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# Understand logistic regression and logit function in depth.

Updated: Nov 2, 2022

Logistic Regression is a classification algorithm where we only have two choices either true or false.

A categorical target variable is used for doing prediction, and a categorical variable is one that represents characteristics and can't be measured or counted.

Here the probability lies in a range of 0 and 1.

If the probability lies between 0 to 1, then why can't we use Logistic Regression?

1. Because it is susceptible to outliers, due to outliers threshold points can shift.

2. Due to the interpretation of the model.

Since it is a type of classification problem, but still used Regression in its name, which is because we need continuous values in the range of 0 to 1.

We need to modify the linear regression equation for achieving this task and need to implement a new logit function.

Logit Function:-

It is a function that has a range between 0 and 1, irrespective of any input it will always give output between 0 and 1.

If (mx+c) is high then the overall Y value comes out to be 1.

If (mx+c ) is low(or negative) then the overall Y value comes out to be 0.

Hence we are getting a new S-shaped curve.

Example: If the probability comes out to be 0.8 then it belongs to class 1.

Therefore if the probability is greater than 0.5 then it belongs to class 1 else class 0.