Need help with this assignment for BAN840 PSU

1.[25 points]Annabel, a retail analyst, has been following Under Armour, Inc., the pioneer in the compression-gear market. Annabel believes that the Under Armour brand attracts a younger customer, whereas the more established companies, Nike and Adidas, draw an older clientele. In order to test her belief, she collectsdataon the age of the customers and whether or not they purchased Under Armour (Purchase = 1 for purchase, 0 otherwise).

a.[5 points]Estimate a logistic regression model where the Under Armour purchase depends on the customer's age. Please include the basic output (regression statistics, analysis of deviance table and regression coefficients table), the confusion matrix and the ROC curve using a 0.5 cutoff in your submission.

b.[5 points]Test Annabel's belief that the Under Armour brand attracts a younger customer at the 5% significance level. Please explain clearly how you tested the belief and what your conclusion is.

c.[4 points]Compute the predicted probability of an Under Armour purchase for a 20-year-old customer.

d.[2 point]How does a one-unit increase in the age of a customer affect the log-odds of purchase (please provide a number)?

e.[4 points]How does the probability of purchase change (in percentage points) if a potential customer was 30 years old instead of being 20 years old? Note: If the probability changes from 25 to 30 percent that is a 5 percentage point increase.

f.[5 points]What is the current sensitivity of the prediction model? How does the sensitivity change if the cutoff level is decreased to 0.40?

2.[25 points]Monstermash, an online game app development company, has built a predictive model to identify gamers who are likely to make in-app purchases. The model classifies gamers who are likely to make in-app purchases in Class 1 and gamers who are unlikely to make in-app purchases in Class 0.

Applying the model on the validation dataset generated atablethat lists the actual class and the predicted class 1 probability of the gamers in the validation data set.

a.[5 points]Specify the predicted class membership using cutoff levels of 0.75. Add a predicted class column to the data and use an Excel function to populate 0 or 1 values based on the cutoff.

b.[10 points]Generate a confusion matrix for the above data and calculate the accuracy rate, misclassification rate, sensitivity, precision, and specificity. You can use Excel functions to count the number of observations in each cell of the confusion matrix. You may find the SUMIF() and AND() functions useful for this exercise. Alternatively, you can apply filters to the table to generate the numbers.

c.[10 points]What is the lift from the classification model if the top 20% of the observations are selected by the model compared to randomly selecting 20% of the observations?