The Ecological Detective (Chapter 5)

As a lab group we are reading the Ecological Detective, a great book that confronts models with data blah blah blah...

Here is the pseudo code for Chapter 5, on least squares. I wrote in Matlab. You can just cut and paste this into the command window. Or save it as a .m file.

% One iteration of the Monte Carlo Method is below:
% We do this to generate a random-ish data set.

A=1;
B=0.5;
C=0.25;
w=-3+(3-(-3)).*rand(10,1) % this is code for generating ten (a vector) of random unifor variables between [-3,3]
Data=zeros(1,10) % getting an empty vector to collect our resulting Data's

for i=1:10 % this loop fills up the Data vector with values from the poly and random var
Y(i)=A+B*(i)+C*(i)^2+w(i);
end

Data

plot(Data,'o','MarkerFaceColor','g')




%%%%% Now we fit a model to the data we just generated %%%%%%%%%%%

Amin=0;Amax=3;Bmin=0;Bmax=2;Cmin=0;Cmax=1;
cat=10000000000;
ABC=[0,0,0]
x=[1 2 3 4 5 6 7 8 9 10];
for A=Amin:0.1:Amax
for B=Bmin:0.05:Bmax
for C=Cmin:0.025:Cmax
Data=[3.638342118359073 5.434751622453716 2.511920897761036 9.480255136834117 10.544155477352458 10.585242429996457 15.420989313202291 21.281289115229903 28.495041012605785 33.789331211195659];
lsq=sum(Data-(A+B*x+C*x.^2)).^2
if lsqABC=[A,B,C]
cat=lsq
end
end
end
end

ABC
plot(Data,'o','MarkerFaceColor','r')
hold on;
plot(ABC(1)+ABC(2)*x+ABC(3)*x.^2,'-k')
hold on;
plot(1+0.5*x+0.25*x.^2,'--b')