Linear-Regression

Median house values for 20,640 California census block groups from the 1990 census. The modern default for “show me a real regression problem”: big enough to be non-trivial, small enough to fit anywhere, and full of instructive pathologies — capped targets, aggregate features, and spatial structure.

Provenance#

Constructed by R. Kelley Pace and Ronald Barry for Sparse Spatial Autoregressions, Statistics and Probability Letters 33(3), 1997 — the point of the paper was spatial statistics, not machine learning. The data derive from the 1990 US census at the block group level (the smallest census unit, typically 600 to 3,000 people). It was long distributed via CMU’s StatLib archive; sklearn’s fetch_california_housing mirrors that original. A cosmetically extended variant (with an ocean_proximity categorical) is the running example in Geron’s Hands-On Machine Learning, chapter 2 — numbers from the two variants are not interchangeable.

Intro#

The focus here is on EDA (Exploratory Data Analysis) and investigating the best choice for the \(\lambda\) hyperparameter for LASSO and Ridge Regression.

We will be working on the Life Expectancy CSV data obtained from WHO.

Peeking at Data#

We begin by viewing the columns of the Life Expectancy Dataframe:

import seaborn as sns
import pandas as pd
import matplotlib.pyplot as plt

pd.options.display.float_format = '{:.2f}'.format
le_df = pd.read_csv("life_expectancy.csv")
le_df.columns

We can then view the range of our life expectancy values with a box plot: