R2 with a loglog plot
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Hi everyone.
I am quite new to matlab and I'd like to add a R2 to my loglog plot. I've seen some solution from few other posts, but none really does the job. My code is really simple:
bx= figure;
set(bx,'visible', 'on');
f = fit(x,y,'power1');
loglog(x,y,'O');
hold on;
plot(f);
[...]
the result look like that:
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/155536/image.png)
So far I haven't find any way of determining the r2: That post (https://uk.mathworks.com/matlabcentral/answers/182998-r-squared-value-for-fitted-line) overestimates my r2, and this bit of code found somewhere on the ML forum as well:
ba = [x,ones(size(x))]\y;
ypred = ba(1)*x + ba(2);
SSE=sum((y-ypred).^2);
SST=sum((y-mean(y)).^2);
Rsq = 1 - (SSE/SST);
I also tried that way, but I think it works fine only for linear distributions:
X = [ones(length(x),1) x];
b = X\y;
yCalc = X*b;
r = 1 - sum((y - yCalc).^2)/sum((y - mean(y)).^2);
Thank you very much for your help :)
Flo
PS: the the r2 on excel is equal to 0.9597
0 件のコメント
回答 (1 件)
dpb
2016 年 8 月 8 日
I see nothing wrong with Star's Answer nor follow-up comment. To compute SSE from such a model requires evaluating the residual of the fit in original metric, not in log space.
But, fit returns a cfit for curves (your case) and some additional optional outputs, the second of which is a goodness-of-fit structure, gof in the documentation. Fields in gof include
sse - Error SSquares
R2 - Coefficient of determination ("raw" R-square)
adjustedR2 - DOF-adjusted R-square
stdError - RMS (or "standard") error
so to save yourself some effort, use it...
[f,gof] = fit(x,y,'power1');
7 件のコメント
dpb
2016 年 8 月 12 日
編集済み: dpb
2016 年 8 月 12 日
Well, you need to look at the results obtained from the models (for the same, not disparate datasets) from Excel and Matlab to uncover where there's a difference. Clearly the results for the data you posted appear correct; if you got wildly different results from Excel, the most likely cause given the plot you posted is that it isn't the same dataset you're actually comparing to.
ADDENDUM
I attempted to read values off the above plot to see what kind of fit it actually provided; the Rsq was lower some but about 0.998 as 0.95 altho I could see guesstimating didn't work to get terribly close to the plot.
Agan, I can only suggest if you can reproduce the results you first quote in Excel, attach that set of data and model coefficients and results.
>> [f,gof]=fit(x,y,'power1')
f =
General model Power1:
f(x) = a*x^b
Coefficients (with 95% confidence bounds):
a = 1.026 (1.011, 1.04)
b = 1.013 (0.9852, 1.042)
gof =
sse: 1.6864e-04
rsquare: 0.9997
dfe: 13
adjrsquare: 0.9996
rmse: 0.0036
>> B % results from S-S:
B =
0.0254
1.0134
>> Rsq
Rsq =
0.9997
>>
BTW, I used fit in comparison to the fminsearch solution--results are essentially identical--
ADDENDUM 2
"*fit* in comparison to the fminsearch"
Actually, I just noticed there are two different solutions reached; the power term with fminsearch is about the magnitude of that of the fit solution less 1.0 -- 0.0254 vis a vis 1.026. How can that be???
Oh,
yfit = @(b,x) exp(b(1)) .* x.^b(2); % Power Function
has a definition problem; it's estimating log(B(1)) instead of B(1) directly...let's see what happens if redefine in same model space as fit uses--
>> yfit = @(b,x) b(1).*x.^b(2); % model A*x^B; B(1),B(2)-->A,B
>> SSECF = @(b) sum((yfit(b,x) - y).^2);
>> B = fminsearch(SSECF, [1; 1]);
>> B
B =
1.0256
1.0134
>>
Ah! As expected, now we agree...whew! :) Was worried there for a minute...
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