Logistic regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. The dependent variable in logistic regression is a binary variable, meaning it can take on one of two possible values, such as 0 or 1. Logistic regression is used to model the probability of the dependent variable taking on the value 1, based on the values of the independent variables.
In logistic regression, we use a logistic function (also known as the sigmoid function) to model the probability of the dependent variable taking on the value 1. The logistic function is of the form:
p = 1 / (1 + e^(-z))
where p is the probability of the dependent variable taking on the value 1, and z is a linear combination of the independent variables, with coefficients b0, b1, b2, ..., bn:
z = b0 + b1x1 + b2x2 + ... + bn*xn
The coefficients are estimated using a method called maximum likelihood estimation, which maximizes the likelihood of the observed data given the model.
Logistic regression is widely used in many applications, such as binary classification problems, such as predicting whether a customer will churn or not, or whether a credit card transaction is fraudulent or not. Logistic regression is a simple and effective method for modeling the probability of binary outcomes, but it may not be suitable for more complex relationships or multiclass classification problems.