Bivariate and Correlation Analysis
Explore relationships between pairs of columns using scatter plots, box plots, and a correlation heatmap.
Bivariate and Correlation Analysis is a free Pandas & NumPy Academy lesson on CoddyKit — lesson 3 of 4. You can read the complete lesson below for free — then practise it hands-on in the browser with a built-in code editor and a 24/7 AI tutor. It is part of the Pandas & NumPy Academy learning path, one of 4 lessons in the course, and your progress syncs across the web and the CoddyKit app.
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.
Frequently asked questions
Is the “Bivariate and Correlation Analysis” lesson free?
Yes — the full text of “Bivariate and Correlation Analysis” is free to read here on the web, and the Pandas & NumPy Academy course includes 4 lessons in total. To practise it interactively (a built-in code editor and a 24/7 AI tutor) and unlock the rest of the Pandas & NumPy Academy course, upgrade to CoddyKit PRO.
What will I learn in “Bivariate and Correlation Analysis”?
Explore relationships between pairs of columns using scatter plots, box plots, and a correlation heatmap. You practise Pandas & NumPy Academy with hands-on code you run directly in the browser, and a 24/7 AI tutor answers your questions as you work through the lesson.
Do I need any experience to start Pandas & NumPy Academy?
No prior experience is required. Pandas & NumPy Academy on CoddyKit is structured for beginners through advanced learners; this is — lesson 3 of 4, so you can start here or from the beginning and move at your own pace.
How long does the “Bivariate and Correlation Analysis” lesson take?
Most CoddyKit lessons take about 5–10 minutes. Each one is bite-sized and interactive, so you make steady progress and pick up exactly where you left off across the web and the app.
Can I write and run code in this Pandas & NumPy Academy lesson?
Yes. Every Pandas & NumPy Academy lesson includes a built-in code editor, so you write and run real code right in your browser and get instant AI feedback — no local setup required.
All lessons in this course
- Dataset Profiling Checklist
- Univariate Analysis
- Bivariate and Correlation Analysis
- Summarising Findings in a Report