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## rsquared

version 1.0.0.0 (2.05 KB) by R P

### R P (view profile)

calculate standard and adjusted R-squared (coefficient of determination)

Updated 05 Dec 2016

rsquared calculates the coefficient of determination (r2) from the original
data (ydata) and fited data (yestimation). It also calculates the adjusted
coefficient (r2adj) considering the number of parameters of the model
(nparam).

Syntax:
r2 = rsquared(ydata,yestimation)

Example:
xdata = [1 5 14 23 25 48 49 59 73 77 99 ];
ydata = [-100 70 100 450 550 2200 2300 3400 5300 5906 9600];
plot(xdata,ydata,'ok'), hold on
param_1 = polyfit(xdata,ydata,1);
yestimation_1 = polyval(param_1,xdata);
plot(xdata,yestimation_1,'-r')
param_2 = polyfit(xdata,ydata,2);
yestimation_2 = polyval(param_2,xdata);
plot(xdata,yestimation_2,'-b')
legend({'data',['r2=' num2str(r2_1) ', r2adj=' ...
'Location','best')

Equations
SSres=sum( (ydata-yestimation).^2 ); % residual sum of squares
SStot=sum( (ydata-mean(ydata)).^2 ); % total sum of squares
r2=1-SSres/SStot; % standard rsquared
r2adj = 1 - SSres/SStot * (length(ydata)-1)/(length(ydata)-nparam); % adjust for the number of parameters

Check https://en.wikipedia.org/wiki/Coefficient_of_determination

### Cite As

R P (2020). rsquared (https://www.mathworks.com/matlabcentral/fileexchange/60577-rsquared), MATLAB Central File Exchange. Retrieved .