Question at position 6 In a logistic regression model of customer churn (unsubscribing), a positive coefficient for a price means that as that price increases, the predicted probability of customer churn always increases.TrueFalseSingle choice
A
True
B
False

Question

Question at position 6 In a logistic regression model of customer churn (unsubscribing), a positive coefficient for a price means that as that price increases, the predicted probability of customer churn always increases.TrueFalseSingle choice

A

True

B

False

BlackTom AI · Accepted Answer

The logistic model uses the logistic (sigmoid) function p = 1 / (1 + e^(-η)), where η = β0 + β_price·price + (other terms). Because the sigmoid is a strictly increasing function of η, the sign of β_price determines whether p rises or falls as price increases (holding other covariates constant). 1) Relevant knowledge points and concepts - Logistic regression models the log-odds (η) as a linear function of predictors: η = β0 + β1·x + .... - The predicted probability p = σ(η) = 1/(1+e^{-η}) is a monotonic increasing function of η. - The derivative dp/dx = (dp/dη)·(dη/dx) = β1 · p(1 − p). Since 0 < p < 1, p(1 − p) > 0 for finite η. 2) Complete reasoning step by step - If β_price > 0 then dη/d(price) = β_price > 0. - dp/d(price) = β_price · p(1 − p). Because p(1 − p) > 0, dp/d(price) > 0 whenever β_price > 0. - A positive derivative means p strictly increases as price increases (for any finite change in price, holding other variables fixed). 3) Calculations with intermediate steps (symbolic and numeric example) - Symbolic: dp/dprice = β_price · p(1 − p). For β_price = 0.5 and p =, say, 0.2, dp/dprice = 0.5 · 0.2 · 0.8 = 0.08 > 0. - Numeric example: β0 = −2, β_price = 0.5. - At price = 0: η = −2 ⇒ p = 1/(1+e^{2}) ≈ 0.1192. - At price = 1: η = −1.5 ⇒ p = 1/(1+e^{1.5}) ≈ 0.1824. p increased. 4) Why the correct answer is correct - The logistic link is strictly increasing in η; a positive coefficient increases η as price increases, which increases the predicted probability. There is no non-monotonic behavior introduced by the logistic transform. 5) Why the other option (False) is incorrect - Saying the predicted probability does not always increase contradicts the monotonicity shown above. Only if β_price ≤ 0 would increases in price not increase the predicted probability. Interaction terms or simultaneous changes in other covariates could alter the net effect, but the statement implicitly considers the marginal effect holding others fixed. 6) Conclusion - Therefore the correct answer is True, which matches the provided answer.

Question at position 6 In a logistic regression model of customer churn (unsubscribing), a positive coefficient for a price means that as that price increases, the predicted probability of customer churn always increases.TrueFalseSingle choice

Similar Questions

What type of outcome does logistic regression predict?

What is the probability of occurrence of the event given the coefficients below for 1 inbound call and 1 tech visit (assume gender identity is coded as 0 for this observation).

In R, after running a logistic model 𝑚 𝑦 log 𝑖 𝑡 , what does exp ( 𝑐 𝑜 𝑒 𝑓 ( 𝑚 𝑦 log 𝑖 𝑡 ) ) provide?

In the R script for Logistic Regression, what argument is required in 𝑔 𝑙 𝑚 ( ) to specify a logistic model?

If the coefficient of 'Income' in a logistic regression is 0.005, and the Odds Ratio is 1.005, what happens when income increases by 1 unit?

In the Logistic Regression model for predicting churn based on number of complaints, if a customer has 0 complaints and the constant is -2.57, what is the estimated odds of churning?

In a logistic regression, if the predicted logit function is 0, what's the transformed probability?

For stock A, we have 𝛽 𝑖 = 0.70. Suppose the expected market risk premium next year is 9% and the risk-free rate is 3%. What is the expected return of this stock based on the CAPM? (Please answer in % and round to 2 decimal places. If the answer is 8.057%, then in the box, write 8.06)

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler