In logistic regression, the dependent variable is the what?

In logistic regression, the dependent variable is the what?

• A. Probability of success
• B. The logistic transformation of the dependent variable
• C. Logarithm of the Probabilities
• D. Odds ratio

Answer: (C)

In logistic regression, you model the probability of the event through a transformation that maps probabilities (which are between 0 and 1) onto the entire real line. This transformation is the logit: log(p/(1−p)). In other words, the quantity that the linear predictor β0 + β1X is tied to is the logarithm of the odds of success. This makes the relationship linear in the predictors and keeps the back-transformed predictions between 0 and 1. Describing this as the “logarithm of the probabilities” is capturing the idea that you’re applying a logarithmic transformation to a function of the probability—the odds—not the probability itself, which is why the logit is used. It’s not simply log(p) or the odds ratio itself, and the dependent variable is not the raw probability. The model uses the log-odds (the log of p/(1−p)) as the outcome in the linear equation.

In logistic regression, you model the probability of the event through a transformation that maps probabilities (which are between 0 and 1) onto the entire real line. This transformation is the logit: log(p/(1−p)). In other words, the quantity that the linear predictor β0 + β1X is tied to is the logarithm of the odds of success. This makes the relationship linear in the predictors and keeps the back-transformed predictions between 0 and 1.

Describing this as the “logarithm of the probabilities” is capturing the idea that you’re applying a logarithmic transformation to a function of the probability—the odds—not the probability itself, which is why the logit is used. It’s not simply log(p) or the odds ratio itself, and the dependent variable is not the raw probability. The model uses the log-odds (the log of p/(1−p)) as the outcome in the linear equation.