palmer-penguins-linear-models

🐧 Penguins of the Palmer Archipelago: A Linear Modeling Field Guide

Do flipper length and species predict a penguin's body mass?
Can we detect differences in bill length across species after controlling for body size?

ANCOVA fitted lines

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📋 Table of Contents

• Problem
• Data
• Methods
• Key Results
• How to Reproduce
• What I'd Do Next

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Problem

This project uses the Palmer Penguins dataset to practice four classical statistical techniques:

1. Simple linear regression how well does flipper length predict body mass?
2. One-way ANOVA do the three penguin species differ in bill length?
3. Two-way ANOVA is there an interaction between species and sex on body mass?
4. ANCOVA after controlling for flipper length, do species-level differences in body mass remain?

The same analysis is implemented in both R and Python to demonstrate cross-language fluency.

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Data

Property	Detail
Source	palmerpenguins R package / seaborn.load_dataset("penguins")
Collector	Dr. Kristen Gorman, Palmer Station LTER, Antarctica
Size	344 penguins → 333 after dropping 11 rows with NAs
Species	Adélie (n=146), Chinstrap (n=68), Gentoo (n=119)
Key variables	bill_length_mm, bill_depth_mm, flipper_length_mm, body_mass_g, species, sex, island, year
License	CC-0 (public domain)

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Methods

R Implementation (R/penguins_analysis.R)

Step	Function	Package
EDA pairs plot	ggpairs()	GGally
Linear regression	lm()	base R
Model diagnostics	plot(model)	base R
One-way ANOVA	aov() + TukeyHSD()	base R
Two-way ANOVA	aov(y ~ A * B)	base R
ANCOVA	lm() + Anova(type=III)	car
Adjusted means	emmeans()	emmeans

Python Implementation (Python/penguins_analysis.py)

Step	Function	Package
EDA pairs plot	pairplot()	seaborn
Linear regression	smf.ols().fit()	statsmodels
ANOVA	anova_lm(model, typ=2)	statsmodels
Tukey post-hoc	pairwise_tukeyhsd()	statsmodels
ANCOVA	smf.ols("y ~ C(A) + x")	statsmodels
Diagnostics	qqplot()	statsmodels

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Key Results

1. Linear Regression

• R² = 0.759 flipper length alone explains ~76% of the variance in body mass
• Slope: each additional mm of flipper length → ~50 g more body mass
• Residual plots confirm linearity and constant variance ✅

2. One-Way ANOVA

• F(2, 330) = 410.6, p < 0.001 strong evidence of species differences in bill length
• Tukey post-hoc: all three pairwise comparisons (Adélie vs Chinstrap, Adélie vs Gentoo, Chinstrap vs Gentoo) are significant

3. Two-Way ANOVA

• Both sex (p < 0.001) and species (p < 0.001) have significant main effects on body mass
• Interaction term p = 0.057 marginal; the sex gap is similar across species

4. ANCOVA

• After controlling for flipper length, species differences in body mass remain significant (p < 0.001)
• Adjusted R² = 0.869 adding species after flipper length improves the model substantially
• Adjusted means at mean flipper length (200.9 mm): Adélie ≈ 3706 g, Chinstrap ≈ 3734 g, Gentoo ≈ 5075 g

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How to Reproduce

R

# Install once
install.packages(c("palmerpenguins","tidyverse","broom","car","emmeans","GGally"))

# Run
source("R/penguins_analysis.R")

Python

pip install pandas numpy matplotlib seaborn statsmodels scipy
python Python/penguins_analysis.py

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What I'd Do Next

• Extend to a linear mixed-effects model (lme4::lmer) with island as a random effect
• Fit a classification model (logistic regression / LDA) to predict species from measurements
• Add a Shiny app (R) or Streamlit dashboard (Python) for interactive exploration

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Data: Gorman KB, Williams TD, Fraser WR (2014). PLoS ONE. | Package: Horst AM, Hill AP, Gorman KB (2020).