How to compute the correlation coefficient in the two data set.

How to compute the correlation coefficient between the two data sets (this is a graphic with 2 function) I need some helps or see any example, and the image is on the paper

[Mathieu NOE]

Hi

we need a bit more info , data and code ? to help you

[Franco]

It is just an image see below

[Franco]

It is just an image

[Franco]

I'm not sure if X= 0,50,10,150,200,250,300,350

Y= 93,94,95,96,97,98,99,100

[Mathieu NOE]

hello

FYI we can use grabit to scan the picture and get data

GRABIT - File Exchange - MATLAB Central (mathworks.com)

Answer 1

[Mathieu NOE]

hello

so once we have digitized the picture with grabit , we have two data mat files (attached) available for further processing

first step is to make sure the two datasets have common x axis so we must sort out , remove duplicates and interpolate.

then we can compute either one single cor coefficient for the entire data length

%% full data length single cor coeff value
    M = corrcoef(y1_new,y2_new);
    corcoefficient = M(2,1)

will give : corcoefficient = 0.6209

or make a kind of running buffer version of it

full code :

%% load data
load('Data001.mat')
x1 = Data001(:,1);
y1 = Data001(:,2);
% make sure data are unique and sorted in ascending order
[x1,ind] = sort(x1);
x1 = x1(ind);
y1 = y1(ind);
% remove duplicates 
[x1,IA,IC] = unique(x1);
y1 = y1(IA);

load('Data002.mat')
x2 = Data002(:,1);
y2 = Data002(:,2);
% make sure data are unique and sorted in ascending order
[x2,ind] = sort(x2);
x2 = x2(ind);
y2 = y2(ind);
% remove duplicates 
[x2,IA,IC] = unique(x2);
y2 = y2(IA);

% interp data on common x axis
x_min = ceil(max(x1(1),x2(1)));
x_max = floor(min(x1(end),x2(end)));

x = x_min:x_max;
y1_new = interp1(x1,y1,x);
y2_new = interp1(x2,y2,x);

%% full data length single cor coeff value
    M = corrcoef(y1_new,y2_new);
    corcoefficient = M(2,1)

%% running buffer cor coeff value
mybuffer = 10;  % nb of samples in one buffer (buffer size) 
overlap = mybuffer-1; % overlap expressed in samples

%%%% main loop %%%%
m = length(x);
shift = mybuffer-overlap;    % nb of samples between 2 contiguous buffers  
for ci=1:fix((m-mybuffer)/shift +1)
    start_index = 1+(ci-1)*shift;
    stop_index = min(start_index+ mybuffer-1,m);
    time_index(ci) = floor((start_index+stop_index)/2);  % time index expressed as sample unit (dt = 1 in this simulation)
    M = corrcoef(y1_new(start_index:stop_index),y2_new(start_index:stop_index));
    corcoefficient(ci) = M(2,1); 

end
t2 = x(time_index);

figure(1),
subplot(2,1,1),plot(x,y1_new,x,y2_new);
legend('signal x ','signal y ');
subplot(2,1,2),plot(t2,corcoefficient,'-+r');
legend('cor coefficient');