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BU.330.780.T2.SP25 Quiz 1- Requires Respondus LockDown Browser

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Entropy =ย  ฮฃ โˆ’ ๐‘ ๐‘– log 2 โก ๐‘ ๐‘– = โˆ’ ๐‘ 1 log โก ( ๐‘ 1 ) โˆ’ ๐‘ 2 log 2 โก ( ๐‘ 2 ) Whereย  ๐‘ ๐‘– is the relative proportion of class i within the set. The Carey Business School has a large alumni base but has only recently begun efforts to foster a lifelong relationship with its graduates. Constantly soliciting alumni for every possible fundraising opportunity is not an effective strategy. Instead, the school aims to offer a variety of engagement and fundraising opportunities, matching each one with alumni for whom it is most appropriate. As a pilot initiative, the school is focusing on a single fundraising effort: the Carey Scholarship Drive (CSD). By analyzing data from a previous CSD campaign, the school hopes to develop a model predicting which alumni will likely donate. The target variable for this model is "Give," with possible values of "Yes" or "No." Your task is to use the data in the accompanying table to build a classification tree model. Which of the following is the entropy of the population (the set of all students before any segmentation)? Program MBA MS MBA MBA MS MBA MS MBA MS MBA International Yes No Yes No Yes No No Yes Yes No Give Yes No No Yes Yes No Yes No No No

Options
A.โˆ’ 2 4 log 2 โก 2 4 โˆ’ 4 6 log 2 โก 4 6
B.โˆ’ 4 10 log 2 โก 4 10 โˆ’ 6 10 log 2 โก 6 10
C.โˆ’ 4 10 log 2 โก 4 10
D.โˆ’ 2 4 log 2 โก 2 4 โˆ’ 2 6 log 2 โก 2 6
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Step-by-Step Analysis
First, we identify the quantity being asked: the entropy of the population before any segmentation, using the given binary target variable Give with values Yes or No across the entire dataset. Option 1 presents a form that combines fractions and logs but the coefficients shown (2/4 and 4/6) do not align with the actual population proportions; this makes the expression suspect for representing population entropy. Option 2 writes t......Login to view full explanation

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