Weights and bias' relative to preprocessed X

Question

I am currently using sklearn scale to preprocess my X data before being put into a perceptron - mean/stddev so as to prevent the data converging to infinity or 0. My perceptron returns the weights + bias after the network has been trained:

X = preprocessing.scale(X)

After processing the X and Y data through my perceptron I am returned with weights. From these weights I can calculate the line of best fit:

ls = cp.linspace(cp.min(X), cp.max(X))
best_fit = w[1]+w[0]*ls

where w[1] is a bias. This best_fit line is accurate but it is relative to the preprocessed X rather than the original X which I would like to plot. What is the technique to make these weights relative to the original X values if it is possible?

Answer 1

If $$y = w_1 + w_0 \left(\frac{x_{}-\mu_1}{\sigma_1} \right),$$

then we have $$y = \left(w_1-\frac{\mu_1}{\sigma_1}\right)+ \left(\frac{w_0}{\sigma_1}\right)x$$