%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%      The University of Texas at Dallas     
%        ECON 7309 - Econometrics II
%        Professor Donggyu Sul, Ph.D.
%                                            
%               Cesar Zamudio                
%          Ph.D. Student, Marketing          
%                 Fall 2010                 
%                                            
%               Assignment 1
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
clear;clc;
%Download X and Y variables from the class homepage.
%Throughout I assume Column 1 is Variable X, and Column 2 is Variable Y.
%data=load('Assignment 1 - Data X and Y.csv');
data=load('datayx.csv');
X=data(:,1);
Y=data(:,2);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%QA. Sort X from smallest to largest.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%We will use the straight insertion algorithm.
n=size(X,1);
Xsorted=X;
subplot(2,1,1)
for j=1:1:n
    target=Xsorted(j,1);
    i=j-1;
    while (i>0 && Xsorted(i,1)>target)
        Xsorted(i+1,1)=Xsorted(i);
        i=i-1;
    end
    Xsorted(i+1)=target;
    pause(.005)
    plot(Xsorted,'bo-')        
    title('Sorting using straight insertion algorithm - X')
end
disp('Sorted elements of X (smallest to largest)')
Xsorted

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%QB. Sort Y from largest to smallest.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%We could simply "flip" a vector sorted from smallest to largest. For the
%purposes of the assignment, however, we will modify the algorithm above to
%sort in the opposite way. This can be done by reversing the inequality in
%the while loop.
subplot(2,1,2)
n=size(Y,1);
Ysorted=Y;
for j=1:1:n
    target=Ysorted(j,1);
    i=j-1;
    while (i>0 && Ysorted(i,1)<target)
        Ysorted(i+1,1)=Ysorted(i);
        i=i-1;
    end
    Ysorted(i+1)=target;
    pause(.025)
    plot(Ysorted,'ro-')        
    title('Sorting using straight insertion algorithm - Y')
end
disp('Sorted elements of Y (largest to smallest)')
Ysorted

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%QC: Calculate the mean and variance of X and Y.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%First let us calculate the mean of both variables.
%I assume we cannot use any built-in MATLAB function throughout.

%%%%%%%%%%%% MEANS
%Mean of X.
sumx=0;
for i=1:1:size(X,1)
    sumx=sumx+X(i,1);
end
meanX=sumx/size(X,1);
%Check whether the calculation is right.
[meanX mean(X)]
if meanX==mean(X)
    disp('Calculated mean of X is equal to MATLAB mean function result!')
else
    disp('Mean of X is wrong')
end
%Mean of Y.
sumY=0;
for i=1:1:size(Y,1)
    sumY=sumY+Y(i,1);
end
meanY=sumY/size(Y,1);
%Check whether the calculation is right.
[meanY mean(Y)]
if meanY==mean(Y)
    disp('Calculated mean of Y is equal to MATLAB mean function result!')
else
    disp('Mean of Y is wrong')
end

%%%%%%%%%%%% VARIANCES
%Variance of X
varX=0;
n=size(X,1);
for i=1:1:size(X,1)
    varX=varX+(X(i,1)-meanX)*(X(i,1)-meanX);
end
varX=varX/(n-1);
%Check whether the calculation is right
[varX var(X)]
if varX==var(X)
    disp('Calculated variance of X is equal to MATLAB variance function result!')
else
    disp('Variance of X is wrong')
end

%Variance of Y
varY=0;
n=size(Y,1);
for i=1:1:size(Y,1)
    varY=varY+(Y(i,1)-meanY)*(Y(i,1)-meanY);
end
varY=varY/(n-1);
%Check whether the calculation is right
[varY var(Y)]
if varY==var(Y)
    disp('Calculated variance of Y is equal to MATLAB variance function result!')
else
    disp('Variance of Y is wrong')
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%QD: Calculate the correlation between X and Y.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%To obtain the sample correlation of X and Y, we first need their sample
%covariances.
n=size(X,1);
covXY=0;
for i=1:1:size(X,1)
    covXY=covXY+(X(i,1)-mymean(X))*(Y(i,1)-mymean(Y));
end
covXY=covXY/(n-1);
covariance=cov(X,Y);
%Here we need the covariance from the var-covar matrix, not the variance
%(e.g. not the diagonal)
disp('Difference between my covariance and MATLAB covariance function')
covXY-covariance(1,2)
%Here there is an error of 4.4409E-16 in the correspondence between my
%formula and MATLAB, so I'm not reporting the checking.
%Now we can calculate the correlation.
corrXY=covXY/(sqrt(varX)*sqrt(varY));
disp('Difference between my correlation and MATLAB correlation function')
corrXY-corr(X,Y)
%MATLAB functions are in separate files.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%QE: Make functions (mymean, myvar, mycorr) and calculate C,D,E.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
disp('Means of X and Y')
[mymean(X) mymean(Y)]
disp('Variances of X and Y')
[myvar(X) myvar(Y)]
disp('Correlation between X and Y')
mycorr([X Y])
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %QF: Program OLS function.
% %    Input: X and Y, Tx1 vectors
% %    Regression: y=bX+u
% %    Output: b, rē, t-values
% %    Function: [b,rē,tb] = myols(y,x)
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% disp('Result from OLS with intercept')
% myOLS(X,Y)