SciPy

Master statistical computations, optimization, and scientific computing with Python's most powerful mathematical library for data analysis.

What Makes SciPy Essential

SciPy builds on NumPy to deliver advanced scientific computing capabilities. While NumPy handles arrays, SciPy tackles complex mathematical problems. Statistical hypothesis testing. Optimization algorithms. Signal processing. Advanced clustering. The heavy mathematical lifting that separates basic analysis from serious data science.

Think of it this way — NumPy is your calculator, SciPy is your engineering toolkit. Every Fortune 500 data team uses SciPy for statistical inference. Amazon for A/B testing. Netflix for recommendation optimization. Google for clustering algorithms. The mathematical foundation behind machine learning frameworks.

Statistical Testing with SciPy

The scenario: Flipkart's pricing team needs to test if Electronics category customers spend significantly more than Clothing customers. Statistical significance determines pricing strategy.

# Import SciPy's statistics module for hypothesis testing
import scipy.stats as stats
import pandas as pd
import numpy as np

# Load our ecommerce dataset for analysis
df = pd.read_csv('dataplexa_ecommerce.csv')
print(f"Dataset shape: {df.shape}")
print(f"Columns: {list(df.columns)}")

Dataset shape: (10000, 11)
Columns: ['order_id', 'date', 'customer_age', 'gender', 'city', 'product_category', 'product_name', 'quantity', 'unit_price', 'revenue', 'rating']

Now separate revenue data by category. Independent samples t-test compares means between two groups. Perfect for category comparison analysis.

# Extract revenue data for Electronics category customers
electronics_revenue = df[df['product_category'] == 'Electronics']['revenue']

# Extract revenue data for Clothing category customers  
clothing_revenue = df[df['product_category'] == 'Clothing']['revenue']

# Display basic statistics for comparison
print(f"Electronics: Mean ₹{electronics_revenue.mean():.0f}, Count {len(electronics_revenue)}")
print(f"Clothing: Mean ₹{clothing_revenue.mean():.0f}, Count {len(clothing_revenue)}")

Electronics: Mean ₹45,234, Count 2,847
Clothing: Mean ₹28,156, Count 2,129

Time for the independent samples t-test. This determines statistical significance between group means.

# Perform independent samples t-test between the two groups
t_statistic, p_value = stats.ttest_ind(electronics_revenue, clothing_revenue)

# Display test results with interpretation
print(f"T-statistic: {t_statistic:.3f}")
print(f"P-value: {p_value:.6f}")
print(f"Significant at α=0.05: {'Yes' if p_value < 0.05 else 'No'}")

T-statistic: 23.847
P-value: 0.000000
Significant at α=0.05: Yes

Electronics dominates with ₹45K average revenue, 60% higher than lowest category

Electronics clearly leads revenue generation across all product categories. The ₹17K difference between Electronics and Clothing represents substantial business impact. Statistical significance confirms this isn't random variation — it's a real pattern worth strategic attention.

This analysis supports focused marketing spend on Electronics customers. Higher lifetime value justifies premium acquisition costs. Clothing customers might need different engagement strategies or upselling to premium products.

Optimization and Curve Fitting

The scenario: Zomato's data team wants to model the relationship between customer age and average order value. Finding the optimal curve helps predict spending patterns for different demographics.

# Import optimization module for curve fitting
from scipy.optimize import curve_fit

# Calculate average revenue by customer age
age_revenue = df.groupby('customer_age')['revenue'].mean().reset_index()
print(f"Age range: {age_revenue['customer_age'].min()} to {age_revenue['customer_age'].max()}")
print(f"Revenue range: ₹{age_revenue['revenue'].min():.0f} to ₹{age_revenue['revenue'].max():.0f}")

Age range: 18 to 65
Revenue range: ₹28,945 to ₹52,180

# Define quadratic function to model age-revenue relationship
def quadratic_model(x, a, b, c):
    return a * x**2 + b * x + c

# Extract data arrays for curve fitting
x_data = age_revenue['customer_age'].values
y_data = age_revenue['revenue'].values
print(f"Fitting model to {len(x_data)} age groups")

Fitting model to 48 age groups

# Fit quadratic curve to age-revenue data using optimization
optimal_params, covariance = curve_fit(quadratic_model, x_data, y_data)

# Extract optimized parameters
a, b, c = optimal_params
print(f"Optimal parameters: a={a:.3f}, b={b:.3f}, c={c:.0f}")
print(f"R² coefficient: {np.corrcoef(y_data, quadratic_model(x_data, a, b, c))[0,1]**2:.3f}")

Optimal parameters: a=-2.847, b=298.456, c=25789
R² coefficient: 0.847

Quadratic model captures peak spending around age 52, then declining revenue in older customers

The fitted curve reveals critical business insights. Revenue peaks around age 52, then declines — likely reflecting peak earning years followed by retirement-driven spending reduction. This inverted parabola pattern suggests targeting mid-career professionals for premium offerings.

With R² = 0.847, this model predicts 84.7% of revenue variation from age alone. Marketing teams can now forecast demographic spending, optimize age-targeted campaigns, and identify high-value customer segments with mathematical precision.

Clustering and Spatial Analysis

The scenario: Swiggy wants to group cities by customer behavior patterns. Hierarchical clustering reveals natural market segments for targeted expansion strategies.

# Import clustering modules from SciPy
from scipy.cluster import hierarchy
from scipy.spatial.distance import pdist

# Calculate city-level metrics for clustering analysis
city_metrics = df.groupby('city').agg({
    'revenue': 'mean',
    'customer_age': 'mean', 
    'rating': 'mean',
    'quantity': 'mean'
}).round(2)
print("City metrics for clustering:")
print(city_metrics)

City metrics for clustering:
            revenue  customer_age  rating  quantity
city                                               
Bangalore     38420         41.2    4.12      3.8
Chennai       35680         39.8    4.08      3.6
Delhi         42150         42.1    4.15      4.1
Mumbai        44890         43.2    4.18      4.3
Pune          36240         40.5    4.09      3.7

# Calculate pairwise distances between cities using Euclidean metric  
distances = pdist(city_metrics.values, metric='euclidean')

# Perform hierarchical clustering using Ward linkage method
linkage_matrix = hierarchy.linkage(distances, method='ward')

# Display clustering results 
print("Hierarchical clustering complete")
print(f"Distance matrix shape: {distances.shape}")
print(f"Linkage matrix shape: {linkage_matrix.shape}")

Hierarchical clustering complete
Distance matrix shape: (10,)
Linkage matrix shape: (4, 4)

# Extract cluster assignments at 2-cluster level
cluster_labels = hierarchy.fcluster(linkage_matrix, t=2, criterion='maxclust')

# Display clustering results with city names
cluster_results = pd.DataFrame({
    'City': city_metrics.index,
    'Cluster': cluster_labels,
    'Revenue': city_metrics['revenue']
})
print("City clustering results:")
print(cluster_results.sort_values('Cluster'))

City clustering results:
      City  Cluster  Revenue
2    Delhi        1    42150
3   Mumbai        1    44890
0  Bangalore      2    38420
1    Chennai      2    35680
4     Pune        2    36240

Metro cities (blue) outperform growth cities (red) across all customer behavior metrics

The radar chart clearly shows metro cities dominating across all dimensions. Mumbai and Delhi form a premium segment with older, higher-spending customers who order larger quantities. This clustering analysis drives market-specific strategies — premium products for metros, value offerings for growth cities.

SciPy's clustering capabilities extend beyond simple grouping. The mathematical rigor ensures statistically valid segments. Marketing teams can now allocate budgets based on cluster characteristics, customize product catalogs, and predict expansion success in similar cities.

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