%   Seong Byun
%   Assignment 1

clc
clear all

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

%------------------------------------------------------------------------%
%   A. Sort X from smallest to largest

    %STRATEGY:  Write my own codes for finding min (mymin) and max (mymax)
    %           Then use these commands to sort the vectors
    %           Refer to mymin.m and mymax.m files

l=length(x);
z=x;
for i=1:l,
    [a b]=mymin(x(i:l));
    z(i)=x(b+i-1);
    z(b+i-1)=x(i);
    x=z;
end;
xsorted=x;

%------------------------------------------------------------------------%
%   B. Sort Y from largest to smallest
l=length(y);
z=y;
for i=1:l,
    [a b]=mymax(y(i:l));
    z(i)=y(b+i-1);
    z(b+i-1)=y(i);
    y=z;
end;
ysorted=y;

clear a b i l z ans;

%------------------------------------------------------------------------%
%   C. Calculate mean and variance of x and y
l=length(x);
xy=[x y];
xy_bar=(xy'*ones(l,1))'./l;
xy_dev=xy-repmat(xy_bar,l,1);
xy_var=((xy_dev.*xy_dev)'*ones(l,1))'./(l-1);
xy_std=sqrt(xy_var);

% Or directly get variance-covariance matrix by
xy_cov=xy_dev'*xy_dev./(l-1);


%------------------------------------------------------------------------%
%   D. Calculate correlation between x and y
xy_corr=xy_cov(1,2)/(sqrt(xy_cov(1,1))*sqrt(xy_cov(2,2)));

% or get a correlation coefficient matrix
xy_corr=xy_cov.*((xy_std.^-1)'*(xy_std.^-1));



%------------------------------------------------------------------------%
%   E. Make functions (mymean,myvar,mycorr)

%   refer to mymean.m myvar.m, mycorr.m files

mymean(xy);
mydemean(xy);
myvar(xy);
mycorr(xy);


%------------------------------------------------------------------------%
%   F. Program OLS function

%   Refer to myols.m file
clear l ans
load datayx.csv;
x=datayx(:,1);
y=datayx(:,2);
clear datayx

[b,R,ehat,tval]=myols(x,y);