2.3 Linear Model in Action

 Let's actually train a single-input linear neuron model using the gradient descent algorithm. First, we need to sample multiple data points. For a toy example with a known model, we directly sample from the specified real model:

y = 1.477x  + 0.0089

01. Sampling data

In order to simulate the observation errors, we add an independent error variable e to the model, where e follows a Gaussian distribution with a mean value of 0 and a standard deviation of 0.01(i.e., variance of 0.01):

y = 1.477x + 0.089 + e, e ~ N(0.01)