Which of the following represents gain across the database of customers and prospects assuming that desired outcome is purchase?

Question

BlackTom AI · Accepted Answer

Gain is the proportion of all purchasers that a model captures when you target the top-ranked subset — mathematically, cumulative number of purchasers divided by total number of purchasers.

1. Relevant knowledge points and concepts
- A gain chart measures how many of the desired outcomes (here, purchasers) are captured by targeting a top fraction of the population. 
- Gain is a ratio that normalizes the captured purchasers by the total number of purchasers in the entire population, so it is independent of sample size.
- Symbols: let C = cumulative number of purchasers captured by the subset, T = total number of purchasers in the whole database, N = total number in sample, overall purchase rate r = T/N.

2. Step-by-step reasoning
- The intuitive quantity we want is “what fraction of all purchasers have we captured?” That is C/T.
- Option 2 explicitly states Cumulative number of purchasers/Total number of purchasers = C/T, which matches the definition.

3. Calculations and algebraic confirmation
- For option 3: Cumulative number of purchasers/(Total number in sample * Overall purchase rate) = C / (N * r). Since r = T/N, N * r = N * (T/N) = T. So option 3 simplifies to C/T, exactly the same as option 2.
- For option 1: (Cumulative percentage of purchasers) * (Overall purchase rate) = (C/T) * (T/N) = C/N. That equals the proportion of the total population that are purchasers within the targeted subset, not the fraction of all purchasers — so it’s C/N, not C/T.
- For option 4: Cumulative number of purchasers = C (unnormalized). That raw count doesn’t express gain as a fraction of all purchasers.

4. Why the correct answer is correct
- Gain by definition is the fraction of total purchasers captured, C/T. Option 2 gives this directly and thus correctly represents gain.

5. Why other options are incorrect
- Option 1 yields C/N (proportion of population), not C/T (proportion of purchasers).
- Option 3, though algebraically identical to option 2, is a more convoluted expression; option 2 is the direct, standard form.
- Option 4 is unnormalized and so doesn’t represent gain as a proportion.

6. Conclusion
- The correct representation of gain is Cumulative number of purchasers / Total number of purchasers, matching the provided answer.

Which of the following represents gain across the database of customers and prospects assuming that desired outcome is purchase?单项选择题

类似问题

With these data the specificity of the reading test to identify children with no learning difficulty is equal to:

Of the following, which is the BEST statistical practice?

Which of the following statements about Type 1 and Type 2 error is TRUE?

What effect size measure should they calculate for this dataset?

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单