Practical Linear Algebra for Data Science

Chapter 12. Least Squares Applications

In this chapter, you will see a few applications of least squares model fitting in real data. Along the way, you will learn how to implement least squares using several different—​and more numerically stable—​Python functions, and you will learn some new concepts in statistics and machine learning such as multicollinearity, polynomial regression, and the grid search algorithm as an alternative to least squares.

By the end of this chapter, you will have a deeper understanding of how least squares is used in applications, including the importance of numerically stable algorithms for “difficult” situations involving reduced-rank design matrices. And you will see that the analytic solution provided by least squares outperforms an empirical parameter search method.

Predicting Bike Rentals Based on Weather

I’m a big fan of bicycles and a big fan of bibimbap (a Korean dish made with rice and veggies or meat). Therefore, I was happy to find a publicly available dataset about bike rentals in Seoul.¹ The dataset contains nearly nine thousand observations of data about the number of bikes that were rented in the city and variables about the weather including temperature, humidity, rainfall, windspeed, and so on.

The purpose of the dataset is to predict the demand for bike sharing based on weather and season. That is important because it will help bike rental companies and local governments optimize the availability of healthier modes of transportation. ...