% fitting world population data to exponential model

clear all

% data
popdt=[-10000     1;  
 -8000     5;  
 -6500     5;  
 -5000     5;  
 -4000     7;  
 -3000    14;  
 -2000    27;  
 -1000    50;  
  -500   100;  
  -400   162; 
  -200   150;  
     1   170;  
   200   190;  
   400   190;  
   500   190;  
   600   200;  
   700   207;  
   800   220;  
   900   226;  
  1000   254;  
  1100   301;  
  1200   360;  
  1250   400;  
  1300   360;  
  1340   443;  
  1400   350;  
  1500   425;  
  1600   545;  
  1650   470;  
  1700   600;  
  1750   629;  
  1800   813; 
  1850 1128; 
  1900 1550; 
  1910 1750; 
  1920 1860; 
  1930 2070; 
  1940 2300; 
  1950 2400];

tim=popdt(:,1);
popul=popdt(:,2);

% matrix and vector to define min squares problem
A=[tim ones(size(tim))];
B=log(popul);
   
   
% our estimated parameters 
PAR=A\B


% now let us see how our estimates compare to data
for kk=1:length(B)
   ppl(kk)=PAR(1)*tim(kk)+PAR(2);
end


% comparing logarithms
plot(tim,ppl,tim,log(popul),'or')
pause

% or

% comparing values
plot(tim,exp(ppl),tim,popul,'or')