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

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Rui
Rui 2012-10-26
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

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回答（2 个）

Chris A
Chris A 2012-10-26
编辑：Chris A 2012-10-26
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
Tom Lane
Tom Lane 2012-10-27
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.

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