# r squared comparing sine waves

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C.G. on 18 May 2022
Answered: Rishav on 11 Oct 2023
I have a dataset to which I have asked matlab to fit a sine wave. I want to find the r^2 value to see how well the sine curve I have generated fits the data.
Is there a simple way of doing this?
x1 = time';
y = Qe_mean;
yu = max(y);
yl = min(y);
yr = (yu-yl);
yz = y-yu+(yr/2);
zx = time(yz .* circshift(yz,[0 1]) <= 0);
P = period;
ym = mean(Qe_mean);
fit = @(b,x) b(1).*(sin(2*pi*x./P + 2*pi/b(2))) + b(3);
fcn = @(b) sum((fit(b,x1) - y).^2);
s = fminsearch(fcn, [yr; -1; ym])
xp = linspace(min(x1),max(x1),P);
figure()
plot(xp,fit(s,xp), 'b')
hold on
plot(time,y,'k','Linewidth',1)

Rishav on 11 Oct 2023
Hi C.G.,
I understand that you want to find the r^2 value to see how well the generated sine curve fits the data.
To calculate the coefficient of determination (R-squared) for your sine wave fit in MATLAB, you can use the following steps. You can use the corrcoef function to calculate the correlation between your observed data and the fitted sine wave. Here's how you can do it:
Calculate the R-squared value:
% Calculate the fitted sine wave
fitted_sine_wave = fit(s, x1);
% Calculate the correlation coefficient
corr_matrix = corrcoef(y, fitted_sine_wave);
% Extract the R-squared value
r_squared = corr_matrix(1, 2)^2;
disp(['R-squared value: ', num2str(r_squared)]);
The corrcoef function calculates the correlation matrix between two datasets, and corr_matrix(1, 2) gives you the correlation coefficient between your observed data (y) and the fitted sine wave (fitted_sine_wave). The R-squared value is simply the square of this correlation coefficient.
Here's the modified code with the R-squared value calculation included:
x1 = time';
y = Qe_mean;
yu = max(y);
yl = min(y);
yr = (yu - yl);
yz = y - yu + (yr / 2);
zx = time(yz .* circshift(yz, [0 1]) <= 0);
P = period;
ym = mean(Qe_mean);
fit = @(b, x) b(1) * (sin(2 * pi * x ./ P + 2 * pi / b(2))) + b(3);
fcn = @(b) sum((fit(b, x1) - y).^2);
s = fminsearch(fcn, [yr; -1; ym]);
xp = linspace(min(x1), max(x1), P);
figure();
plot(xp, fit(s, xp), 'b');
hold on;
plot(time, y, 'k', 'Linewidth', 1);
% Calculate the R-squared value
fitted_sine_wave = fit(s, x1);
corr_matrix = corrcoef(y, fitted_sine_wave);
r_squared = corr_matrix(1, 2)^2;
disp(['R-squared value: ', num2str(r_squared)]);
The R-squared value indicates how well the sine wave fits your data, with a value of 1 indicating a perfect fit and lower values indicating a less perfect fit.
Thank you,
Rishav Saha

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