In a logistic regression, if the predicted logit function is 0, what's the transformed probability?Single choice
A
1
B
0.05
C
0
D
0.5

Question

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

BlackTom AI · Accepted Answer

The logit link is defined as log(p/(1−p)), so when the predicted logit equals 0 the probability is the inverse-logit (sigmoid) of 0, which is 0.5.

1) Relevant knowledge points and concepts
- Logistic regression models the log-odds (logit) of a probability p: logit(p) = ln(p/(1−p)).
- The inverse of the logit is the logistic (sigmoid) function: p = e^{logit}/(1 + e^{logit}).
- A logit value of 0 corresponds to equal odds for success and failure, so p = 0.5.

2) Step-by-step reasoning
Start from the definition with logit = 0:
0 = ln(p/(1−p)).
Exponentiate both sides to remove the natural log:
e^0 = p/(1−p).

3) Intermediate calculation steps
e^0 = 1, so:
1 = p/(1−p).
Multiply both sides by (1−p):
1(1−p) = p
1 − p = p
Bring p terms together:
1 = 2p
Divide by 2:
p = 1/2 = 0.5.

4) Why the correct answer is correct
The algebra shows directly that a log-odds of zero means the odds ratio is 1 (equal odds), which translates to probability 1/(1+1) = 0.5. Using the inverse-logit formula also gives p = e^0/(1+e^0) = 1/(1+1) = 0.5.

5) Why the other options are incorrect
- 1: logit = ln(1/(1−1)) is undefined because p = 1 gives division by zero and infinite log-odds, not 0.
- 0.05: ln(0.05/0.95) ≈ −2.944, not 0.
- 0: p = 0 gives ln(0/(1−0)) which is −∞, not 0.

6) Conclusion
The transformed probability corresponding to a predicted logit of 0 is 0.5, which matches the provided correct answer.

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

Similar Questions

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.TrueFalse

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?

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