%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% Ryan Davis
% Metrics 2 - HW#1
% September 1st, 2010
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%
clear, clc

% get data
data = importdata('datayx.csv', ',')

% since the filename lists y first, then assume y is in first column

Y = data(:,1);
X = data(:,2);



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

% can get bonus points for faster search (more efficient)
% hint: what if split into 2, do loops for each
% use mean perhaps

% Now, we sort using bubble sort
% Number of entries, n
X_sort_bubble = X;
n=length(X);

% since we compare the current number (i) to the next number i+1, 
% then we have i=1,...,n-1 so that i+1=2,...n
% since we only have n numbers (length of vector X)
for j=1:1:n-1
    for i=1:1:n-1
    % note that the loops are nested, since we must compare each number to
    % every other number in the sort, and swapping the items if they are
    % not in the right order.
    if X_sort_bubble(i)>X_sort_bubble(i+1);
        temp=X_sort_bubble(i);
        X_sort_bubble(i)=X_sort_bubble(i+1);
        X_sort_bubble(i+1)=temp;
    end
    end
end

% display sorted list
X_sort_bubble

% check results using built in function
X_sort = sort(X,'ascend');

if X_sort_bubble == X_sort
    disp('X matches!')
else
    disp('Error: X does not match!')
end



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

% Just use the same procedure as above, flopping the inequality sign

Y_sort_bubble = Y;
n=length(Y);

for j=1:1:n-1
    for i=1:1:n-1
    if Y_sort_bubble(i)<Y_sort_bubble(i+1);
        temp=Y_sort_bubble(i);
        Y_sort_bubble(i)=Y_sort_bubble(i+1);
        Y_sort_bubble(i+1)=temp;
    end
    end
end

% display sorted list
Y_sort_bubble

% check results using built in function
Y_sort = sort(Y,'descend');

if Y_sort_bubble == Y_sort
    disp('Y matches!')
else
    disp('Error: Y does not match!')
end



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% C. Calculate mean and variance of X and Y
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% mean of X
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

n = length(X);
X_sum = 0;
for i=1:1:n
    X_sum = X_sum + X(i);
end

X_mean = X_sum/n

% matches: mean(X)



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% mean of Y
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

n = length(Y);
Y_sum = 0;
for i=1:1:n
    Y_sum = Y_sum + Y(i);
end

Y_mean = Y_sum/n

% matches: mean(Y)



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% variance of X
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

n = length(X);
X_sum_sq_dev = 0;
for i=1:1:n
    X_sum_sq_dev = X_sum_sq_dev + (X(i) - X_mean)^2;
end

X_var = X_sum_sq_dev/(n-1)

% matches: var(X)
% 1.3512



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% variance of Y
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

n = length(Y);
Y_sum_sq_dev = 0;
for i=1:1:n
    Y_sum_sq_dev = Y_sum_sq_dev + (Y(i) - Y_mean)^2;
end

Y_var = Y_sum_sq_dev/(n-1)

% matches: var(X)
% 1.3530



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% D. Calculate correlation between X and Y.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% assume that "correlation" implies the correlation coefficient.
% recall basic formula for correlation:
% r_xy = (SUM_1toN [(xi-xbar)(yi-ybar)] ) / ((n-1)*sx*sy)
% where sx and sy are sample standard deviations.

X_stdev = sqrt(X_var)
Y_stdev = sqrt(Y_var)

% matches: std(X), std(Y)
% 1.1624, 1.1632

% now let's get the numerator of the r_xy equation

n = length(X);
sum_prod_devs = 0;
for i=1:1:n
    sum_prod_devs = sum_prod_devs + (X(i) - X_mean)*(Y(i) - Y_mean);
end

r_xy = sum_prod_devs / ((n-1)*X_stdev*Y_stdev)

% matches: corr(X,Y)
% 1.0000



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% E. Make functions to calculate C and D.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% see separate matlab (.m) files

X_mymean = mymean(X)
% matches: X_mean = 0.1231

Y_mymean = mymean(Y)
% matches: Y_mean = 0.1224

X_myvar = myvar(X)
% matches: X_var = 1.3512

Y_myvar = myvar(Y)
% matches: Y_var = 1.3530

r_mycorr = mycorr(X,Y)
% matches: r_xy = 1.0000