MATLAB: Plotregression fitlm rsquare difference

fitlmOptimization ToolboxplotregressionrsquareStatistics and Machine Learning Toolbox

Hello

Could you help explain why there is a difference between r-squared calculated using plotregression() and fitlm()?

R-squared: 0.968 from fitlm() R = 0.98364 from plotregression()

The code to produce the two r-squared values is below.

%% set up variable from neural network output = net(input); outputTest = output(tr.testInd); targetTest = target(tr.testInd);

%% first method to produce r-squared plotregression(targetTest,outputTest,'Testing')

%% second method to produce r-squared mdl = fitlm(targetTest,outputTest); r2 = mdl.Rsquared.Ordinary;

Regards

William Bell

Best Answer

>> 0.98364^2

ans =

    0.9675

Thank you for formally accepting my answer

Greg

Related Solutions

MATLAB: How to calculate the MSE for multi-output neural network

It is better to combine scalars into vectors and matrices when they have the same numerical scale. My ideal is to STANDARDIZE inputs and targets to zero mean and unit variance. As shown below, this leads to the dimensionless normalized mean-square-error figure of merit related to the regression R-squared (see Wikipedia) via

           NMSE = 1 - Rsq
with
        0 <= NMSE, Rsq <= 1

Calculate the mean and standard deviations of all input and target rows. Remove or modify values which are more than a specified number of standard deviations from the mean (scatter plots are especially useful here). Then recalculate means and standard deviations and standardize.

I always use NMSE (in [0,1]), the normalized mean-square error obtained using the constant reference output

outref = mean(target')'
MSEref = mse( target- outref )
       = mean( var(target',1) )

Then

NMSE = mse(target-output)/ MSEref
    = 1 - Rsquare      % See Wikipedia

Hope this helps.

Thank you for formally acceoting my answer

Greg

MATLAB: What is MSE00 and MSE00a and R

Unfortunately, I just saw this post.

MSE00 is the MSE for a naïve constant output model that always outputs the average of the target data. MSE = SSE/Neq where Neq is the number of equations that are used to estimate the unknown weights.

MSE00a is the MSE "a"djusted for the loss in estimation degrees of freedom caused by the bias of evaluating the MSE with the same data that was used to build the model. MSEa = SSE/Ndof where Ndof is the number of estimation degrees of freedom Ndof = Neq-Nw where Nw is the number of unknown weights that are estimated.

It is not hard to show that MSE00 is the average biased target variance (divide by N)and MSE00a is the average unbiased target variance (divide by N-1).

NMSE = MSE/MSE00 is the normalized MSE for an arbitrary model

NMSEa = MSEa/MSE00a is the normalized "a"djusted MSE

R^2 = 1-NMSE and Ra^2 = 1-NMSEa are the coefficient of determination and DOF "a"djusted value.

R^2 is often interpreted as the fraction of the target variance that is "explained" by the model.

R turns out to be the slope of the output vs target linear regression line.

Look up Rsquare and coefficient-of-determination in Wikipedia and other statistics references.

Best Answer

Related Solutions

MATLAB: How to calculate the MSE for multi-output neural network

MATLAB: What is MSE00 and MSE00a and R

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