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% Function:  mymean.m
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% this code will resolve Metrics II Assignment HW#1
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% Author:  Will Grover
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clear all;  % clear all variables
clc;        % clear command window
close all;  % This closes all plot windows
%path(path,'H:\Metrics II')      % set path
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fprintf(1,'\n')
fprintf(1, '\tTITLE: Metrics_II_HW_1.m \n') 
fprintf(1, '\t       \n') 
fprintf(1, '\t       Author:  Will Grover\n') 
fprintf(1,'\n')
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% import data flie
a=importdata('datayx.csv');
x=a(:,1);
y=a(:,2);
lx=length(x);
ly=length(y);
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% sort X
fprintf(1,'\n')
fprintf(1, '\tA: Sort X from smallest to largest.\n') 
fprintf(1,'\n')
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lx=length(x);
xtemp=0;
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for i=1:1:lx;
  for j=1:1:lx;
    if x(i,1) < x(j,1);
      xtemp=x(i,1);
      x(i,1)=x(j,1);
      x(j,1)=xtemp;
    end
   end
end
clear xtemp i j;
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fprintf(1, '\t Here is first 5 rows and last 5 rows of X:') 
x(1:5)
x(lx-4:lx)
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% sort Y
fprintf(1,'\n')
fprintf(1, '\tB: Sort Y from largest to smallest.\n') 
fprintf(1,'\n')
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ly=length(y);
ytemp=0;
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for i=1:1:ly;
  for j=1:1:ly;
    if y(i,1) > y(j,1);
      ytemp=y(i,1);
      y(i,1)=y(j,1);
      y(j,1)=ytemp;
    end
   end
end
clear ytemp i j;
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fprintf(1, '\t Here is first 5 rows and last 5 rows of Y:') 
y(1:5)
y(ly-4:ly)
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clear ans;
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% C: Find mean and variance of X and Y
fprintf(1,'\n')
fprintf(1, '\tC: Find mean and variance of X and Y.\n') 
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% Mean of X
xsum=0;
for i=1:1:lx;
    xsum=xsum+x(i);
end
xmean=xsum/lx;
clear xsum i;
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%
% Mean of Y
ysum=0;
for i=1:1:ly;
    ysum=ysum+y(i);
end
ymean=ysum/ly;
clear ysum i;
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% Variance of X
xxsum=0;
for i=1:1:lx;
    xxsum=xxsum+(x(i)-xmean)^2;
end
xxvar=xxsum/lx-1;
clear xxsum i;
%
%
% Variance of Y
yysum=0;
for i=1:1:ly;
    yysum=yysum+(y(i)-ymean)^2;
end
yyvar=yysum/ly-1;
clear yysum i;
%
% display mean and variance of X and Y
fprintf(1,'\n')
fprintf(1, '\t     sample mean of X: %7.5f \n',xmean)
fprintf(1, '\t     sample var. of X: %7.5f \n',xxvar)
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fprintf(1,'\n')
fprintf(1, '\t     sample mean of Y: %7.5f \n',ymean)
fprintf(1, '\t     sample var. of Y: %7.5f \n',yyvar)
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% d: Find correlation between X and Y
% fprintf(1,'\n')
% fprintf(1, '\tD: correlation between X and Y.\n') 
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ppsum=0;
if lx==ly;
    for i=1:1:ly;
        ppsum=ppsum+(x(i)-xmean)*(y(i)-ymean);
    end
    xstd=sqrt(xxvar);
    ystd=sqrt(yyvar);
    xycorr=ppsum/((ly-1)*ystd*xstd);
else
   fprintf(1,'error: length of x is not same as length of y.') 
end
clear i xstd ystd;
% display correlation between X and Y
fprintf(1,'\n')
fprintf(1, '\tD: Correlation between X and Y: %7.5f \n',xycorr)
%