Matlab_05b

% OK for the next example you have a bunch of empirical data like this:

%

A = [11 42 141 587 2093 7792 23643 93437 331519];    

S = [1.0759 0.5925 0.3407 0.1796 0.1089 0.0621 0.0340 0.0272 0.0155];    

%

% let us see if we can make any sense of it.

% first lets plot it

%

figure(1);

subplot(2,2,1);

plot(A,S,'b');

legend({'raw plot'})

%

% not easy to see what is going on

% now let's look on the log log plot of the data:

%

subplot(2,2,2);

loglog(A,S,'c')

legend({'loglog plot'})

%

% which looks far more useful

% we will plot this again in a slightly 

% different way

%

subplot(2,2,3);

ALog = log10(A);

SLog = log10(S);

plot(ALog,SLog,'ko');

legend({'plot of log values'})

%

% it certainly looks linear in loglog space!

% which means it has the form

% S = K*A^M

% it would be very easy to fit a line to the loglog plot using polyfit

%

pfit = polyfit(ALog, SLog,1);

%

% this gives us a K value of 10^0.4247 = 2.6589 (remember we are in log

% space) and the best-fit slope of -0.41

%

% we can plot the fitted line in red next to the experimental points

%

subplot(2,2,4);

xVals = 0:0.5:max(ALog);

wrong_yVals = polyval(pfit,xVals);

plot(ALog,SLog,'ko'); hold on;

plot(xVals,wrong_yVals,'r');

legend({'data' '[-0.41,0.42]'})