linfit.m

人工神经网络：MATLAB源程序用于训练测试

%#											
%# function [yhat,F,Ftab,lof,b0,b1] = linfit(x,y,intercept);		
%#										
%# AIM:		Construct a linear regression model to fit a calibration line and 
%#		estimate lack-of-fit.					
%#										
%# PRINCIPLE:	A univariate linear regression is performed to fit the calibration line.
%#		If replicate measurements are available, ANOVA for lack-of-fit is 
%# 		also performed.							
%#										
%# INPUT:	x: 	Vector of descriptor levels, in any order. Can be a row vector
%#			or a column vector. Some replicate measurements are necessary
%#			to perform ANOVA.					
%#		y: 	Vector of the same format as x, with corresponding experimental
%#			responses.						
%#		intercept: Intercept for regression model. 1:Intercept, 0: no intercept
%#			(Optional. Default: intercept = 1); 		
%#										
%#		Example of inputs:						
%#			x =    [2.00  3.00  1.00  2.00  2.00  4.00  5.00  3.00];
%#			y =    [0.65  0.82  0.25  0.53  0.66  0.91  1.10  0.73];
%#										
%# OUTPUT:	yhat:	Vector of responses estimated with linear model.(Column vector)
%#		F: 	The ANOVA calculated variance ratio.		
%#		Ftab: 	The tabulated F-value at level p, to be compared with F.
%#		lof:	Ratio F/Ftab. If lof>1 --> Significant lack-of-fit at level p.
%#		b0:	Model intercept.					
%#		b1:	Model slope.						
%#										
%# SUBROUTINES: anovalof.m : performs ANOVA for lack-of-fit		
%#										
%# AUTHOR:	Frederic Despagne					
%#		Copyright(c) 1998 for ChemoAC				
%#		Dienst FABI, Vrije Universiteit Brussel			
%#		Laarbeeklaan 103, 1090 Jette				
%#										
%# VERSION: 1.2 (07/05/1998)						
%#										
%# TEST: 							
%#										

function [yhat,F,Ftab,lof,b0,b1] = linfit(x,y,intercept);

if nargin == 2
	intercept = 1;				% By default, an intercept is calculated.
end

lx = length(x);
x = reshape(x,lx,1);				% Input vectors are systematically ordered in column.
y = reshape(y,lx,1);

[b0,b1] = mlr(x,y,intercept);			% Estimation of linear model parameters.
yhat = b0+x*b1;					% Responses predicted with linear model.
[F,Ftab,lof] = anovalof(x,y,yhat,2,0.05);	% ANOVA for lack-of-fit.