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(Not recommended) Perform linear regression of shallow network outputs on targets

regression is not recommended. Use fitlm (Statistics and Machine Learning Toolbox) instead. For more information, see Compatibility Considerations.



[r,m,b] = regression(t,y) calculates the linear regression between each element of the network response and the corresponding target.

This function takes cell array or matrix target t and output y, each with total matrix rows of N, and returns the regression values, r, the slopes of regression fit, m, and the y-intercepts, b, for each of the N matrix rows.

[r,m,b] = regression(t,y,'one') combines all matrix rows before regressing, and returns single scalar regression, slope, and offset values.


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This example shows how to train a feedforward network and calculate and plot the regression between its targets and outputs.

Load the training data.

[x,t] = simplefit_dataset;

The 1-by-94 matrix x contains the input values and the 1-by-94 matrix t contains the associated target output values.

Construct a feedforward neural network with one hidden layer of size 20.

net = feedforwardnet(20);

Train the network net using the training data.

net = train(net,x,t);

{"String":"Figure Neural Network Training (31-Aug-2022 01:58:30) contains an object of type uigridlayout.","Tex":[],"LaTex":[]}

Estimate the targets using the trained network.

y = net(x);

Calculate and plot the regression between its targets and outputs.

[r,m,b] = regression(t,y)
r = 1.0000
m = 1.0000
b = 1.0878e-04

{"String":"Figure Regression (plotregression) contains an axes object. The axes object with title : R=1 contains 3 objects of type line. These objects represent Y = T, Fit, Data.","Tex":": R=1","LaTex":[]}

Input Arguments

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Network targets, specified as a matrix or cell array.

Network outputs, specified as a matrix or cell array.

Output Arguments

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Regression value, returned as a scalar.

Slope of regression fit, returned as a scalar.

Offset of regression fit, returned as a scalar.

Version History

Introduced in R2010b

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See Also

| | (Statistics and Machine Learning Toolbox)