Data Science from Scratch

Chapter 14. Simple Linear Regression

Art, like morality, consists in drawing the line somewhere.

G. K. Chesterton

In Chapter 5, we used the correlation function to measure the strength of the linear relationship between two variables. For most applications, knowing that such a linear relationship exists isn’t enough. We’ll want to be able to understand the nature of the relationship. This is where we’ll use simple linear regression.

The Model

Recall that we were investigating the relationship between a DataSciencester user’s number of friends and the amount of time he spent on the site each day. Let’s assume that you’ve convinced yourself that having more friends causes people to spend more time on the site, rather than one of the alternative explanations we discussed.

The VP of Engagement asks you to build a model describing this relationship. Since you found a pretty strong linear relationship, a natural place to start is a linear model.

In particular, you hypothesize that there are constants (alpha) and (beta) such that:

where is the number of minutes user i spends on the ...