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Análise bivariada e de correlação

Explore relações entre pares de colunas usando gráficos de dispersão, gráficos de caixa e um mapa de calor de correlação.

Análise bivariada e de correlação é uma aula grátis de Pandas & NumPy Academy no CoddyKit. Esta é a aula 3 de 4. Você pode ler a aula completa abaixo gratuitamente — depois pratica ao vivo no navegador com um editor de código integrado e um tutor de IA 24/7. Faz parte do caminho de aprendizado de Pandas & NumPy Academy, e seu progresso é sincronizado entre a web e o app CoddyKit. O curso de Pandas & NumPy Academy inclui 4 aulas no total.

Partes desta aula ainda não foram traduzidas e aparecem em inglês.

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.

Perguntas Frequentes

A aula “Análise bivariada e de correlação” é grátis?

Sim — o texto completo de “Análise bivariada e de correlação” é grátis para ler aqui na web. Para praticá-la interativamente (um editor de código integrado e um tutor de IA 24/7) e desbloquear o restante do curso de Pandas & NumPy Academy, atualize para CoddyKit PRO. O curso de Pandas & NumPy Academy inclui 4 aulas no total.

O que vou aprender em “Análise bivariada e de correlação”?

Explore relações entre pares de colunas usando gráficos de dispersão, gráficos de caixa e um mapa de calor de correlação. Você pratica Pandas & NumPy Academy com código prático que executa diretamente no navegador, e um tutor de IA 24/7 responde suas dúvidas enquanto trabalha na aula.

Preciso ter experiência prévia para começar Pandas & NumPy Academy?

Nenhuma experiência prévia é necessária. Pandas & NumPy Academy no CoddyKit é estruturado para alunos iniciantes até avançados, então você pode começar aqui ou desde o início e aprender no seu ritmo. Esta é a aula 3 de 4.

Quanto tempo leva a aula “Análise bivariada e de correlação”?

A maioria das aulas CoddyKit leva cerca de 5–10 minutos. Cada uma é compacta e interativa, então você faz progresso constante e retoma exatamente de onde parou entre web e app.

Posso escrever e executar código nesta aula de Pandas & NumPy Academy?

Sim. Cada aula de Pandas & NumPy Academy inclui um editor de código integrado, então você escreve e executa código real direto no navegador e recebe feedback de IA instantaneamente — nenhuma configuração local necessária.

Todas as aulas deste curso

  1. Lista de verificação para criação de perfil do conjunto de dados
  2. Análise univariada
  3. Análise bivariada e de correlação
  4. Resumindo descobertas em um relatório
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