ln(p1−p)=β0+β1x1+...+βnxnl n open paren the fraction with numerator p and denominator 1 minus p end-fraction close paren equals beta sub 0 plus beta sub 1 x sub 1 plus point point point plus beta sub n x sub n Usually, if the predicted probability is ≥0.5is greater than or equal to 0.5 , it’s classified as "1"; otherwise, it's "0." 2. Multinomial Logistic Regression
Use if you are answering a "True/False" style question.
This is used when your target variable has exactly (e.g., Yes/No, Pass/Fail, Spam/Not Spam). Logistic Regression: Binary and Multinomial
The categories must be nominal (no inherent order). If the categories have a natural ranking (like "Low, Medium, High"), you should use Ordinal Logistic Regression instead.
It outputs a vector of probabilities for all classes that sum up to 1.0. The class with the highest probability is the predicted outcome. Key Differences at a Glance Multinomial Outcome Classes Function Example Fraud vs. Not Fraud Red vs. Blue vs. Green Complexity Simple; one set of weights Higher; weights for each class When to Use Which? ln(p1−p)=β0+β1x1+
It uses the Sigmoid function to map any real-valued number into a value between 0 and 1. The Math: It models the "log-odds" of the probability
Use if you are choosing between several distinct labels where one choice doesn't "outrank" another. The categories must be nominal (no inherent order)
Instead of one sigmoid function, it uses the Softmax function . It essentially runs multiple binary regressions comparing each category to a "reference" category.