LOGISTIC REGRESSION

 INTRODUCTION:

It is a statistic method that is used for building machine learning models where the dependent variable is binary. It is used to describe data and the relationship between one dependent variable and one or more independent variables. The name "logistic regression" is derived from the concept of the logistic function that is uses. The logistic function is also known as the sigmoid function. The value of this logistic function lies between zero(0) and one(1). It is Supervised Classification Algorithm. The value of the logistic regression must be between 0 and 1, which cannot go beyond this limit, so it forms a curve like the "S" form. The S-form curve is called the Sigmoid function or the logistic function. 

LOGISTIC REGRESSION EQUATION:

The Logistic regression equation can be obtained from the Linear Regression equation. The mathematical steps to get Logistic Regression equations are given below:

The equation of the straight line can be written as:

                       Y = b₀ + b₁x₁ + b₂x₂ + b₃x₃ +…+ b_nx_n      

In Logistic Regression y can be between 0 and 1 only, so for this let's divide the above equation by (1-Y):

                          Y/1-Y; 0 for y=0 and infinity for Y=1

But we need range between -[infinity] to +[infinity], then take logarithm of the equation it will become:

                         log(y/1-y) = b₀ + b₁x₁ + b₂x₂ + b₃x₃ +…+ b_nx_n  

     

TYPE OF LOGISTIC REGRESSION:

On the basis of the categories, Logistic Regression can be classified into three types:

Binomial: In binomial Logistic regression, there can be only two possible types of the dependent variables, such as 0 or 1, Pass or Fail, etc.

Multinomial: In multinomial Logistic regression, there can be 3 or more possible unordered types of the dependent variable, such as "cat", "dogs", or "sheep"

Ordinal: In ordinal Logistic regression, there can be 3 or more possible ordered types of dependent variables, such as "low", "Medium", or "High".

        

ADVANTAGES OF LOGISTIC REGRESSION:

• Logistic regression performs better when the data is linearly separable.
• It does not require too many computational resources as it's highly interpretable.
• There is no problem scaling the input features-it does not require tuning.
• It is easy to implement and train a model using logistic regression.
• It gives a measure of how relevant a predictor(coefficient size) is, and it's direction of association(positive or negative).

 

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