Customer Churn Analysis

Author

Aheer Srabon

Published

September 18, 2025

1 Uni-variate & Distributional Analysis

Summary of the Dataset
Variable Mean Median Sd Min Q1 Q2 Q3 Q4 Max
Age 49.09 50.00 18.17 18 34.00 50.00 65.00 80.00 80.00
Tenure 34.68 34.00 21.04 0 16.00 34.00 52.25 72.00 72.00
MonthlyCharges 68.51 69.02 29.07 18 43.74 69.02 92.65 119.77 119.77
TotalCharges 2339.68 1900.12 1808.26 0 938.64 1900.12 3380.87 8444.03 8444.03
Random 10 samples from the dataset
Gender Age Tenure PhoneService InternetService Contract MonthlyCharges TotalCharges Churn
Male 21 14 No Fiber optic One year 26.52 371.28 No
Female 25 64 Yes DSL One year 24.08 1541.12 No
Female 20 8 No None Month-to-month 106.34 850.72 No
Male 80 68 No Fiber optic One year 100.87 6859.16 No
Female 26 24 No DSL Month-to-month 87.13 2091.12 Yes
Female 52 7 No None One year 18.00 126.00 No
Male 64 34 Yes None Two years 86.90 2954.60 No
Female 40 30 No None Month-to-month 74.62 2238.60 Yes
Male 42 5 Yes DSL Month-to-month 79.93 399.65 No
Male 74 24 No Fiber optic Two years 113.12 2714.88 No

1.1 Numeric Distributions (Histograms)

1.2 Categorical Counts (Phone/Internet/Contract)

1.3 Categorical Proportions by Churn

1.4 Missingness Overview

As can be seen from the following table, there is no missing data.

1.5 Skewness

1.5.1 Quick skew check (numeric)

Skewness
feature n mean median sd p99 skew_hint
TotalCharges 1000 2339.68 1900.12 1808.26 7247.88 Right-skewed
Age 1000 49.09 50.00 18.17 80.00 Left-skewed
Tenure 1000 34.68 34.00 21.04 72.00 Right-skewed
MonthlyCharges 1000 68.51 69.02 29.07 118.93 Left-skewed

1.5.2 Skew check

The last plot suggest that most customers generate relatively low revenue, but a smaller group contributes disproportionately higher revenue. This suggest that the company may rely heavily on a minority of high-value customers.

1.6 Churn vs Non-Churn Proportions

Categorical features of interest
Churn Feature Level
Yes Contract Month-to-month
No Contract Two years
No Gender Male
No PhoneService Yes
No PhoneService No

1.6.1 Stacked bar (counts by category)

1.6.2 Normalized bar (proportions within each category)

2 Bivariate (Churn vs. Features)

2.1 Churn rate by Tenure bins (0-6, 6-12, 12-24, 24-48, 48+)

Tenure is how long a customer has been with the company (in months). Following is the hypothesis,

Customer who are new (short tenure) are more likely to churn; customers who have stayed longer are “stickier”

To test this,

  1. Group customers into bins of tenure (0-6 months, 6-12, etc.).
  2. Compute churn rate = (# churned customers) / (total customers) in each bin.
  3. Plot churn rate across bins to visualize patterns.

If churn is very high in 0-6 months bin, that means the company has an onboarding / early experience problem.

Data Frame with Tenure Bin tags
Gender Age Contract Tenure Bin
Male 71 One year 12–24
Male 26 Two years 48+
Female 73 Two years 48+
Male 46 Month-to-month 48+
Female 37 Two years 6–12

  • n = number of customers

  • churn_yes = number of churned customers

  • p = churn_yes / n = churn proportion

Tenure statistics
level churn_yes n p p_lo p_hi
0–6 18 98 0.18 0.12 0.27
6–12 18 96 0.19 0.12 0.28
12–24 34 178 0.19 0.14 0.26
24–48 51 333 0.15 0.12 0.20
48+ 56 295 0.19 0.15 0.24

Because churn rate is an estimate from data, we add 95% confidence interval using the Wilson method.

2.1.1 Chi-Square test


    Pearson's Chi-squared test

data:  table(df_tenure$tenure_bin, df_tenure$Churn)
X-squared = 1.9758, df = 4, p-value = 0.7402

Not significant.

2.1.2 Logistic regression test


Call:
glm(formula = Churn ~ tenure_bin, family = binomial, data = df_tenure)

Coefficients:
                Estimate Std. Error z value Pr(>|z|)    
(Intercept)     -1.49165    0.26087  -5.718 1.08e-08 ***
tenure_bin6–12   0.02532    0.36937   0.069    0.945    
tenure_bin12–24  0.04820    0.32313   0.149    0.881    
tenure_bin24–48 -0.21843    0.30201  -0.723    0.470    
tenure_bin48+    0.04054    0.30016   0.135    0.893    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 933.63  on 999  degrees of freedom
Residual deviance: 931.61  on 995  degrees of freedom
AIC: 941.61

Number of Fisher Scoring iterations: 4

Only the Intercept is statistically significant. So, we can’t accept out hypothesis.

2.2 Contract Type vs. Churn

Goal: Show how churn differs by contract type.

Hypothesis: Month-to-month has higher churn than One/Two year contracts.

2.3 Internet Service vs. Churn

Goal: Compare churn across DSL / Fiber optic / No Internet.

2.4 Numeric Densities by Churn

2.5 Numeric Box Plots by Churn

2.6 Numeric Violin Plots by Churn

3 Multivariate Relationships

3.1 Age x Tenure x Churn

Data for `Tenure Distribution by Age Group and Churn'
Gender Age Tenure PhoneService InternetService Contract MonthlyCharges TotalCharges Churn AgeGroup
Male 48 6 Yes None One year 60.76 364.56 No 30-50
Male 74 13 Yes DSL One year 100.15 1301.95 No 50+
Female 74 46 Yes DSL Month-to-month 73.52 3381.92 Yes 50+
Male 24 2 Yes None One year 22.97 45.94 No <30
Male 28 4 No None Two years 35.16 140.64 No <30

Following plot shows distributions of Tenure across age groups and split by Churn,

For extra clarity, following is a Heatmap,

AgeBin TenureBin ChurnRate
[68,78] [72,Inf] 0.50
[18,28) [48,72) 0.13
[38,48) [48,72) 0.27
[58,68) [72,Inf] 1.00
[18,28) [12,24) 0.03

3.2 MonthlyCharges x Contract x Churn

3.3 InternetService x Contract (churn risk heatmap)

4 Feature Engineering for EDA

4.1 Customer lifetime value proxy

Gender Age Tenure PhoneService InternetService Contract MonthlyCharges TotalCharges Churn CLTV
Male 25 30 Yes None Month-to-month 41.60 1248.00 Yes 1248.00
Female 72 29 Yes None Two years 33.94 984.26 No 984.26
Male 71 44 No Fiber optic Month-to-month 107.69 4738.36 No 4738.36
Male 62 55 Yes DSL Two years 73.99 4069.45 No 4069.45
Female 40 4 Yes DSL Two years 119.24 476.96 No 476.96

4.2 At-risk cohorts (cohort flagging)

Create a derived feature for risk segments,

Risk Cohort table
Gender Age Tenure PhoneService InternetService Contract MonthlyCharges TotalCharges Churn RiskCohort
Male 79 37 Yes Fiber optic One year 26.29 972.73 No Low/Mediium Risk
Male 49 4 Yes DSL Two years 35.33 141.32 No Low/Mediium Risk
Female 80 28 Yes Fiber optic Month-to-month 109.59 3068.52 Yes Low/Mediium Risk
Male 21 21 No None Month-to-month 61.76 1296.96 No Low/Mediium Risk
Male 35 34 No DSL Month-to-month 93.71 3186.14 Yes Low/Mediium Risk

High-risk customers churn much more, with over half leaving. Low/medium-risk customers mostly stay, with only a small fraction churning. This highlights the value of risk segmentation: high-risk cohorts require targeted retention strategies to reduce churn and improve overall customer retention.

5 Correlation & Association

5.1 Numeric-only correlation matrix

5.2 Chi-square + Cramer’s V for categorical vs. Churn

Cramér’s V - Effect size measure
variable chisq_stat df p_value cramers_v
Contract 436.65 2 0.00 0.66
Gender 2.34 1 0.13 0.05
PhoneService 0.88 1 0.35 0.03
InternetService 1.30 2 0.52 0.04

Which shows that, to predict churn, Contract is a strong (because of low p_value) predictor. Next up are, Gender, PhoneService, and InternetService.

5.3 Mutual information (any type \(\rightarrow\) Churn)

Mutual Information serves to rank all features (numeric + categorical) together by how much they help explain churn. It complements correlation, Chi-square, and Cramér’s V by giving a unified importance measure.

Importance of variables
attributes importance
Contract 0.238949
Gender 0.001304
InternetService 0.000644
PhoneService 0.000519

6 Survival-style Analysis

The Kaplan-Meier estimator generates the survival curves for different contract types. It answers the following simple yet important question,

What percentage of customers are still active after X months, depending on their contract type?

The Kaplan–Meier survival curves show how long customers remain active without churning, based on contract type. Month-to-month customers (red) churn steadily, with survival probability dropping below 50% by around 40–50 months. In contrast, one-year (green) and two-year contracts (blue) maintain nearly perfect retention over time, with very little churn observed. The p-value (<0.0001) indicates these differences are highly statistically significant. In short, customers on longer-term contracts are far less likely to churn, while month-to-month customers have much higher and earlier churn rates. Contract length is thus a critical factor in customer retention.

7 Feature Importance

7.1 Logistic Regression for Feature Importance

Logistic model estimates
feature Estimate Std. Error z value Pr(>|z|)
GenderMale -0.54 0.29 -1.88 0.06
(Intercept) 1.56 0.97 1.62 0.11
InternetServiceFiber optic -0.55 0.35 -1.60 0.11
InternetServiceNone -0.41 0.34 -1.21 0.23
MonthlyCharges -0.01 0.01 -1.12 0.26
TotalCharges 0.00 0.00 0.80 0.42
PhoneServiceYes -0.15 0.28 -0.54 0.59
Tenure -0.01 0.02 -0.38 0.71
Age 0.00 0.01 -0.30 0.76
ContractOne year -20.84 1121.38 -0.02 0.99

The above table is sorted with respect to p-value. The only significant feature for predicting Churn according to this model is InternetServiceFiber optic. Even though, PhoneService and the intercept has a low p-value, they are not significant.

7.2 Random Forest for Feature Importance

Random forest estimates
feature No Yes MeanDecreaseAccuracy MeanDecreaseGini
Contract 39.05 51.17 51.44 83.57
TotalCharges 3.78 -4.51 1.18 23.13
MonthlyCharges 0.66 -1.74 -0.59 23.07
Age 1.86 2.24 2.86 21.91
Tenure 3.90 -2.09 2.14 20.05
InternetService -1.72 1.23 -0.36 6.38
Gender 1.19 -0.32 0.63 3.81
PhoneService -0.23 1.18 0.72 3.72

The random forest importance table shows that Contract is the most influential predictor of churn, with the highest values in both MeanDecreaseAccuracy (44.71) and MeanDecreaseGini (79.11). MonthlyCharges, Age, TotalCharges, and Tenure also contribute meaningfully, though at lower levels, indicating that financial and tenure-related variables affect churn risk. InternetService, Gender, and PhoneService have much smaller importance scores, suggesting they add little predictive value. Overall, contract type dominates as the key driver, followed by monetary and tenure factors, while demographic or service-type variables play a minor role in predicting churn.