the free variables.

exss - Vector(1..maxip, datatype=float[8]);

On exit: the first ifr values of exss contain what would be the change in regression sum of squares if the free variables had been added to the model, i.e., the extra sum of squares for the free variables. contains what would be the change in regression sum of squares if the variable had been added to the model.

q - Matrix(1..dim1, 1.., datatype=float[8], order=order);

Note: this array may be supplied in Fortran_order or C_order , as specified by order. All array parameters must use a consistent order.

On entry: if , q need not be set.

If , q must contain the values returned by the previous call to nag_step_regsn (g02eec).

On exit: the results of the decomposition for the current model:

the first column of q contains (or where is the vector of weights if used);

the upper triangular part of columns 2 to contain the matrix;

the strictly lower triangular part of columns 2 to contain details of the matrix;

the remaining to columns of contain (or ),

where , or if .

p - Vector(1.., datatype=float[8]);

On entry: if , p need not be set.

If , p must contain the values returned by the previous call to nag_step_regsn (g02eec).

On exit: the first elements of p contain details of the decomposition, where , or if .

'n'=n - integer; (optional)

On entry: the number of observations.

Constraint: . .

'm'=m - integer; (optional)

On entry: , the total number of independent variables in the data set.

Constraint: . .

'maxip'=maxip - integer; (optional)

Default value: the dimension of .

On entry: the maximum number of independent variables to be included in the model.

Constraints:

if , number of values of ;

if , number of values of .

'wt'=wt - Vector(1..dim, datatype=float[8]); (optional)

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

On entry: , wt must contain the weights to be used in the weighted regression.

If , then the th observation is not included in the model, in which case the effective number of observations is the number of observations with non-zero 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 , for . .

'fin'=fin - float; (optional)

On entry: the critical value of the statistic for the term to be included in the model, .

Suggested value: is a commonly used value in exploratory modelling. (default: )

Constraint: . .

'fail'=fail - table; (optional)

The NAG error argument, see the documentation for NagError.

Description

	Purpose
	nag_step_regsn (g02eec) carries out one step of a forward selection procedure in order to enable the "best" linear regression model to be found.

Description

One method of selecting a linear regression model from a given set of independent variables is by forward selection. The following procedure is used:

Select the best fitting independent variable, i.e., the independent variable which gives the smallest residual sum of squares. If the -test for this variable is greater than a chosen critical value, , then include the variable in the model, else stop.

Find the independent variable that leads to the greatest reduction in the residual sum of squares when added to the current model.

If the -test for this variable is greater than a chosen critical value, , then include the variable in the model and go to (b), otherwise stop.

At any step the variables not in the model are known as the free terms.

nag_step_regsn (g02eec) allows you to specify some independent variables that must be in the model, these are known as forced variables.

The computational procedure involves the use of decompositions, the and the matrices being updated as each new variable is added to the model. In addition the matrix , where is the matrix of variables not included in the model, is updated.

nag_step_regsn (g02eec) computes one step of the forward selection procedure at a call. The results produced at each step may be printed or used as inputs to g02ddc (nag_regsn_mult_linear_upd_model), in order to compute the regression coefficients for the model fitted at that step. Repeated calls to nag_step_regsn (g02eec) should be made until is indicated.

Error Indicators and Warnings

"NE_ALLOC_FAIL"

Dynamic memory allocation failed.

"NE_BAD_PARAM"

On entry, argument had an illegal value.

"NE_DENOM_ZERO"

Denominator of f statistic is .

"NE_FREE_VARS"

There are no free variables in the regression.

"NE_FULL_RANK"

Forced variables not of full rank.

"NE_INT"

On entry, . Constraint: .

"NE_INT_2"

On entry, , . Constraint: if , .

On entry, istep and nterm are inconsistent: , .

"NE_INT_ARRAY"

On entry, maxip is too small for number of terms given by sx: .

"NE_INT_ARRAY_ELEM_CONS"

On entry, .

"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 consult NAG for assistance.

"NE_REAL"

On entry, . Constraint: .

On entry, with non-zero istep, : .

"NE_REAL_ARRAY_ELEM_CONS"

On entry, .

"NE_ZERO_DF"

Degrees of freedom for error will equal 0 if new variable is added.

On entry, number of forced variables , i.e., idf would be zero.

"NE_ZERO_VARS"

Maximum number of variables to be included is 0.

	Accuracy
	As nag_step_regsn (g02eec) uses a transformation the results will often be more accurate than traditional algorithms using methods based on the cross-products of the dependent and independent variables.

	Further Comments
	None.

Examples

istep := 0:
mean := "Nag_MeanInclude":
n := 20:
m := 6:
maxip := 6:
fin := 2.0:
nterm := 24641422:
rss := 4.855329318214986e-270:
idf := 0:
ifr := -1084618888:
x := Matrix([[0, 1125, 232, 7160, 85.90000000000001, 8905], [7, 920, 268, 8804, 86.5, 7388], [15, 835, 271, 8108, 85.2, 5348], [22, 1000, 237, 6370, 83.8, 8056], [29, 1150, 192, 6441, 82.09999999999999, 6960], [37, 990, 202, 5154, 79.2, 5690], [44, 840, 184, 5896, 81.2, 6932], [58, 650, 200, 5336, 80.59999999999999, 5400], [65, 640, 180, 5041, 78.40000000000001, 3177], [72, 583, 165, 5012, 79.3, 4461], [80, 570, 151, 4825, 78.7, 3901], [86, 570, 171, 4391, 78, 5002], [93, 510, 243, 4320, 72.3, 4665], [100, 555, 147, 3709, 74.90000000000001, 4642], [107, 460, 286, 3969, 74.40000000000001, 4840], [122, 275, 198, 3558, 72.5, 4479], [129, 510, 196, 4361, 57.7, 4200], [151, 165, 210, 3301, 71.8, 3410], [171, 244, 327, 2964, 72.5, 3360], [220, 79, 334, 2777, 71.90000000000001, 2599]], datatype=float[8]):
var_names := Vector(["DAY", "BOD", "TKN", "TS", "TVS", "COD"], datatype=string):
sx := Vector([0, 1, 1, 1, 1, 2], datatype=integer[kernelopts('wordsize')/8]):
y := Vector([1.5563, 0.8976, 0.7482, 0.716, 0.301, 0.3617, 0.1139, 0.1139, -0.2218, -0.1549, 0, 0, -0.0969, -0.2218, -0.3979, -0.1549, -0.2218, -0.3979, -0.5229, -0.0458], datatype=float[8]):
wt := Vector([], datatype=float[8]):
newvar := Vector(1, datatype=string, fill=""):
model := Vector(maxip,fill="", datatype=string):
free_vars := Vector(maxip,fill="", datatype=string):
exss := Vector(6, datatype=float[8]):
q := Matrix([[0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0, 0, 0]], datatype=float[8]):
p := Vector([0, 0, 0, 0, 0, 0, 0], datatype=float[8]):
NAG:-g02eec(istep, mean, x, var_names, sx, y, addvar, newvar, chrss, f, model, nterm, rss, idf, ifr, free_vars, exss, q, p, 'n' = n, 'm' = m, 'maxip' = maxip, 'wt' = wt, 'fin' = fin):

istep;

addvar;

chrss;

nterm;

rss;

idf;

ifr;

exss;

newvar;

model;

	See Also
	Draper N R and Smith H (1985) Applied Regression Analysis (2nd Edition) Wiley Weisberg S (1985) Applied Linear Regression Wiley g02 Chapter Introduction. NAG Toolbox Overview. NAG Web Site.