Figure 9.20:

Uncertainty in activation energy E and rate constant ln k_m versus number of replicated experiments.

Code for Figure 9.20

Text of the GNU GPL.

main.m


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% 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.

alpha = 0.95;
p     = 2;
chisq = chi2inv(alpha,p);
lnk0  = 1;
E     = 100;
Tmin  = 300;
Tmax  = 500;
nTvals = 10;
n0 = 1;
Tmeas    = linspace(Tmin,Tmax,nTvals)';
S = eye(2);
%meanT = 1/(0.5*(1/Tmin+1/Tmax));
meanT = mean(Tmeas);
sets = [1; 2; 5; 100];
nsets = length(sets);
measvar= 1e-3;
measstddev = sqrt(measvar);
for i = 1:nsets
  %
  % stack Tmeas on top of itself sets(i) times
  %
  Tmeasset = kron(ones(sets(i),1), Tmeas);
  ndata = size(Tmeasset,1);
  Tcenter = -1./Tmeasset + 1/meanT;
  X=[ones(ndata,1) Tcenter];
  amat = S*X'*X*S/measvar;
  level = chisq;
  %
  % 95% confidence ellipse
  %
  [x, y] = ellipse (amat, level, 150);
  idx = (i-1)*2+1;
  table(:,idx:idx+1) = [x y];
end
save -ascii replicate.dat table;
if (~ strcmp (getenv ('OMIT_PLOTS'), 'true')) % PLOTTING
plot (table(:,1), table(:,2), ...
      table(:,3), table(:,4), ...
      table(:,5), table(:,6), ...
      table(:,7), table(:,8));
% TITLE
end % PLOTTING