Explain the mathematical foundation of Logistic Regression

Logistic Regression models the probability of a categorical outcome using a linear combination of features transformed through the sigmoid function.

Logistic Regression is fundamentally based on probability theory and statistical modeling. The model predicts the probability that a given input belongs to a particular class. Instead of directly predicting class labels, it estimates probabilities using the logistic (sigmoid) function.

The linear equation is:

z = b0 + b1x1 + b2x2 + ... + bnxn

This linear output is then transformed using the sigmoid function:

P(y=1|x) = 1 / (1 + e^-z)

The sigmoid function compresses any real-valued number into the range [0,1], making it suitable for probability estimation.…