Raphael was interested in understanding the factors related to churn for a telco provider. The available database had only a limited set of variables, so he was limited to looking at long distance, toll free, equipment, calling card, and wireless usage for the past month (all measured as scalar or metric variables) and whether the customer had multiple lines, voice mail, paging, internet, caller ID, call waiting, call forwarding, 3-way calling, and electronic billing services (measured as dummy yeso variables). He ran a logistic regression with churn last month as the dependent variable and got the output displayed below.

i) (5 points) Why did Raphael decide to oversample customers who had churned last month to run the model? ii) (5 points) Which variables appear to be significantly related to churn (if 0=no and 1=yes) at the .05 significance level? iii) (4 points) Which factors appear to decrease the probability that a customer churned? iv) (6 points) Outline the steps that Raphael might take to develop a churn management program using this model.

S.E 1 529 Variables in the Equation B Wald df Sig Exp(B) Step 1 Long distance last month -.126 .018 47.667 1 .000 .882 Toll free last month -.002 .007 .062 .803 .998 Equipment last month .016 .006 6.619 1 .010 1.016 Calling card last month - 007 ,008 848 1 .357 .993 Wireless last month -002 .007 067 1 .795 .998 Multiple lines -.095 .191 .249 1 .618 909 Voice mail 228 5.381 1 020 1.697 Paging service .072 .257 080 1 .778 1.075 Internet .525 .203 6.682 1 010 1.690 Caller ID .153 237 413 1 521 1.165 Call waiting - 358 237 2.278 1 .131 .699 Call forwarding 207 234 .778 1 378 1.230 3-way calling - 388 .228 2.897 1 ,089 .679 Electronic billing 305 202 2.295 1 .130 1.357 Constant - 275 .198 1.929 1 165 759 a. Variable(s) entered on step 1: Long distance last month, Toll free last month, Equipment last month, Calling card last month, Wireless last month, Multiple lines, Voice mail, Paging service, Internet, Caller ID, Call waiting, Call forwarding, 3-way calling, Electronic billing