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Analyse bivariée et analyse des corrélations

Explorez les relations entre paires de colonnes à l’aide de nuages de points, de boîtes à moustaches et d’une carte thermique des corrélations.

Analyse bivariée et analyse des corrélations est une leçon Pandas & NumPy Academy gratuite sur CoddyKit. Ceci est la leçon 3 sur 4. Tu peux lire la leçon complète ci-dessous gratuitement — puis la pratiquer en direct dans le navigateur avec un éditeur de code intégré et un tuteur IA 24/7. Elle fait partie du parcours d'apprentissage Pandas & NumPy Academy, et ta progression se synchronise sur le web et l'application CoddyKit. Le cours Pandas & NumPy Academy comprend 4 leçons au total.

Certaines parties de cette leçon n'ont pas encore été traduites et s'affichent en anglais.

From One Variable to Two

Bivariate analysis examines the relationship between exactly two columns at a time. After profiling each column individually (univariate analysis), you ask: how do these two variables relate? The analysis method depends on the combination of variable types: numeric vs. numeric (scatter plot + correlation), categorical vs. numeric (box/violin plot), or categorical vs. categorical (crosstab + chi-squared). Each combination requires a different technique.

import pandas as pd
import seaborn as sns

df = sns.load_dataset('titanic')

# Relationship types present in the dataset
print('Numeric columns:', df.select_dtypes('number').columns.tolist())
print('Categorical columns:', df.select_dtypes('object').columns.tolist())
print('Boolean columns:', df.select_dtypes('bool').columns.tolist())

Numeric vs. Numeric: Scatter Plot

For two numeric variables, a scatter plot is the primary bivariate tool. It shows each observation as a point at (x, y) coordinates, revealing the direction, strength, and form of the relationship. Always look at the plot before computing a correlation coefficient — a correlation of 0 can still show a strong non-linear (curved) relationship that the coefficient misses.

import seaborn as sns
import matplotlib.pyplot as plt

df = sns.load_dataset('titanic')

sns.scatterplot(data=df, x='age', y='fare', alpha=0.4)
plt.title('Age vs. Fare — Is There a Linear Relationship?')
plt.xlabel('Age')
plt.ylabel('Fare ($)')
plt.show()

Pearson Correlation Coefficient

The Pearson r quantifies the strength and direction of the linear relationship between two numeric variables. Compute it with df[['col1', 'col2']].corr() or scipy.stats.pearsonr(x, y) which also returns a p-value for significance testing. Always pair r with a scatter plot — high r can be driven by a few outliers, and the same r can describe very different scatter shapes (Anscombe's Quartet famously illustrates this).

import pandas as pd
import seaborn as sns
from scipy import stats

df = sns.load_dataset('titanic').dropna(subset=['age', 'fare'])

# Pearson correlation
r, p = stats.pearsonr(df['age'], df['fare'])
print(f'Pearson r = {r:.3f}, p-value = {p:.4f}')

# Spearman for robustness check
rho, p_sp = stats.spearmanr(df['age'], df['fare'])
print(f'Spearman rho = {rho:.3f}, p-value = {p_sp:.4f}')

Categorical vs. Numeric: Box and Violin Plots

When one variable is categorical and the other is numeric, the question is: does the numeric distribution differ across categories? Use a box plot or violin plot to compare. For example, does survival status affect the fare paid? Does the passenger class affect age? These plots immediately reveal whether category membership is associated with higher or lower values of the numeric variable.

import seaborn as sns
import matplotlib.pyplot as plt

df = sns.load_dataset('titanic')

fig, axes = plt.subplots(1, 2, figsize=(12, 5))

sns.boxplot(data=df, x='class', y='fare',
            order=['First', 'Second', 'Third'], ax=axes[0])
axes[0].set_title('Fare by Passenger Class')

sns.violinplot(data=df, x='survived', y='age',
               inner='quartile', ax=axes[1])
axes[1].set_title('Age Distribution by Survival')

plt.tight_layout()
plt.show()

GroupBy Statistics for Categorical vs. Numeric

Complement the visual comparison with numeric group statistics using groupby. Compute the mean, median, and count for each category to quantify the differences seen in plots. Look for categories where the mean and median diverge (indicating outliers within a group), and check whether group sizes are balanced — very small groups (<5 observations) make comparisons unreliable.

import pandas as pd
import seaborn as sns

df = sns.load_dataset('titanic')

stats = df.groupby('class')['fare'].agg(['mean', 'median', 'std', 'count'])
stats.columns = ['Mean Fare', 'Median Fare', 'Std Fare', 'Count']
print(stats.round(2))

print('\nSurvival rate by class:')
print(df.groupby('class')['survived'].mean().round(3))

Categorical vs. Categorical: Crosstabs

For two categorical variables, use pd.crosstab(df['var1'], df['var2']) to create a frequency table showing how many observations fall in each combination of categories. Normalise by row or column with normalize='index' or normalize='columns' to get proportions instead of counts. This is the foundation for studying whether two categorical variables are independent or associated.

import pandas as pd
import seaborn as sns

df = sns.load_dataset('titanic')

# Frequency table
counts = pd.crosstab(df['class'], df['survived'])
counts.columns = ['Died', 'Survived']
print('Counts:')
print(counts)

# Row-normalised proportions (survival rate per class)
props = pd.crosstab(df['class'], df['survived'], normalize='index')
props.columns = ['Died', 'Survived']
print('\nSurvival Rate per Class:')
print(props.round(3))

Visualising Crosstabs as Heatmaps

Turn a crosstab into a heatmap for instant visual comparison of cell frequencies. This is more scannable than a printed table when there are many category combinations. Annotate each cell with its value using annot=True and choose a sequential colour map (like 'YlOrRd') since all values are non-negative. Heatmaps of row-normalised proportions effectively show the conditional distribution of one category given another.

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

df = sns.load_dataset('titanic')
props = pd.crosstab(df['class'], df['sex'], normalize='index')

sns.heatmap(props, annot=True, fmt='.2f', cmap='YlOrRd')
plt.title('Gender Mix by Passenger Class (Row %)')
plt.xlabel('Sex')
plt.ylabel('Class')
plt.show()

Chi-Squared Test for Independence

The chi-squared test of independence checks whether two categorical variables are statistically independent. scipy.stats.chi2_contingency(crosstab) returns the chi-squared statistic, p-value, degrees of freedom, and expected frequencies. A small p-value (typically < 0.05) means there is a statistically significant association between the two variables — the distribution of one varies systematically with the other.

import pandas as pd
import seaborn as sns
from scipy.stats import chi2_contingency

df = sns.load_dataset('titanic')

# Test if passenger class and survival are independent
crosstab = pd.crosstab(df['class'], df['survived'])
chi2, p, dof, expected = chi2_contingency(crosstab)

print(f'Chi-squared: {chi2:.2f}')
print(f'P-value: {p:.6f}')
print(f'Degrees of freedom: {dof}')
print(f'\nConclusion: {"Significant association" if p < 0.05 else "No significant association"}')

Full Correlation Matrix for Numeric Columns

Rather than examining pairs one at a time, compute the full correlation matrix for all numeric columns and visualise it as a heatmap. This reveals which pairs of variables are strongly correlated in one glance. High correlations between independent features (multicollinearity) can cause problems in regression models — knowing about them early allows you to remove or combine redundant features before modelling.

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

df = sns.load_dataset('titanic')
corr = df.select_dtypes('number').corr()
mask = np.triu(np.ones_like(corr, dtype=bool))

sns.heatmap(corr, mask=mask, annot=True, fmt='.2f',
            cmap='coolwarm', vmin=-1, vmax=1,
            linewidths=0.5, square=True)
plt.title('Correlation Matrix — Titanic Numeric Columns')
plt.tight_layout()
plt.show()

Interactions Across Subgroups

Sometimes a relationship between two variables differs dramatically across subgroups — a phenomenon known as Simpson's Paradox. For example, the correlation between age and fare might be positive for first-class passengers but negative for third-class. Always segment your bivariate analysis by key categorical variables (using hue in Seaborn or separate groupby aggregations) to check whether the relationship is consistent or reverses across subgroups.

import seaborn as sns
import matplotlib.pyplot as plt

df = sns.load_dataset('titanic')

# Scatter coloured by passenger class
sns.scatterplot(
    data=df.dropna(subset=['age', 'fare']),
    x='age',
    y='fare',
    hue='class',
    alpha=0.5,
    palette='deep'
)
plt.title('Age vs Fare — Does Class Change the Relationship?')
plt.legend(title='Class')
plt.yscale('log')  # log scale due to fare skewness
plt.show()

Documenting Bivariate Findings

After completing bivariate analysis, document key findings: which pairs of features are correlated (and how strongly), whether categorical variables show meaningful group differences in numeric outcomes, and any subgroup interactions or paradoxes found. These insights should drive feature selection decisions — highly correlated feature pairs may need one dropped, and strong categorical predictors of the target variable should be flagged as high-priority inputs for modelling.

Quick Check

Test your understanding of bivariate and correlation analysis from this lesson.

Lesson Recap

In this lesson you learned: scatter plots and Pearson r analyse numeric-numeric relationships, box/violin plots and groupby compare numeric variables across categories, and crosstabs with chi-squared tests measure association between categorical variables. Next up we cover how to compile EDA findings into a structured summary report.

Questions Fréquemment Posées

La leçon « Analyse bivariée et analyse des corrélations » est-elle gratuite ?

Oui — le texte complet de « Analyse bivariée et analyse des corrélations » est gratuit à lire ici sur le web. Pour la pratiquer de manière interactive (un éditeur de code intégré et un tuteur IA 24/7) et déverrouiller le reste du cours Pandas & NumPy Academy, passe à CoddyKit PRO. Le cours Pandas & NumPy Academy comprend 4 leçons au total.

Qu'est-ce que j'apprendrai dans « Analyse bivariée et analyse des corrélations » ?

Explorez les relations entre paires de colonnes à l’aide de nuages de points, de boîtes à moustaches et d’une carte thermique des corrélations. Tu pratiques Pandas & NumPy Academy avec du code pratique que tu exécutes directement dans le navigateur, et un tuteur IA 24/7 répond à tes questions au fur et à mesure que tu avances dans la leçon.

Dois-je avoir de l'expérience pour commencer Pandas & NumPy Academy ?

Aucune expérience préalable n'est requise. Pandas & NumPy Academy sur CoddyKit est structuré pour les débutants jusqu'aux apprenants avancés, donc tu peux commencer ici ou depuis le début et avancer à ton rythme. Ceci est la leçon 3 sur 4.

Combien de temps prend la leçon « Analyse bivariée et analyse des corrélations » ?

La plupart des leçons CoddyKit prennent environ 5–10 minutes. Chacune est courte et interactive, tu progresses régulièrement et tu repiques exactement où tu t'es arrêté sur le web et l'app.

Peux-tu écrire et exécuter du code dans cette leçon Pandas & NumPy Academy ?

Oui. Chaque leçon Pandas & NumPy Academy inclut un éditeur de code intégré, tu écris et exécutes du vrai code directement dans ton navigateur et tu reçois des retours IA instantanés — aucune configuration locale requise.

Toutes les leçons de ce cours

  1. Liste de contrôle pour le profilage d’un jeu de données
  2. Analyse univariée
  3. Analyse bivariée et analyse des corrélations
  4. Résumer les résultats dans un rapport
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