Before we build our first model

When we talk about models, you can think of them as simplified theoretical approximations of complex reality. As such, there is always some inferiority involved, also called the approximation error. This error will guide us in choosing the right model among the many choices we have. We will calculate this error as the squared distance of the model's prediction to the real data; for example, for a learned model function, f, the error is calculated as follows:

def error(f, x, y):
    return np.sum((f(x)-y)**2)

The vectors x and y contain the web stats data that we extracted earlier. It is the beauty of NumPy's vectorized functions, which we exploit here with f(x). The trained model is assumed to take a vector and return the results again as a vector of the same size so that we can use it to calculate the difference to y.