Question

Which of the following statement is NOT correct about logistic regression?

a. The probabilities of success and failure adds up to 1 in a binary logistic regression model
b. The sum of the probabilities of success and failure could be smaller than 1 in a binary logistic regression model
c. The left-hand side of the logistic model is log(p/(1-p)), the log of the odds ratio
d. The right-hand side of the logistic model is the same as in linear regression

Answer 1

The incorrect statement about logistic regression is that the sum of the probabilities of success and failure could be less than 1; binary logistic regression mandates that the sum must always be 1.

Step-by-step explanation:

The statement that is NOT correct about logistic regression is 'b. The sum of the probabilities of success and failure could be smaller than 1 in a binary logistic regression model'. In binary logistic regression, the probabilities of success (p) and failure (q) must always add up to 1, meaning p + q = 1, where q is defined as 1 - p. This is a fundamental property of any binary probability distribution. Other key aspects of logistic regression are that the left-hand side of the model is the log of the odds ratio, log(p/(1-p)), and the right-hand side typically contains a linear combination of predictors, similar to that in linear regression, which is then used to calculate the log odds of the probability of success.