Corrcoef and R^2 definition give different R^2 values

Hi everyone,

I am trying to calculate R^2 value for my data and simulation. I used two different ways.

First one,

     C = corrcoef(ydata,simulation); 
     rsq1 = C(1,2).^2;

Second one,

     rsq2 = 1 - norm(ydata-simulation)^2 / norm(ydata-mean(ydata))^2;

They should be the same, but actually, the second one is smaller than the first one. Could anyone tell me what is a possible reason for that? Thanks a lot!

Rui

Answer 1

[Chris A]

Try the following code:

a=rand(100,1);
c=10*a;
corrcoef(a,c); % This should be the matrix [1 1; 1 1]

% Why should this number be equal to 1.
rsq2 = 1 - norm(a-c)^2 / norm(a-mean(c))^2; % rsq2 is not 1

Answer 2

[Tom Lane]

I would expect your formula to work if simulation is a set of predicted values from fitting ydata using least squares as a function of a set of predictors, including a constant term. Otherwise maybe not.