Statistical Tests for Customer Churn Prediction using Machine Learning

Scenario: A telecommunications company wants to predict customer churn based on various customer attributes. They have collected data on independent variables such as customer age, gender, subscription type, monthly charges, tenure, and usage of specific services. The dependent variable is binary: churned (1) or not churned (0).

The dependent variable is binary: churned (1) or not churned (0).

Logistic Regression Model: Logit(p) = ln(p / (1 - p)) = β₀ + β₁(age) + β₂(tenure) + β₃(monthly charges) + β₄(service feature)

In this scenario, the logistic regression model predicts the log-odds of a customer churning based on their age, tenure, monthly charges, and service feature usage.

Odds Ratio: OR(age) = exp(β₁) OR(tenure) = exp(β₂) OR(monthly charges) = exp(β₃) OR(service feature) = exp(β₄)

The odds ratio quantifies the change in the odds of churn associated with a one-unit increase in each independent variable. For example, if OR(age) = 1.5, it means that for every one-year increase in age, the odds of churn are 1.5 times higher.

Logistic Function (Sigmoid Function): p = 1 / (1 + exp(-(β₀ + β₁(age) + β₂(tenure) + β₃(monthly charges) + β₄(service feature))))

The logistic function converts the linear combination of the independent variables and regression coefficients into a predicted probability (p) of a customer churning. It maps the log-odds to a probability between 0 and 1.

Maximum Likelihood Estimation (MLE): Maximum likelihood estimation is used to estimate the regression coefficients (β₀, β₁, β₂, β₃, β₄) that maximize the likelihood of observing the data given the logistic regression model. The specific formulas for the likelihood function and the log-likelihood function would be used to perform the estimation.

By applying these formulas to the given scenario, the company can estimate the regression coefficients, interpret the odds ratios, calculate the predicted probabilities, and make predictions on whether a customer is likely to churn based on their age, tenure, monthly charges, and service feature usage.

For churn prediction using a CSV file, several statistical tests and techniques can be applied. Here are some common ones:

Logistic Regression: Apply logistic regression to model the relationship between the independent variables (age, gender, subscription type, monthly charges, tenure, services) and the probability of churn. Estimate the regression coefficients and odds ratios to determine the significance and direction of the relationships.

Chi-Square Test of Independence: Perform chi-square tests to assess the independence between churn and categorical variables such as gender, subscription type, and service usage. Determine if there is a significant relationship between these variables and the churn outcome.

T-Test or Mann-Whitney U Test: Conduct t-tests or Mann-Whitney U tests to compare the means or distributions of continuous variables (e.g., age, monthly charges, tenure) between churned and non-churned groups. Determine if there are significant differences in these variables based on the churn status.

Variable Importance Analysis: Use techniques like Information Gain, Gini Index, or Recursive Feature Elimination to determine the relative importance of independent variables. Identify which variables have the most predictive power in predicting churn.

Cross-Validation: Employ k-fold cross-validation to estimate the performance and generalizability of the churn prediction model. Split the data into training and testing sets, fit the model on the training set, and evaluate its accuracy and stability on the testing set.

Receiver Operating Characteristic (ROC) Curve: Plot the ROC curve by calculating the true positive rate and false positive rate at different classification thresholds. Calculate the area under the curve (AUC) to assess the discriminatory power of the churn prediction model.

Confusion Matrix and Performance Metrics: Construct a confusion matrix to evaluate the model's performance. Calculate metrics like accuracy, precision, recall, and F1-score to assess how well the model predicts churned and non-churned customers.

Residual Analysis: Analyze the residuals of the logistic regression model to assess model fit. Plot deviance residuals or perform a Hosmer-Lemeshow test to identify potential outliers or influential observations.

By applying these statistical tests and techniques in the churn prediction analysis, the telecommunications company can gain insights into the relationships between customer attributes and churn, identify significant variables, evaluate the model's performance, and assess the robustness of the predictions.

Article By:-

Er. Sumit Malhotra

Assistant Professor 

Chandigarh University

Gharuan (Mohali),Punjab