# What is logistic regression?
**Logistic regression** is a common machine learning algorithm for binary classification and predicts a binary categorical variable through a logistic function.


The logistic regression model passes the outcome of a linear function of features through a logistic function to calculate the probability of an occurrence. The model then maps the probability to binary outcomes.

# What is a sigmoid function?
The logistic function in linear regression is a type of sigmoid, a class of functions with the same specific properties.

Sigmoid is a mathematical function that takes any real number and maps it to a probability between 1 and 0.

The sigmoid function forms an *S* shaped graph, which means as $x$ approaches infinity, the probability becomes 1, and as $x$ approaches negative infinity, the probability becomes 0. The model sets a threshold that decides what range of probability is mapped to which binary variable.

Suppose we have two possible outcomes, *true* and *false*, and have set the threshold as *0.5*. A probability less than *0.5* would be mapped to the outcome *false*, and a probability greater than or equal to *0.5* would be mapped to the outcome *true*.

# Example
Suppose, a regression model is fit using some training data to obtain *β* and *x* represents the input features:

The probability of $z$ being mapped to 1 is given by the equation:

What is sigmoid and its role in logistic regression?

What is logistic regression? Logistic regression is a common machine learning algorithm for binary classification and predicts a binary categorical variable through a logistic function. 