Categorical explanatory variables

Introduction to Regression with statsmodels in Python

Maarten Van den Broeck

Content Developer at DataCamp

Fish dataset

Each row represents one fish.
There are 128 rows in the dataset.
There are 4 species of fish:
- Common Bream
- European Perch
- Northern Pike
- Common Roach

species	mass_g
Bream	242.0
Perch	5.9
Pike	200.0
Roach	40.0
...	...

Visualizing 1 numeric and 1 categorical variable

import matplotlib.pyplot as plt
import seaborn as sns

sns.displot(data=fish,
            x="mass_g",
            col="species",
            col_wrap=2,
            bins=9)

plt.show()

A faceted histogram of fish counts versus their weights. Each panel contains a species: bream, perch, pike, or roach.

Summary statistics: mean mass by species

summary_stats = fish.groupby("species")["mass_g"].mean()
print(summary_stats)

species
Bream    617.828571
Perch    382.239286
Pike     718.705882
Roach    152.050000
Name: mass_g, dtype: float64

Linear regression

from statsmodels.formula.api import ols 
mdl_mass_vs_species = ols("mass_g ~ species", data=fish).fit()

print(mdl_mass_vs_species.params)

Intercept           617.828571
species[T.Perch]   -235.589286
species[T.Pike]     100.877311
species[T.Roach]   -465.778571

Model with or without an intercept

From previous slide, model with intercept

mdl_mass_vs_species = ols(
  "mass_g ~ species", data=fish).fit()

print(mdl_mass_vs_species.params)

Intercept           617.828571
species[T.Perch]   -235.589286
species[T.Pike]     100.877311
species[T.Roach]   -465.778571

The coefficients are relative to the intercept: $617.83 - 235.59 = 382.24!$

Model without an intercept

mdl_mass_vs_species = ols(
  "mass_g ~ species + 0", data=fish).fit()

print(mdl_mass_vs_species.params)

species[Bream]    617.828571
species[Perch]    382.239286
species[Pike]     718.705882
species[Roach]    152.050000

In case of a single, categorical variable, coefficients are the means.

Let's practice!

Introduction to Regression with statsmodels in Python