Regarding Regression cofficient in ANN

Regression plot which we are getting in ANN showing value of R. How the R is calculated and what is the equation of it. what is the difference between correlation factor and this regression coefficient and coefficient of determination.

Answer 1

[Ayush Aniket]

In the context of Artificial Neural Networks (ANN) in MATLAB, the regression plot typically shows the correlation coefficient (R), which is a measure of how well the predicted outputs from the network match the actual target values.

The coefficient of determination ( R^2 ) is the square of the correlation coefficient and provides the proportion of the variance in the dependent variable that is predictable from the independent variable(s). The value ranges from 0 to 1, where 1 indicates perfect prediction.

The difference between these coefficients are as follows:

• Correlation Factor : Measures the linear relationship between variables.
• Regression Coefficient: Refers to the coefficients in a regression equation that quantify the relationship between predictor variables and the response variable.
• Coefficient of Determination: Indicates the proportion of variance explained by the model.

Refer to the following documentation links to read about the coefficients:

• https://www.mathworks.com/help/matlab/ref/corrcoef.html#bunkanr
• https://www.mathworks.com/help/stats/coefficient-of-determination-r-squared.html

Also, refer these MATLAB answers link to better understand the regression plot for the ANN:

• https://www.mathworks.com/matlabcentral/answers/1870742-how-to-calculate-the-coefficient-of-determination-r-2-of-a-neural-network
• https://www.mathworks.com/matlabcentral/answers/510075-can-anyone-interpret-this-regression-plot-for-neural-networks