Logistic Regression

Logistic regression is a classification method used in statistical modeling and machine learning for situations where the dependent variable has limited categories. It is typically developed to predict binary outcomes (e.g. yes/no, 0/1), and for more complex structures, multinomial or ordinal logistic regression models are also employed. At its core, it relates probabilities to independent variables through a logit transformation.

Working Principle

Unlike linear regression, logistic regression does not estimate continuous values for the dependent variable but calculates the probabilities of belonging to specific classes. Mathematically, the model is based on the sigmoid (S-curve) function, which ensures that predicted values are constrained between 0 and 1.

The formula is expressed as:

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Types

Binary Logistic Regression

Used when the dependent variable has only two categories. For example, it can predict whether a patient has a disease or not.

Multinomial Logistic Regression

Used for problems where the dependent variable has more than two categories. For example, it can classify consumer preferences as “Brand A, Brand B, Brand C”.

Ordinal Logistic Regression

Preferred when the categories of the dependent variable are ordered. For example, it is applied to describe customer satisfaction using ordered categories such as “poor, fair, good, excellent”.

Advantages

• Computationally relatively simple.
• Produces fast results on large datasets.
• Model parameters and prediction process are transparent and easy to interpret.

Disadvantages

• Assumes a linear relationship between dependent and independent variables.
• May be insufficient compared to methods like deep learning for complex nonlinear relationships.
• Can be sensitive to outliers.

Applications

• Healthcare: Predicting disease risks.
• Finance: Evaluating loan applications, detecting fraud.
• Marketing: Estimating the probability of ad clicks.
• Manufacturing: Predicting machine failures.