R-squared value for fitted line
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I have plotted log-log graph for data series. than fit a line by ployfit i want to find R-squared for line and data how it can be done (R-squared is explained variance)
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Star Strider
2015-3-13
Using the Wikipedia article on Coefficient of Determination, it’s easiest (and likely correct) to compute the R-squared value on your data using the nonlinear regression and not the log-log linear fit:
dry=[49 12 5 1 1 1 0 0 0 ];
x1=[1 2 3 4 5 6 7 8 9];
x1dry = linspace(min(x1), max(x1));
pwrfit = @(b,x) b(2) .* x.^b(1);
OLSCF = @(b) sum((dry-pwrfit(b,x1)).^2);
B = fminsearch(OLSCF, [-2; 50]);
SStot = sum((dry - mean(dry)).^2); % Compute R-squared
SSres = OLSCF(B);
Rsq = 1 - (SSres/SStot);
When I did this calculation, I got R-squared to be 0.998. Do the same with your ‘wet’ value, with the appropriate changes in the code.
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Nabeel
2015-3-14
Star Strider
2015-3-14
编辑：Star Strider
2015-3-14
My pleasure.
When I run this code:
wet=[120 49 30 21 12 10 9 7 4];
dry=[49 12 5 1 1 1 0 0 0 ];
x1=[1 2 3 4 5 6 7 8 9];
pwrfit = @(b,x) b(2) .* x.^b(1);
% ‘Dry’ Calculations
OLSCF = @(b) sum((dry-pwrfit(b,x1)).^2);
Bdry = fminsearch(OLSCF, [-2; 50]);
SStot = sum((dry - mean(dry)).^2); % Compute R-squared
SSres = OLSCF(Bdry);
RsqDry = 1 - (SSres/SStot);
% ‘Wet’ Calcualtions
OLSCF = @(b) sum((wet-pwrfit(b,x1)).^2);
Bwet = fminsearch(OLSCF, [-2; 50]);
SStot = sum((wet - mean(wet)).^2); % Compute R-squared
SSres = OLSCF(Bwet);
RsqWet = 1 - (SSres/SStot);
fprintf(1, '\n\t Wet = %8.3f * x^%.3f,\t\tRsq = %.4f\n', Bwet(2), Bwet(1), RsqWet)
fprintf(1, '\n\t Dry = %8.3f * x^%.3f,\t\tRsq = %.4f\n', Bdry(2), Bdry(1), RsqDry)
I get:
Wet = 120.447 * x^-1.323, Rsq = 0.9980
Dry = 49.123 * x^-2.148, Rsq = 0.9977
I have no idea why you’re getting 0 for those. At worst, if your default format is set to something that rounds to integers, you should get 1 instead.
Copy and paste my code and run it. You should get the same results.
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