Figure 9.9 (page 517):

Several replicate data sets, ln k versus 1/T.

Code for Figure 9.9

Text of the GNU GPL.

main.m

%% Copyright (C) 2001, James B. Rawlings and John G. Ekerdt
%%
%% This program is free software; you can redistribute it and/or
%% modify it under the terms of the GNU General Public License as
%% published by the Free Software Foundation; either version 2, or (at
%% your option) any later version.
%%
%% This program is distributed in the hope that it will be useful, but
%% WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
%% General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program; see the file COPYING.  If not, write to
%% the Free Software Foundation, 59 Temple Place - Suite 330, Boston,
%% MA 02111-1307, USA.

%
% Arhenius.m
%
chisq = 5.99;  % chi square value for 95% confidence level with 2 parameters
lnk0  = 1;
E     = 100;
ndata = 10;
Tmin  = 300;
Tmax  = 500;
Tmeas = linspace(Tmin,Tmax,ndata)';
X     = [ones(ndata,1) -1./Tmeas];
lnk   = X*[lnk0; E];
k     = exp(lnk);
measvar= 1e-3;
measstddev = sqrt(measvar);
%
% set seed for 'reproducible' random numbers
%
randn('seed',0);
%
%just a few noisy points
%
nexpts = 500;
clear lnkmeas;
for i = 1:nexpts lnkmeas(:,i) = lnk + measstddev*randn(ndata,1); end
%for i = 1:nexpts kmeas(:,i) = k + measstddev*randn(ndata,1); end
%lnkmeas = log(kmeas);
theta = (inv(X'*X)*X' * lnkmeas)';
%%
%%center the data first
%%
Tcenter = -1./Tmeas + 1/mean(Tmeas);
Xcenter=[ones(ndata,1) Tcenter];
thetacenter = (inv(Xcenter'*Xcenter)*Xcenter' * lnkmeas)';
tmp = [1./Tmeas, lnkmeas(:,1:10)];
plot (tmp(:,1), tmp(:,2), '.', ...
       tmp(:,1), tmp(:,3), 'o', ...
       tmp(:,1), tmp(:,4), '+', ...
       tmp(:,1), tmp(:,5), '*', ...
       tmp(:,1), tmp(:,6), 'x', ...
       tmp(:,1), tmp(:,7), 'o', ...
       tmp(:,1), tmp(:,8), '+', ...
       tmp(:,1), tmp(:,9), '*', ...
       tmp(:,1), tmp(:,10), 'x', ...
       tmp(:,1), tmp(:,11), 'o');
title ('Figure 9.9')