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Posted: December 14th, 2023

Consider using a logistic regression model to predict whether a potential customer

Hi there - looking for answers to these three questions ASAP!Consider using a logistic regression model to predict whether a potential customer will respond to an offer that costs $1 to mail and is expected to yield $5 revenue if the contact responds. A pilot study has been conducted in which offers were made to people on whom three predictor variables were also measured: R (recency), F (frequency), M (monetary). The resulting logistic regression model estimated from the training data leads to the equation:Probability of response = 1/(1+exp(0.5–0.2R–0.1F–0.3M))Six customers in the validation sample are then sorted in order of the probability of a response, and it is possible to calculate how expected responses and net profits change as the number of offers increases, both for sending offers using the ordered customers from the model and for sending offers at random. Note that there were a total of 3 responses from 6 offers in this sample, and total net profit from making all 6 offers is 3×5–6×1=$9 (remember it costs $1 to mail and is expected to yield $5 revenue if the contact responds). So, for example, making 1 offer to the top person on the list yields 1 response, whereas making 1 offer at random yields (3/6)=0.5 expected responses. Net profit for making 1 offer to the top person on the list yields 1×5–1×1=$4, whereas making 1 offer at random yields an expected profit of (1/6)×9=$1.50. The next three questions will ask you to complete the following entries in the table for the 5th customer in the validation sample.RFMProb. of ResponseCumulative OffersRespond (1: Yes, 0: No)Model: ResponsesRandom: Expected ResponseModel: Net ProfitRandom: Expected Net Profit1230.6901110.541.52310.6222121.083.02210.5993021.574.51200.4754132.0116.00015032.50000.3786033.099.0What is the "Probability of Response" for the 5th customer? (Round to two decimal places.)Flag this QuestionWhat is the "Model: Net Profit" for the 5th customer? (Round to nearest whole number.)Flag this QuestionWhat is the "Random: Expected Net Profit" for the 5th customer? (Round to one decimal place.)

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