Dimension reduction and regularization

You are a summer intern at one of the major private insurance companies in Norway. It is important for the company to not loose existing customers. At your department you have access to data on all current and earlier customers. In total the dataset includes observations on 10000 current and earlier customers and 100 characteristics on each customer (e.g., current customer or not, gender, age, family status, insurance price, etc.). Your boss is interested in figuring out the characteristics that might best predict whether or not a customer terminates the insurance contract.

1, What would be the natural outcome variable in this case?

2, Explain the conceptual difference between LASSO penalization and Principal Component Analysis (PCA). Which of these two approaches would you have used to address the question from your boss? Explain why.

3, In terms of regularization, mention at least one alternative to the LASSO and explain the difference.

4, Explain two approaches you can use to interpret the results from Principal Component Analysis.

5, What does it mean to standardize the variables prior to estimation, and why is it important to do so when performing regularization or PCA?