Customer churn is a binary classification problem, where the target variable is whether a customer has churned or not. Therefore, a logistic regression model is more suitable than a linear regression model, which is used for regression problems.  A logistic regression model can output the probability of a customer churning, which can be used to rank the customers by their churn risk and take appropriate actions 1 .

BigQuery ML is a service that allows you to create and execute machine learning models in BigQuery using standard SQL queries 2 .  You can use BigQuery ML to create a logistic regression model for customer churn prediction by using the  CREATE MODEL  statement and specifying the  LOGISTIC_REG  model type 3 .  You can use the historical customer data as the input table for the mo del, and specify the features and the label columns 3 .

Vertex AI Model Registry is a central repository where you can manage the lifecycle of your ML models 4 .  You can import models from various sources, such as BigQuery ML, AutoML, or custom models, and assign them to different versions and aliases 4 . You can also deploy models to endpoints, which are resources that provide a service URL for online prediction.

By registering the BigQuery ML model in Vertex AI Model Registry, you can leverage the Vertex AI features to evaluate and monitor the model performance 4 . You can use Vertex AI Experiments to track and compare the metrics of different model versions, such as accuracy, precision, recall, and AUC. You can also use Vertex AI Explainable AI to generate feature attributions that show how much each input feature contributed to the model’s prediction.

The other options are not suitable for your scenario, because they either use the wrong model type, such as linear regression, or they do not use Vertex AI to evaluate the model performance, which would limit the insights and actions you can take based on the model results.