Logistic Regression is used for binary classification of data-points. It performs categorical classification that results in the output belonging to either of the two classes (1 or 0). For example, predicting whether it would rain or not, based on the weather condition is an example of logistic regression.
The two important parts of Logistic Regression are Hypothesis and the Sigmoid Curve. Using this hypothesis, we derive the likelihood of an event.
The data that is produced from our hypothesis is fit into the log function that ultimately forms an S shaped curve called ‘sigmoid’. Based on this log function, we are able to determine the category of the class.
The sigmoid is an S-shaped curve which is represented as follows:
We generate this with the help of logistic function –
1 / (1 + e^-x)
Here, e represents base of natural log and we obtain the S-shaped curve with values between 0 and 1. The equation for logistic regression is written as:
y = e^(b0 + b1*x) / (1 + e^(b0 + b1*x))
Here, b0 and b1 are the coefficients of the input x. These coefficients are estimated using the data through “maximum likelihood estimation”.