Final answer:
A total predicted logit of 0 corresponds to a probability of 0.5. This is because the logistic function used to transform logits to probabilities yields a value of 0.5 when the logit is 0, indicating equal chances of occurrence or non-occurrence for the event in question. The correct option is b.
Step-by-step explanation:
The predicted logit is a linear function of predictors used in logistic regression. The logit links the probability of the binary outcome to the predictors. A predicted logit of 0 indicates that the event has equal chances of occurring or not occurring. To transform a logit to a probability, we use the logistic function, which is
P(Y=1) = 1 / (1 + e-logit).
For a logit of 0, this becomes:
P(Y=1) = 1 / (1 + e0) = 1 / (1 + 1) = 1/2 = 0.5.
Thus, the probability corresponding to a total predicted logit of 0 is 0.5.
Therefore, when you encounter a total predicted logit of 0, you can confidently transform it to a probability of 0.5, which corresponds to option b. This is an important concept in statistics, specifically in logistic regression analysis.