1. Sigmoid Function: Logistic regression uses the logistic function (also known as the sigmoid function) to model the relationship between the input features and the probability of the binary outcome. The sigmoid function is an S-shaped curve that maps any real-valued number to a value between 0 and 1, making it suitable for representing probabilities. The formula for the sigmoid function is:

2. Linear Combination: Logistic regression assumes that the log-odds (logit) of the probability of the positive class is a linear combination of the input features. In mathematical terms, this is represented as:

3. Training: The goal in logistic regression is to find the values of the coefficients (β) that maximize the likelihood of the observed data. This is typically done using optimization algorithms like gradient descent.

4. Prediction: Once the model is trained, it can be used to predict the probability of the positive class for new input data. If the predicted probability is greater than 0.5, the model classifies the input as belonging to the positive class; otherwise, it's classified as the negative class.