%   Ryan E. Freling
%   Econometrics II
%   Fall 2010
%   Assignment 1

clc 
clear

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%	Load datayx.csv
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
load datayx.csv;
y=datayx(:,1);
x=datayx(:,2);

n=size(datayx,1);
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%	A. Sort X from smallest to largest
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

xsort=x;
t=0;
for j=1:n;
    for i=1:n-1;
        if xsort(i,1)>xsort(i+1,1);
            t=xsort(i,1);
            xsort(i,1)=xsort(i+1,1);
            xsort(i+1,1)=t;
            t=0;
        end;
    end;
end;
disp('Sorted Values of X (ascending)');
xsort

% test result of sort program
z=sort(x);
[xsort-z];
% test result of sort program
zx=[xsort-z];
disp('Test result of sort program')
disp(' ')
disp('If sumtest=0, sort program matches MATLAB');
sumtest=sum(zx)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%	B. Sort Y from largest to smallest
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

ysort=y;
t=0;
for j=1:n;
    for i=1:n-1;
        if ysort(i,1)<ysort(i+1,1);
            t=ysort(i,1);
            ysort(i,1)=ysort(i+1,1);
            ysort(i+1,1)=t;
            t=0;
        end;
    end;
end;

disp('Sorted Values of Y (descending)');
ysort

% test result of sort program
z=sort(y,'descend');
zy=[ysort-z];
disp('Test result of sort program')
disp(' ')
disp('If sumtest=0, sort program matches MATLAB');
sumtest=sum(zy)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   C. Calculate Mean and Variance of X and Y
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

xmean=0;
ymean=0;
xx=0;
yy=0;

for i=1:n;
    xmean=xmean+xsort(i);
    ymean=ymean+ysort(i);
    xx=xx+xsort(i)*xsort(i);
    yy=yy+ysort(i)*ysort(i);
end;

disp('average of X values')
xmean=xmean/n                       %calculate average of x;
disp('average of X calculated by matlab Mean function')
mean(x)
disp('average of Y values')
ymean=ymean/n
disp('average of Y calculated by matlab Mean function')
mean(y)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Calculate Variance
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%xxm=xx/n;                           %calculate average of x^2;
%yym=yy/n;

%xvar=xxm-xmean*xmean                %population variance
%yvar=yym-ymean*ymean                %var(u)=E(u^2)-(E(u))^2;

%sample variance;
xv=0;
yv=0;

for i=1:n;
    xv=xv+(xsort(i)-xmean)*(xsort(i)-xmean);
    yv=yv+(ysort(i)-ymean)*(ysort(i)-ymean);
end;

disp('Variance of X values')
xvars=xv/(n-1)
disp('variance of X using MATLAB function')
var(x)
disp('average of Y values')
yvars=yv/(n-1)
disp('variance of Y using MATLAB function')
var(y)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   D. Calculate the correlation between X and Y
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Pearson's Correlation
    %population standard deviation
%xstd=sqrt(xvar);
%ystd=sqrt(yvar);
%dcor=xstd*ystd;

    %sample standard deviations (use variance from C.):
xstds=sqrt(xvars);
ystds=sqrt(yvars);
dcors=ystds*xstds;

%calculate covariance;
xycv=0;

for i=1:n;
    xycv=xycv+(xsort(i)-xmean)*(ysort(i)-ymean);
end;

%sample covariance;
xycov2=xycv/(n-1);

disp('Sample correlation coefficient for sorted values of X and Y')
xycor2=xycov2/dcors
disp('correlation coefficient using MATLAB function')
corr(xsort,ysort)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   E.  Make functions (mymean, myvar, mycorr) and use them to 
%       Calculate C., D., and E.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

disp('difference between mymean and MATLAB mean function');
[mymean(xsort) mean(xsort) mymean(xsort)-mean(xsort)]

disp('difference between myvar and MATLAB var function');
[myvar(x) var(x) myvar(x)-var(x)]

disp('difference between mycorr and MATLAB corr function');
[mycorr(xsort,ysort) corr(xsort,ysort) mycorr(xsort,ysort)-corr(xsort,ysort)]