correlation-analysis

name	Correlation Analysis
description	Measure relationships between variables using correlation coefficients, correlation matrices, and association tests for correlation measurement, relationship analysis, and multicollinearity detection

Correlation Analysis

Overview

Correlation analysis measures the strength and direction of relationships between variables, helping identify which features are related and detect multicollinearity.

When to Use

• Identifying relationships between numerical variables
• Detecting multicollinearity before regression modeling
• Exploratory data analysis to understand feature dependencies
• Feature selection and dimensionality reduction
• Validating assumptions about variable relationships
• Comparing linear and non-linear associations

Correlation Types

• Pearson: Linear correlation (continuous variables)
• Spearman: Rank-based correlation (ordinal/non-linear)
• Kendall: Rank correlation (robust alternative)
• Cramér's V: Association for categorical variables
• Mutual Information: Non-linear dependencies

Key Concepts

• Correlation Coefficient: Ranges from -1 to +1
• Positive Correlation: Variables move together
• Negative Correlation: Variables move oppositely
• Multicollinearity: High correlations between predictors

Implementation with Python

import pandas as pd
import numpy as np
import matplotlib.pyplot  plt
 seaborn  sns
 scipy.stats  pearsonr, spearmanr, kendalltau


np.random.seed()
n = 
age = np.random.uniform(, , n)
income = age *  + np.random.normal(, , n)
education_years = age /  + np.random.normal(, , n)
satisfaction = income /  + np.random.normal(, , n)

df = pd.DataFrame({
    : age,
    : income,
    : education_years,
    : satisfaction,
    : age - education_years - 
})


corr_matrix = df.corr(method=)
()
(corr_matrix)


corr_coef, p_value = pearsonr(df[], df[])
()


spearman_matrix = df.corr(method=)
()
(spearman_matrix)

spearman_coef, p_value = spearmanr(df[], df[])
()


kendall_coef, p_value = kendalltau(df[], df[])
()


fig, axes = plt.subplots(, , figsize=(, ))


sns.heatmap(corr_matrix, annot=, cmap=, center=,
            square=, ax=axes[], vmin=-, vmax=)
axes[].set_title()


sns.heatmap(spearman_matrix, annot=, cmap=, center=,
            square=, ax=axes[], vmin=-, vmax=)
axes[].set_title()

plt.tight_layout()
plt.show()


 ():
    rows, cols = [], []
     col1  df.columns:
         col2  df.columns:
             col1 < col2:  
                r, p = pearsonr(df[col1], df[col2])
                rows.append({
                    : col1,
                    : col2,
                    : r,
                    : p,
                    :   p <   
                })
     pd.DataFrame(rows)

corr_table = correlation_with_pvalue(df)
()
(corr_table)


fig, axes = plt.subplots(, , figsize=(, ))

pairs = [(, ), (, ),
         (, ), (, )]

 idx, (var1, var2)  (pairs):
    ax = axes[idx // , idx % ]
    ax.scatter(df[var1], df[var2], alpha=)

    
    z = np.polyfit(df[var1], df[var2], )
    p = np.poly1d(z)
    x_line = np.linspace(df[var1].(), df[var1].(), )
    ax.plot(x_line, p(x_line), , linewidth=)

    r, p_val = pearsonr(df[var1], df[var2])
    ax.set_title()
    ax.set_xlabel(var1)
    ax.set_ylabel(var2)
    ax.grid(, alpha=)

plt.tight_layout()
plt.show()


 statsmodels.stats.outliers_influence  variance_inflation_factor

X = df[[, , ]]
vif_data = pd.DataFrame()
vif_data[] = X.columns
vif_data[] = [variance_inflation_factor(X.values, i)  i  (X.shape[])]

()
(vif_data)
()
()


 ():
     scipy.stats  linregress

    
    x_residuals = df[x] - np.poly1d(
        np.polyfit(df[control_vars].values, df[x], deg=)
    )(df[control_vars].values)

    
    y_residuals = df[y] - np.poly1d(
        np.polyfit(df[control_vars].values, df[y], deg=)
    )(df[control_vars].values)

     pearsonr(x_residuals, y_residuals)[]

partial_corr = partial_correlation(df, , , [])
()


:
     dcor  distance_correlation
    dist_corr = distance_correlation(df[], df[])
    ()
 ImportError:
    ()


fig, ax = plt.subplots(figsize=(, ))

rolling_corr = df[].rolling(window=).corr(df[])
ax.plot(rolling_corr.index, rolling_corr.values)
ax.set_title()
ax.set_ylabel()
ax.grid(, alpha=)
plt.show()