Calculate R^2 of two graphs

Hi guys,

I wanted to know if it is possible to calculate the goodness of fit or R^2 to evaluate the performance of the fit.

I have two separate graphs which are separately calculated: the probability plot (brown) and the dataset (blue cross).

I know that it is able to fit a predefined graph ( e.g. quadratic, polynomial etc.) to a dataset with the toolbox but is it possible to fit my calculated graph to the dataset ?

Thank you

Answer 1

[Star Strider]

One approach —

x = linspace(0.1, 85, 50);                                              % Create Data
y = atanh((x-mean(x))/max(x)*2)/4+0.5 + randn(size(x))*0.01;            % Create Data

X = [x(:).^3 x(:).^2 x(:) ones(size(x(:)))];                            % Design Matrix

X = 50×4

1.0e+05 * 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000 0.0005 0.0001 0.0000 0.0000 0.0015 0.0003 0.0001 0.0000 0.0035 0.0005 0.0001 0.0000 0.0067 0.0008 0.0001 0.0000 0.0116 0.0011 0.0001 0.0000 0.0183 0.0015 0.0001 0.0000 0.0272 0.0019 0.0001 0.0000 0.0387 0.0025 0.0002 0.0000

[B,Bint,R,Rint,Stats] = regress(y(:), X);
ParameterStats = table(Bint(:,1), B, Bint(:,2), 'VariableNames',{'Lower 95% CI','Parameter Value','Upper 95% CI'}, 'RowNames',{'x^3','x^2','x','Const'})

ParameterStats = 4×3 table
             Lower 95% CI    Parameter Value    Upper 95% CI
             ____________    _______________    ____________

    x^3       5.1529e-06       7.0396e-06        8.9263e-06 
    x^2       -0.0011438       -0.0008994       -0.00065504 
    x           0.031404         0.040307          0.049211 
    Const       -0.21537         -0.12867         -0.041973 

Rsq = Stats(1)

Rsq = 0.9192

F_p = [Stats(2:3)]

F_p = 1×2

174.3300 0.0000

ErrorVar_Est = Stats(4)

ErrorVar_Est = 0.0066

figure
plot(x, y, '+b')
hold on
plot(x, X*B, '-r')
hold off
grid

Experiment with the actual data.

.

[Star Strider]

My pleasure!

‘The regression is a polynomial x^3 regression with x&y graph tested on which data ?’

No data were provided, so the regression here is on the data created by these assignments —

x = linspace(0.1, 85, 50); % Create Data

y = atanh((x-mean(x))/max(x)*2)/4+0.5 + randn(size(x))*0.01; % Create Data

‘additional, is it possible to get the goodness of fit of a function F=exp^(x/d) to the dataset x/y.’

I asked for the ‘Stats’ output, and several statistics are provided and listed in my original Answer —

These of course indicate that it is a very good fit.

‘What does the matrix X stand for ?’

The ‘X’ matrix is the design matrix. It creates the independent variable array for the linear regression. See the regress documentation for a full explanation.

A similar result (without the statistics) could be obtained from —

B = X \ y(:)

since the regress function works essentially the same way. See the documentation on mldivide,\ for a description of that function and operator.

.

[Oliver Makan]

again thank you for your quick reply :)

[Star Strider]

As always, my pleasure!

.

Answer 2

[Oliver Makan]

Hi Star Strider,

thank you for the quick approach.

Just for a better understanding:

The regression is a polynomial x^3 regression with x&y graph tested on which data ?

additional, is it possible to get the goodness of fit of a function F=exp^(x/d) to the dataset x/y.

What does the matrix X stand for ?

again thank you very much.