How to calculate R^2 using 1 - (SSR/SST)? For normal fit distribution.

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Macy 2023-2-15

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1913185-how-to-calculate-r-2-using-1-ssr-sst-for-normal-fit-distribution

评论： Torsten 2023-2-21

采纳的回答： Torsten

practice3.xlsx

在 MATLAB Online 中打开

Hello, I have used the fitlm function to find R^2 (see below), to see how good of a fit the normal distribution is to the actual data. The answer is 0.9172.

How can I manually calculate R^2?

R^2 = 1 - (SSR/SST) or in other words 1 - ((sum(predicted - actual)^2) / ((sum(actual - mean of actual)^2)). I am having a hard time getting the correct answer.

Table = readtable("practice3.xlsx");

actual_values = Table.values;

actual_values = sort(actual_values);

normalfit = fitdist(actual_values,'Normal'); % fit the normal distribution to the data

cdfplot(actual_values); % Plot the empirical CDF

x = 0:2310;

hold on

plot(x, cdf(normalfit, x), 'Color', 'r') % plot the normal distribution

hold off

grid on

nonExceedanceProb = sum(actual_values'<=actual_values,2)/numel(actual_values);

Table.nonExceedanceProb=nonExceedanceProb;

mdl=fitlm(cdf(normalfit, actual_values),Table.nonExceedanceProb);

mdl.Rsquared.Ordinary % R^2

ans = 0.9172

mdl.SSR

ans = 0.7567

mdl.SST

ans = 0.8250

% How can I manually calculate R^2 (or SSR and SST)?

% SSR = sum(((predicted data - actual data).^2))

% TSS = sum((actual data - mean(actual data)).^2)

% Rsquared = 1 - SSR/TSS

采纳的回答

Torsten 2023-2-15

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1913185-how-to-calculate-r-2-using-1-ssr-sst-for-normal-fit-distribution#answer_1172350

编辑：Torsten 2023-2-15

在 MATLAB Online 中打开

practice3.xlsx

In my opinion, it does not make sense to fit a linear function to the value pairs (cdf(normalfit, actual_values),Table.nonExceedanceProb) as you do above.

In principle, the blue points below should lie on the red line. This would mean that the empirical cdf is perfectly reproduced by the normal distribution.

So if you really want to compare the two distributions, you should consider the distance of the blue points (achieved quality of fit) to the red line (perfect fit).

Table = readtable("practice3.xlsx");

actual_values = Table.values;

actual_values = sort(actual_values);

normalfit = fitdist(actual_values,'Normal'); % fit the normal distribution to the data

nonExceedanceProb = sum(actual_values'<=actual_values,2)/numel(actual_values);

hold on

plot(nonExceedanceProb,cdf(normalfit, actual_values),'o')

plot([0 1],[0 1])

xlabel('P(empirical)')

ylabel('P(normal)')

hold off

grid on

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Macy 2023-2-15

编辑：Torsten 2023-2-15

在 MATLAB Online 中打开

practice3.xlsx

Ok, that makes sense. A linear function should not be fitted to the values pairs because they are not linear in pattern. So how would I compare the blue points to the red line in the original plot? I'm able to do it for the linear plot as seen here, and I got 0.8408. But I think I understand that it would be more approriate to compare the blue points to the red line in the second plot (the last one). I am getting stuck on what to input for "predicted".

Table = readtable("practice3.xlsx");

actual_values = Table.values;

actual_values = sort(actual_values);

normalfit = fitdist(actual_values,'Normal'); % fit the normal distribution to the data

nonExceedanceProb = sum(actual_values'<=actual_values,2)/numel(actual_values);

hold on

plot(nonExceedanceProb,cdf(normalfit, actual_values),'o')

plot([0 1],[0 1])

xlabel('P(empirical)')

ylabel('P(normal)')

hold off

grid on

predicted = cdf(normalfit, actual_values);

SSR = sum(((predicted - nonExceedanceProb).^2));

TSS = sum((nonExceedanceProb - mean(nonExceedanceProb)).^2);

Rsquared = 1 - SSR/TSS

Rsquared = 0.8408

cdfplot(actual_values);

x = 0:2310;

hold on

plot(x, cdf(normalfit, x), 'Color', 'r')

hold off

grid on

%So how would I input the red data into my R^2 formula?

%predicted_2 = ?????

%SSR = sum(((predicted_2 - nonExceedanceProb).^2));

%TSS = sum((nonExceedanceProb - mean(nonExceedanceProb)).^2);

%Rsquared = 1 - SSR/TSS

Macy 2023-2-21

Yes, Rsquared1 he said is the "pearson correlation coefficient" and Rsquared2 is the "coefficient of determination".

Torsten 2023-2-21

corr(yi,fi) is the pearson correlation coeffcient - I don't know why he wanted to square it.

Anyway: congratulations that you finished your assignment successfully.

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