Data Science from Scratch, 2nd Edition

Chapter 16. Logistic Regression

A lot of people say there’s a fine line between genius and insanity. I don’t think there’s a fine line, I actually think there’s a yawning gulf.

Bill Bailey

In Chapter 1, we briefly looked at the problem of trying to predict which DataSciencester users paid for premium accounts. Here we’ll revisit that problem.

The Problem

We have an anonymized dataset of about 200 users, containing each user’s salary, her years of experience as a data scientist, and whether she paid for a premium account (Figure 16-1). As is typical with categorical variables, we represent the dependent variable as either 0 (no premium account) or 1 (premium account).

As usual, our data is a list of rows [experience, salary, paid_account]. Let’s turn it into the format we need:

xs = [[1.0] + row[:2] for row in data]  # [1, experience, salary]
ys = [row[2] for row in data]           # paid_account

An obvious first attempt is to use linear regression and find the best model:

$$\text{paid}\text{account}={\beta }_0+{\beta }_1\text{experience}+{\beta }_2\text{salary}+\epsilon$$

Figure 16-1. Paid and unpaid users

And certainly, there’s nothing preventing us from modeling the problem this way. The results are shown in Figure 16-2:

from matplotlib import pyplot as plt
from scratch.working_with_data import rescale
from scratch.multiple_regression import least_squares_fit, predict
from scratch.gradient_descent import gradient_step