Question: Many airlines offer credit cards that reward customers who use

Many airlines offer credit cards that reward customers who use the card with frequent-flyer miles. The more the customer uses the card, the more miles earned. Do these cards work? Do customers who get such a card fly more on that airline? To find out, an airline compared the number of miles flown by a sample of 250 members in its frequent-flyer program. Some of these have its credit card. The variable Has Card in the data is a dummy variable, coded + for those who have a card and 0 for those who do not.
Motivation
(a) How would the results of this comparison affect the use of this promotion by the airline?
Method
(b) Explain why the airline should be concerned about the effects of possible confounding variables in this analysis.
(c) One possible confounding variable is the number of miles flown by the customer in the year prior to getting the airline credit card. How can the airline use regression to mitigate the problems introduced by this lurking variable?
Mechanics
(d) Use a two-sample test to compare the current mileage of those who have a card to those without a card.
(e) Fit the appropriate regression model that adjusts for miles flown last year and check the needed conditions.
Message
(f) Present the results of this regression analysis for an audience who has seen a comparison of the current miles flown using a two-sample t-test with the sample split by whether the customer has a card (see Chapter 17). Be sure to explain why regression gives a different answer.

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