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chap17 - Prelude Mail-order sales company uses many...

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17-2 Prelude Mail-order sales A 1 company uses many different mailed catalogs to sell different types of merchandise. One catalog that features home goods, such as bedspreads and pillows, was mailed to 200,000 people who were not current customers. The response variable is whether or not the person places an order. Logistic regression is used to model the probability of a purchase as a function of five explanatory variables. These are the number of purchases within the last 24 months from a home gift catalog, the proportion of single people in the zip code area based on census data, the number of credit cards, a variable that distinguishes apartment dwellers from those who live in single-family homes, and an indicator of whether or not the customer has ever made a purchase from a similar type of catalog. The fitted logistic model is then used to estimate the probability that a large collection of potential customers will make a purchase. Catalogs are sent to those whose estimated probability is above some cutoff value. p

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17 Logistic Regression* 17.1 The Logistic Regression Model 17.2 Inference for Logistic Regression 17.3 Multiple Logistic Regression * This chapter requires the material on binomial distributions in the optional Chapter 5. Logistic Regression* CHAPTER 17
Logistic Regression 17-4 CHAPTER 17 Introduction 17.1 The Logistic Regression Model BINGE DRINKERS 2 The simple and multiple linear regression methods we studied in Chapters 10 and 11 are used to model the relationship between a quantitative response variable and one or more explanatory variables. In this chapter we describe similar methods for use when the response variable has only two possible values: customer buys or does not buy, patient lives or dies, candidate accepts job or not. In general, we call the two values of the response variable “success” and “failure” and represent them by 1 (for a success) and 0. The mean is then the proportion of ones, (success). If our data are independent observations with the same , this is the (page 319). What is new in this chapter is that the data now include an . The probability of a success depends on the value of . For example, suppose we are studying whether a customer makes a purchase ( 1) or not ( 0) after being offered a discount. Then is the probability that the customer makes a purchase, and possible explanatory variables include (a) whether the customer has made similar purchases in the past, (b) the type of discount, and (c) the age of the customer. Note that the explanatory variables can be either categorical or quantitative. Logistic regression is a statistical method for describing these kinds of relationships. In general, the data for logistic regression are independent observations, each consisting of a value of the explanatory variable and either a success or a failure for that trial. For example, may be the age of a customer, and “success” means that this customer made a purchase. Every observation may have a different value of . To introduce logistic regression, however, it

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