XploRe Help : linregstep

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library:	stats
See also:	linregfs2 linregbs linregopt gls linregfs linregres doglm

Quantlet:		linregstep
Description:		linregstep computes a stepwise regression for a multiple linear regression model.

Reference(s):

Neter, J., Wasserman, W. and Kutner, M. H. (1989), Applied linear regression models, p. 452-460 Kotz, S., Johnson, N. L. and Read, C. B. (1989), Encyclopedia of Statistical Science, Vol.8, p. 766-767

Usage:	`{b,bse,bstan,bpval} = linregstep (x, y, colname{, opt})`
Input:
	`x`	n x p x d1 x ... x dn array
	`y`	n x 1 x d1 x ... x dn array
	`colname`	string vector
	`opt`	parameter vector
Output:
	`b`	p x 1 x d1 x ... x dn array
	`bse`	p x 1 x d1 x ... x dn array
	`bstan`	p x 1 x d1 x ... x dn array
	`bpval`	p x 1 x d1 x ... x dn array

Note:

The regressors x do not contain an intercept column. The optional parameter opt ca be set using linregopt. Otherwise the probabilities of F-to-enter/ F-to-remove will be set 0.05/ 0.10. The stepwise regression routine fits first a simple linear regression for each of the p potential x variables. For each simple linear regression model, a F-statistic for testing whether or not the slope is zero is obtained. After entering a significant variable x_k (in the sense that this variable contributes significant to the SSM ) all regression models with two x variables are fitted where x_k is one of the pair. The partial F-test statistic examines, whether another x variable is significant for inclusion. In each step with p >= 2 x variables a test is undertaken whether any of the variables already in the model be dropped because it is not longer helpful in conjunction with variables added at later stages The procedure stops if no further x variable can either be added or deleted.If there is no variable significant to enter in the first step, the estimation contains only the intercept.

Example:

library("stats") setenv("outputstringformat", "%s") x1 = #(7,1,11,11,7,11,3,1,2,21,1,11,10) x2 = #(26,29,56,31,52,55,71,31,54,47,40,66,68) x3 = #(6,15,8,8,6,9,17,22,18,4,23,9,8) x4 = #(60,52,20,47,33,22,6,44,22,26,34,12,12) x = x1~x2~x3~x4 y = #(78.5,74.3,104.3,87.6,95.9,109.2,102.7,72.5) y = y|#(93.1,115.9,83.8,113.3,109.4) colname=string("X %.f",1:cols(x)) opt = linregopt("Fin", 4.0, "Fout", 3.9) {b,bse,bstan,bpval} = linregstep(x,y,colname,opt)

Result:

Contents of string
[1,] In : X 4
Contents of string
[1,] In  : X 1
Contents of string
[1,] In  : X 2
Contents of string
[1,] Out : X 4

Contents of EnterandOut
[ 1,] Stepwise Regression
[ 2,] -------------------
[ 3,] F-to-enter 4.00
[ 4,] probability of F-to-enter 0.95
[ 5,] F-to-remove 3.90
[ 6,] probability of F-to-remove 0.94
[ 7,]
[ 8,] Variables entered and dropped in the following Steps:
[ 9,]
[10,] Step  Multiple R      R^2        F        SigF       Variable(s)
[11,]  1     0.8213       0.6745     22.799    0.001  In : X 4
[12,]  2     0.9861       0.9725    176.627    0.000  In : X 1
[13,]  3     0.9911       0.9823    166.832    0.000  In : X 2
[14,]  3     0.9893       0.9787    229.504    0.000  Out: X 4

Contents of ANOVA
[ 1,]
[ 2,] A  N  O  V  A                   SS      df     MSS       F-test   P-value
[ 3,] _________________________________________________________________________
[ 4,] Regression                  2657.859     2  1328.929     229.504   0.0000
[ 5,] Residuals                     57.904 1e+01     5.790
[ 6,] Total Variation                 2716    12   226.314
[ 7,]
[ 8,] Multiple R      = 0.98928
[ 9,] R^2             = 0.97868
[10,] Adjusted R^2    = 0.97441
[11,] Standard Error  = 2.40634

Contents of Summary
[1,] Variables in the Equation for Y:
[2,]
[3,]
[4,] PARAMETERS         Beta         SE         StandB      t-test   P-value  Variable
[5,]   __________________________________________________________________________________
[6,] b[ 0,]=         52.5773       2.2862       0.0000     22.9980   0.0000   Constant
[7,] b[ 1,]=          1.4683       0.1213       0.5741     12.1047   0.0000   X 1
[8,] b[ 2,]=          0.6623       0.0459       0.6850     14.4424   0.0000   X 2

Author: K. Zanter, W. Haerdle, 19980331 license MD*Tech