MATH 4397, Intro to Data Science & Machine Learning, Homework # 3 Instructors: Cathy Poliak, Andrey Skripnikov DUE: Friday, October 5th, at 11:59PM Instructions: Submit the solutions as a file (type it up and save as a pdf or a Word file, no hand-written solutions) via UH Blackboard. Keep responses brief and to the point For code & output: lude only pieces that are of utmost relevance to the question Conceptual 1. An array of unrelated conceptual questions: (a) Using a little bit of algebra, prove that p(X) = 1+eMAX is equivalent to p(X) 1p(X) o8 In other words, the logistic function representation 1 and logit representation (b) On average, what fraction of people with an odds of 0.37 of defating on their (c) Suppose that an individual has a 16% chance of defaulting on her credit card (2) for the logistic regression model are equivalent credit card payment wil in fact default? payment. What are the odds that she will default? 2. Suppose we collect data on a group of customers in order o figure out whether they will churn (discontinue relationship with your business) or not. The collected vari ables on customers are Xmonthly service spendings (in thousands of $), X2 - monthly income in thousands of S), X-Age, Y Churn (Yes/No). We fit a lo- gistic regression and produce the following coefficient estimates: Ao =-1, A = 32,--1.33 = 0.02 (a) Estimate the churning probability for a customer of 30 years old, who spend:s 508 a month on the service and earns 3k per month. Provide your calculations. MATH 4397, Intro to Data Science & Machine Learning, Homework # 3 Instructors: Cathy Poliak, Andrey Skripnikov DUE: Friday, October 5th, at 11:59PM Instructions: Submit the solutions as a file (type it up and save as a pdf or a Word file, no hand-written solutions) via UH Blackboard. Keep responses brief and to the point For code & output: lude only pieces that are of utmost relevance to the question Conceptual 1. An array of unrelated conceptual questions: (a) Using a little bit of algebra, prove that p(X) = 1+eMAX is equivalent to p(X) 1p(X) o8 In other words, the logistic function representation 1 and logit representation (b) On average, what fraction of people with an odds of 0.37 of defating on their (c) Suppose that an individual has a 16% chance of defaulting on her credit card (2) for the logistic regression model are equivalent credit card payment wil in fact default? payment. What are the odds that she will default? 2. Suppose we collect data on a group of customers in order o figure out whether they will churn (discontinue relationship with your business) or not. The collected vari ables on customers are Xmonthly service spendings (in thousands of $), X2 - monthly income in thousands of S), X-Age, Y Churn (Yes/No). We fit a lo- gistic regression and produce the following coefficient estimates: Ao =-1, A = 32,--1.33 = 0.02 (a) Estimate the churning probability for a customer of 30 years old, who spend:s 508 a month on the service and earns 3k per month. Provide your calculations