Logistic Regression does not predict probabilities

In logistic regression, the model predicts the odds of an event happening rather than directly predicting probabilities. The odds are defined as:

$\text{Odds}=\frac{P(\text{success})}{P(\text{failure})}=\frac{p}{1-p}$

where $p$ is the probability of success. The log-odds (or logit function) is the natural logarithm of the odds: $\text{Log-Odds}=\ln \left(\frac{p}{1-p}\right)=b_0+b_{1}x$ This transformation makes the relationship between the independent variables and the dependent variable linear, allowing logistic regression to estimate the parameters $b_0$ and $b_1$.

Resources:

• Explanation of log odds
• Explanation of log odd function

What is the difference between odds and probability