# 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:

$paid account equals beta 0 plus beta 1 experience plus beta 2 salary plus epsilon$

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````

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