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).

Question

BlackTom AI · Accepted Answer

Logistic regression uses a linear predictor (logit) that is transformed to a probability via the logistic function: p = exp(logit) / (1 + exp(logit)). Coefficients are on the log-odds scale; multiplying each coefficient by its predictor value and summing with the intercept gives the logit. The odds are exp(logit), and probability = odds/(1+odds).

Step-by-step reasoning:
1. Identify coefficients and coded values from the table:
   - Intercept (constant) = 1.24
   - Inbound calls coefficient = 1.74; here inbound = 1
   - Gender coefficient = -0.103; gender coded 0 for this observation → contribution = -0.103 * 0 = 0
   - Tech visits coefficient = 0; tech visits = 1 → contribution = 0 * 1 = 0

2. Compute the logit (linear predictor):
   logit = intercept + (1 * 1.74) + (0 * -0.103) + (1 * 0)
         = 1.24 + 1.74 + 0 + 0
         = 2.98

3. Convert logit to odds and probability:
   odds = exp(2.98). Calculating: exp(2.98) ≈ 19.7 (since e^3 ≈ 20.085, slightly smaller for 2.98).
   probability = odds / (1 + odds) = 19.7 / (1 + 19.7) = 19.7 / 20.7 ≈ 0.9517

4. Why this is correct:
   The calculated probability ≈ 0.952, which rounds to 0.95. The tech visits coefficient being 0 means a tech visit does not change the logit; gender = 0 removes its effect, so only intercept and inbound calls drive the result.

5. Why other choices are incorrect:
   - 0.45, 0.65, 0.75 are much lower than the computed 0.952; they would correspond to much smaller logits (negative or near zero logit values), inconsistent with the positive large logit (2.98) from the given coefficients.

Conclusion: The correct probability is approximately 0.95, matching the provided answer.

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). Single choice

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