1. Decision Tree: since the output variable is churn/not churn, we can use supervised learning to predict the probability of a current customer churning or not. We can also look at the leaf nodes and “follow up the tree” to create a basic customer profile.

   1. CP – .001

   2. Minsplit Factor – 80

   3. These settings have been established to create an accurate tree that is pruned enough to create an understandable customer profile (see Classification Rate and CP Factor), 

2. Linear Probability Model: this might not be the best model because the dependent variable should be continuous and, in our problem, the dependent variable is not. This is due to the dependent variable being either 1 or 0 for Churn/Not Churn. However, a LPM usually (though not guaranteed) yields consistent results.

   1. We will set a common P-Value of less than .05 to find out whether any of the coefficients of the independent variables are significant and meaningful and are not just up to chance.

   2. From the significant coefficients, we can see which independent variables are most probable to increase or decrease churn.

   3. All data will have to be converted into numerical or binary data (1 if Yes and 0 if No).

      1. In the cases of Gender, it will be converted into 1 for Male and 0 for Female.

      2. For Internet Service, it will be converted into 1 for Fiber Optic and 0 for Other.

      3. For Contract, it will be converted into 1 for Yearly Contract or 0 for Other.

      4. For Payment Method, it will be converted into 1 for Automatic Payment Method or 0 for Not Automatic.

   4. When a customer has phone service with Telco (binary variable) they have a 15.63% less probability of churning (the decision tree though does not list phone service anywhere in the tree).

   5. In terms of prediction for LPM, it yielded a slightly low Multiple R-squared = 0.2803. However, for this set of data this could be acceptable due to a variability and unpredictability in customer’s decisions to churn. There could also be other outside factors not included in the data set (like region, etc.).

   6. Checking Assumptions

      1. Linearity: for there to be linearity the x variables need to be continuous in most cases, so we cannot assume perfect linearity when we used non-continuous data.

      2. Exogeneity: there could be other factors such as region, # of service interruptions, switching due to faster internet providers, etc. which could affect the reasons why customers churn.

      3. Lack of Multicollinearity: (see here) the x variables do not seem to be highly correlated with one another.

      4. Homoscedasticity: because it is a linear probability model there will be some heteroscedasticity. 

3. K-Means Clustering: since we have mixed continuous and binary data, K-Means clustering might not be an ideal model due to the Euclidean distance measure. However, we can cluster the top five or six independent variables in the decision tree with the significant coefficients in the linear regression which we believe are related to Y (churn) and compare different customer groups or profiles.

   1. We will choose 7 clusters to keep a manageable overview of potential customer profiles while also maintaining a higher cohesion, or low Within−Cluster SSE (see here). 

   2. It is important to note that phone service was above average in all clusters so it is hard to determine if it is specific to any type of customer.

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