Question

a. predicit the probability a card holder who charged 31k does not have a credit card will purch a premium card.

b. predicit prob of card holder w/ 31k and HAS a credit card will ourch a premium card.

c. predicit the prob of card holder with 15.5k that does NOT have a credit card to purch a premium.

The marketing department for a credit card company wants to determine which of its existing standard credit pard holders should be targeted for a campaign to convince existing card holders to upgrade to the company's premium card for a nominal annual fee. They have access to data from a sample of 30 cardholders who were contacted during last year's campaign that indicates whether the cardholder upgraded to a premium card (0 =no, 1 = yes). The results for their logistic regression model are - 7.172 +0.15099X, +2.719X2, where X, is the total amount of credit card purchases (in thousands of dollars) in the prior year and X2 is whether the cardholder ordered additional credit cards, at extra cost, for other members of the household (0 =no, 1 = yes). Complete (a) through (d) below. a. Predict the probability that a card holder who charged $31,000 last year and does not have any additional credit cards for members of the household will purchase the premium card during the market campaign. (Round to four decimal places as needed.)

Answer 1

Answer: from the given data, Log (odds) = -7.172 +0.150997, +2.719 K2 a) for this, x = 31 (in $1000) X2=0 (does not have a credit Card) log (od de) = -7.172 +00.15099431) 42-71940) = -2.4913) - odds = e 2-19151 = 0.0828 lit - odds 0.0828 Probability - Itodde = 40-0828 = 0.0765 6 for this, x,=31; 2=1 log (odds) = -7.172+ (0.15099*3))+ (2.719*1) = 0.22769 - odds = e. 22769 = 1.2557

Probability = 1.2557 H12557 c) for this, x,=15.5 i X 2 = 0 s log (oddy)= -7.172+(5.5*0.15099) + 2.71980) - log (oddy) = -4.83166 - odds = è rosto = 0.00797 0.00797 Probability = +0.00797 = 0.0079