R-squared value for fitted line

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)

Answer 1

[Star Strider]

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.

[Nabeel]

Thanks this this graph was a part of research paper which i have studied recently. this code work well for it. but when i apply this on my original data it has r-squared of 0 for both wet and dry......

[Star Strider]

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.