Project: Modeling with Logistic Regression

The marketing department for a retail company was about to embark on a periodic campaign to convince existing customers to apply for one of the company’s discount shopping advantage card with a fixed annual fee. The major decision facing the marketing department concerns which type of customers should be targeted for the campaign. The information from a random sample of 32 current customers who had been invited to apply of shopping card in the past was recorded, and three of the variables that are to be used to assist the marketing department in the analysis are: Shopping card status (1=Yes “have the discount shopping card”, 0=No “don’t have the discount shopping card”), Annual spending in thousands of dollars, Possession of credit card (1=Yes “have credit card”, 0=No “don’t have credit card”).

Data: shoppingcard.sav

Use the data above to evaluate the significance of the two predictor variables selected for predicting the willingness of the customers to obtain the discount shopping advantage card. Answer the following questions.

  1. Analyze the data using logistic regression model to find the significant factors for predicting whether the customer will obtain a shopping card. (Use only the significant factors in the model for the following questions.)
  2. Test to see if the logistic regression model fits the data well at .05 level of significance.
  3. Estimate the odds ratio to see how likely the customers who possessed credit card would obtain a discount shopping card versus those who do not possess credit card, and interpret this number.
  4. Find the 95% confidence interval for the odds ratio above.
  5. Find the prediction equation for estimating the probability of a customer will obtain a discount shopping card.
  6. What is the predicted probability of a customer who own a credit card and spent $50,000 on last year will obtain a discount shopping card?
  7. If the amount of spending last year is the only predictor in the analysis, a customer with how much spending last year will have a probability of at least .5 to obtain a discount shopping card? (Use the logit model and solve for x.)