Using Logistic Regression Models

Objectives

The objectives of this final exercise are to: 1) practice building and evaluating predictive models using logistic regression to identify which customers in our database should receive a future marketing communication from our company, 2) evaluate the lift and gains of the predictive model and 3) evaluate the profitability of the predictive model.

Assignment

 

As a provider of investment advice to real estate investors, The Real Estate Investors Club, has achieved steady growth in its customer base. In addition, the company periodically offers additional newsletters for an additional subscription fee.

Yet while sales have grown steadily, profits began falling when the database got larger and the company increased the number of offers sent to customers. The falling profits have led Dave Lawton, The Real Estate Investors Club’s marketing director, to experiment with different database marketing approaches in order improve the club’s communication yields and profits.

Dave began a series of live market tests, each involving a random sample of customers from the database. An offer for a new newsletter is sent to the sample and then the sample customers’ responses, either subscription or no subscription, are recorded and used to calibrate a response model for the current offering. The response model’s results are then used to “score” the remaining customers in the database and select customers from the full customer database for the ‘rollout’ of the mailing campaign for the new newsletter.

Dave’s team continues to debate whether statistical techniques can help to better identify potential targets for its new newsletter and improve profitability. As a result, the team wants to compare the effectiveness of the predictive model vs. not using any model.

Dave has a dataset containing the responses of a random sample of 1,345 customers to the newsletter offer.  He is eager to assess the potential value of using statistical methods for predicting customer response and has asked you to complete the following analyses.

Note: In order to complete this analysis you will need the two attached files: 1) Subscriber Data.sav, SPSS data file which contains all of the data needed to create volume deciles and to conduct the logistic regression analysis, and 2) Subscriber Analysis.xlsx, which contains a pre-formatted worksheet to assist you in your assessment of lift, gains and profitability. You will need to copy and paste data from SPSS output into Excel to complete your assessment.

Attention: This assignment requires you to perform another lift/gains/profit analysis. If needed, review the three videos in Fox Video Vault: 1) Evaluating Models: Lift Analysis, 2) Evaluating Models: Gains Analysis, and 3) Evaluating Models: Profit  Analysis.

 

Due Date:

 

Monday, December 9 at 11:59 p.m.

 

Question 1: Evaluate the following two Model Comparisons

 

 

Comparison 1:

 

-2LL(C) 1475.918
PC 1
-2LL(A) 1390.470
PA 2
Improvement Chi Square 85.448
Probability of

Improvement Chi Square (sig)

0.000
Interpretation of Findings

(Include Improvement Chi Square and Probability of Improvement Chi Square)

Reject the Ho.

The addition of age significantly improves prediction of subscription

Prediction Equation of

Log Odds for Model A

Ln(p/1-p) =0.795-0.052(age)
What is the predicted probability of subscription for a prospective customer that is 35 years of age? P=e^0.795-0.052(35)/1+e^o.795-0.052(35) =0.36/1.36=0.26

 

 

 

Comparison 2:

 

-2LL(C) 1390.470
PC 2
-2LL(A) 1381.112
PA 3
Improvement Chi Square 9.358
Probability of

Improvement Chi Square

P(X^2) =9.358=0.002<a=0.05
Interpretation of Findings

(Include Improvement Chi Square and Probability of Improvement Chi Square)

Reject Ho

Controlling for age the addition of gender significantly improves prediction of subscription

Prediction Equation of

Log Odds for Model A

Ln(p/1-p) = 0.598-0.052(age)+0.407(gender)

 

 

 

 

 

 

 

Question 2:

 

Which set of variables gives the best prediction of the dependent variable?

The set contains both the age and gender gives the best prediction of the dependent variable.
What is your evidence? The model with age is better than the one without age, and the model with age and gender have improvement compare to the one having age variable. Thus, the model with gender and age is the best.

 

 

 

Question 3:

 

Using the equation with both Age and Gender as independent variables, how are the odds of subscription affected by:

  1. Age – How do the odds of subscription change for an additional year of age?
  2. Gender – How do the odds of subscription for females compare to males?

 

Hint: Interpret the logistic regression coefficients.

 

Question Answer
3a [P/(1-p)] =e^[0.598-0.052(age)+0.407(gender)] =e^0.598*e^-0.052(age)*e^0.407(gender)

e^-0.052=0.949

1-0.949=0.05

When the age increases by 1year, then the odds decrease by 5%.

3b Gender   e^0.407=1.502    1.502-1=0.502

If female (1) then odds of subscription increase by 50.2%.

 

 

 

 

 

 

Question 4:

Conduct a Lift/Gains/Profitability analysis in Excel.

 

Use the following cost information to assess the profitability of both modeling methods.

 

Cost to Mail Offer to Customer $1.00
Selling Price of Newsletter (including shipping) $15.00
Contribution Margin (%) 33%

 

Using the data from the Lift/Gains/Profitability Analysis that you completed in Excel, complete the following table.

 

Method to Identify Customers Maximum Cumulative Operating Profit % of Customers Receiving Mailing Acquisition Costs per Customer ROI = Operating Profit/ Total Fixed Costs of Campaign
Mail All Customers in Database 255 100% = $1345/320 =4.2 = $255/$1345= 19%
Logistic Regression Model 450 = 540/1345= 40% = $540/198= 2.727 = $450/$540= 83%

 

 

Question 5 Based on your analysis of the data table from Question 4, which approach do you recommend be used to identify those existing customers to receive the newsletter: Logistic Regression Model or “Mailing All Customers in the Database”?
Answer

(Cite Evidence)

Logistic regression model approach I recommend be used to identify those existing customers to receive the newsletter. It has higher cumulative operating profit, lower acquisition costs per customer and higher return on investment.

 

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