Asked by Inti Vanmechelen
on 10 Sep 2019

Hi all,

I'm not very good at matlab and trying incorporate the above formula. I'm trying to do part (2) and (3) first, to get them more easily in the complete formula.

I am struggling with (3): Y is in my case a 101x14 matrix and I think the mean should then be one number. I can obviously take the mean of the columns and rows seperately, yielding a 101x1 and a 14x1 vector, but these are obvousily not compatible for matrix multiplication.

Any advice on how to make this work better?

Additionally, am I correct doing the following instead of symsum?

M = 1; % Test day

N = 14; % Number of runs (or repetitions)

T = 101; % Number of time points

for n = 1:N

for t = 1:T

R2 = ....

end

end

Many thanks in advance!

Answer by Thales
on 10 Sep 2019

Accepted Answer

You can use for loops to do the sum or use the sum function:

clc; clear; close all force;

M = 1; % Test day

N = 14; % Number of runs (or repetitions)

T = 101; % Number of time points

Y = rand(M,N,T); % random data to illustrate

% using for loops

Yi_for = zeros(M,1);

for i=1:M

for j=1:N

for t=1:T

Yi_for(i) = Yi_for(i) + Y(i,j,t);

end

end

Yi_for(i) = Yi_for(i)/N/T;

end

% using sums

Yi_sum = zeros(M,1);

for i=1:M

Yi_sum(i) = sum(sum(Y,2),3)/N/T;

end

You can expand this to calculate the average at time point t on the ith test day:

% Yit should be a matrix

Yit = zeros(M,T);

for i=1:M

for t=1:T

for j=1:N

Yit(i,t) = Yit(i,t)+Y(i,j,t);

end

Yit(i,t) = Yit(i,t)/N;

end

end

With Yi and Yit previously calculated, you can define Ra (I splitted the calculations of the numerator and denominator of the fraction to make it clearer):

% Ra

Yi = Yi_sum;

Ra = 1;

% partial sums

num = 0; % numerator

for i=1:M

for j=1:N

for t=1:T

num = num + (Y(i,j,t)-Yit(i,t))^2/M/T/(N-1);

end

end

end

den = 0; % denominator

for i=1:M

for j=1:N

for t=1:T

den = den + (Y(i,j,t)-Yi(i))^2/M/(N*T-1);

end

end

end

Ra2 = 1-num/den

Inti Vanmechelen
on 10 Sep 2019

Thank you for the stepswise explanation!

This was really helpful!

This well definetely get me where I need to be, many thanks :)

darova
on 10 Sep 2019

By my answer is better :(

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Answer by darova
on 10 Sep 2019

Shorter version

clc,clear

Yit = repmat( mean(Yijt,2), [1 N 1] ); % get mean and make 3D matrix

Yi = mean(mean(Yijt,2),3); % get mean 2d and 3d dimensions

Yi = repmat( Yi, [1 N T] ); % make 3D matrix

upsum = (Yijt-Yit).^2;

botsum = (Yijt-Yi).^2;

R2a = 1 - sum(upsum(:))/sum(botsum(:)) * T*(N-1)/(N*T-1);

Inti Vanmechelen
on 10 Sep 2019

Hi Darova,

Since I am still trying get my head around implementing stuff from other in matlab, the long answer helped me a bit better to understand all the steps :) But thank you for the reply!

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