Finding the F statistic of an ANN regression model I am using the neuralnet package in R, and I wish to find out the F-statistic of a model for a particular regression fit.
I have gone through this link, where they tell you the method to find the F - statistic for a linear regression.
For a neural network, the training and test data are first separated. Subsequently, the training is conducted on the training data and then the prediction error is calculated from the test data.
Here, what would be the number of the coefficients (or the degree of freedom)? How do I calculate or find out the degree of freedom, in order for me to find the F-statistic?

Edit: I strongly believe that the system which is use to collect the data, has a strong influence on how a model behaves. I am working on Machining (Lathe CNC Machining) data. According to several papers that I have found on ScienceDirect, there is a strong influence of the type of material used and the method of machining. The most significant variable (explanatory) is different for each type of material.

During training a NN is often overparameterised and only fits well because of some explicit or implicit regularisation. To compute the effective degrees of freedom is very difficult. With elastic net (How can I calculate the number of degrees of freedom in the Elastic Net regularization, specifically in R?) there is a method that approximates the effective degree of freedom by using the hat matrix which expresses the 'flexibility'/variation of the model around the final fitted point. I wouldn't be surprised if equivalent approaches exist for neural networks.
After training a model you have a fixed formula for predictions. Which contains zero parameters. If you test it then there is no parameter fitting anymore. So your F statistic will use the same degrees of freedom in numerator and denominator and the statistic resembles a relative likelihood.
Sidenote: the use of a F-statistic is not very rigorous in this case. Assumptions relating to it's use are independent and identical normal distributed error terms. So theoretical calculations that estimate statistical probabilities, like p-values, are likely wrong. The use of the F-statistic makes more sense when you can apply some statistical model for it's sample distribution. Otherwise it is just a random measure. Maybe you could better use a more intuitive measure like comparing some relevant cost function.
Related: What does "degree of freedom" mean in neural networks?
