Explanation

In logistic regression, the log odds (also called the logit) is calculated using the formula:

$\text{log odds} = \ln\left(\frac{P}{1 - P}\right)$

Given:

• $P = 0.618$
• $1 - P = 1 - 0.618 = 0.382$

Substitute into the formula:

$\text{log odds} = \ln\left(\frac{0.618}{0.382}\right)$

First, calculate the odds:

$\frac{0.618}{0.382} \approx 1.618$

Then take the natural logarithm:

$\ln(1.618) \approx 0.481$

Therefore, the associated log odds are closest to 0.481, which corresponds to Option B.

Verification:

• Option A (0.382) is simply $1 - P$, not the log odds
• Option C (1.618) is the odds ratio $\frac{P}{1-P}$, not the log odds
• Option B (0.481) is the correct log odds value