function P3_14
clear, clc, format short g, format compact
prob_title = (['Antoine Parameters by Linear Regression']);
ind_var_name=[' T (C)  '];
dep_var_name=['TlogPv '];
xyData=[-60.72272	-70.	0.8674675
-59.25998	-60.	0.9876663
-55.01853	-50.	1.100371
-48.3806	-40.	1.209515
-39.22488	-30.	1.307496
-28.06241	-20.	1.403121
-14.9693	-10.	1.49693
0	0	1.582063
16.62758	10.	1.662758
34.88586	20.	1.744293
54.64541	30.	1.821514
75.68378	40.	1.892095
98.14213	50.	1.962843
121.7874	60.	2.029789
146.5395	70.	2.093422
172.3783	80.	2.154728
199.3359	90.	2.214844
227.1842	100.	2.271842
256.1218	110.	2.32838
285.6253	120.	2.380211];
X=xyData(:,2:end);
y=xyData(:,1);
[m,n]=size(X);
freeparm=input(' Input 1 if there is a free parameter, 0 otherwise >  ');
[Beta, ConfInt,ycal, Var, R2]=MlinReg(X,y,freeparm);
disp([' Results,  ' prob_title]);
Res=[];
if freeparm==0, nparm = n-1; else nparm = n; end 
for i=0:nparm
          if freeparm, ii=i+1; else ii=i; end
          Res=[Res; ii Beta(i+1) ConfInt(i+1)];
end
disp('     Parameter No.   Beta      Conf_int');      
disp(Res);
disp(['  Variance ', num2str(Var)]);
disp(['  Correlation Coefficient ', num2str(R2)]);
plot(y,y-ycal,'*')
title(['Residual Plot, ' prob_title]) % residual plot
xlabel([dep_var_name '(Measured)'])
ylabel('Residual')
pause
plot(X(:,1),ycal, 'r-',X(:,1),y,'b+' )
title(['Calculated/Experimental Data ' prob_title])
xlabel([ind_var_name])
ylabel([dep_var_name])
function [Beta, ConfInt, ycalc, Var, R2]=MlinReg(X,y,freeparm)
[m,n]=size(X); % m-number of rows, n-number of columns   
if freeparm				
	X=[ones(m,1) X]; % Add column of ones if there is a free parameter				
	npar=n+1;				
else					
	npar=n;				
end	
A=X'*X
Xty=X'*y
Beta=X\y;  % Solve X'Beta = Y using QR decomposition					
ycalc=X*Beta; % Calculated dependent variable values
Var=((y-ycalc)'*(y-ycalc))/(m-npar); % variance
ymean=mean(y);
R2=(ycalc-ymean)'*(ycalc-ymean)/((y-ymean)'*(y-ymean));%linear correlation coefficient
% Calculate the confidence intervals
A=X'*X;	
Ainv=A\eye(size(A)); %Calculate the inverse of the X'X matrix
tdistr95=[12.7062 4.3027 3.1824 2.7764 2.5706 2.4469 2.3646 2.306 2.2622 2.2281...
            2.2010 2.1788 2.1604 2.1448 2.1315 2.1199 2.1098 2.1009 2.093 2.086 2.0796... 
            2.0739 2.0687 2.0639 2.0595 2.0555 2.0518 2.0484 2.0452 2.0423 2.0395 2.0369...
            2.0345 2.0322 2.0301 2.0281 2.0262 2.0244 2.0227 2.0211 2.0195 2.0181 2.0167...
            2.0154 2.0141]; % 95 percent probability t-distr. values
if (m-npar)>45
   t=2.07824-0.0017893*(m-npar)+0.000008089*(m-npar)^2; % t for degrees of freedom > 45
else
   t=tdistr95(m-npar);
end
for i=1:npar					
   	ConfInt(i,1)=t*sqrt(Var*Ainv(i,i)); %confidence intervals					
end