One of the most used methods in statistics and machine learning for resolving classification issues is logistic regression. Despite its name, logistic regression is employed for classification tasks rather than regression tasks. It is extensively used in many different domains, including consumer segmentation, fraud detection, spam filtering, and medical diagnosis.
To help you understand why logistic regression is such a crucial tool in classification jobs, this blog will describe what it is, how it operates, its benefits and drawbacks, and real-world applications.
What Is Logistic Regression?
A supervised learning approach for categorical outcome prediction is called logistic regression. It calculates, using one or more independent factors, the likelihood that an occurrence falls into a specific category.
Logistic regression predicts probabilities that are subsequently translated into class labels (0 or 1, Yes or No, Fraud or Not Fraud), in contrast to linear regression, which predicts continuous values.
For instance, Logistic Regression provides a probability score ranging from 0 to 1 if you wish to determine whether an email is spam or not. It is categorized as spam if the score is greater than 0.5; if not, it is not.
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Mathematical Formula of Logistic Regression
In Linear Regression, the equation is:
However, Logistic Regression applies the sigmoid function (logistic function) to convert the linear output into a probability:
The logistic function ensures that the output remains between 0 and 1, making it ideal for probability-based classification.
How Does Logistic Regression Work?
Logistic Regression works in three main steps:
1. Model Training
A dataset comprising independent variables (features) and the goal values (labels) that correspond to them is used to train the model. It gains knowledge of how independent variables, or inputs, relate to dependent variables, or outcomes.
In a medical diagnosis dataset, for instance, the dependent variable might be whether a patient has a disease (1) or not (0), while the independent variables might be age, blood pressure, and cholesterol levels.
2. Prediction Using the Sigmoid Function
After training, the model estimates the likelihood of falling into a specific class using fresh input data and the sigmoid function.
For example, the model defines a tumor as malignant if its likelihood of becoming malignant is 0.8 (80%) (1). It is categorized as benign (0) if it is 0.3 (30%).
3. Decision Boundary & Classification
A threshold (typically 0.5) is applied:
If P(Y=1) > 0.5, classify as 1 (Positive class).
If P(Y=1) ≤ 0.5, classify as 0 (Negative class).
For example, if predicting customer churn, customers with P(Churn) > 0.5 are classified as likely to leave, while others are classified as retained.
Types of Logistic Regression
Logistic Regression can be classified into three types:
1. Binary Logistic Regression
Used when there are two potential classes for the target variable (Yes/No, 0/1, Pass/Fail).
For instance, forecasting a loan's approval or denial depending on the income and credit score of the applicant.
2. Multinomial Logistic Regression
Utilized when there are three or more unordered categories in the target variable (such as various product types).
For instance, grouping flower varieties according on the length and width of their petals.
3. Ordinal Logistic Regression
used when there are three or more ordered categories (such as Low, Medium, and High) in the target variable.
Example: Using feedback scores, provide a Poor, Average, or Excellent rating to client satisfaction.
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Advantages of Logistic Regression
1. Interpretability:
Clear insights into the significance of each variable are provided by logistic regression, which simplifies comprehension.
2. In terms of computation efficiency:
It is a straightforward technique that requires little processing power and performs well with small to medium-sized datasets.
3. Effective for Data That Is Linearly Separable:
When there is a roughly linear relationship between the independent and dependent variables, logistic regression works well.
4. Predictions Based on Probability:
It offers likelihood scores that are helpful while making decisions.
5. Preventing Overfitting with Regularization:
By penalizing large coefficients, methods such as Lasso and Ridge Regression can assist in preventing overfitting.
Limitations of Logistic Regression
1. Assumes a Linear Relationship Between Features and Log-Odds:
Without feature engineering or adjustments, logistic regression performs poorly when the dataset contains nonlinear connections.
2. Unsuitable for High-Dimensional, Large Datasets:
It may be difficult for Logistic Regression to generalize effectively when working with large data sets with thousands of features.
3. Sensitive of Outliers:
Extreme values have the potential to skew the findings of logistic regression.
4. Ideal for Binary Categorization:
Other algorithms, such as Decision Trees, Random Forest, and Neural Networks, frequently outperform it, even though it may be extended to multiclass situations.
Real-World Applications of Logistic Regression
1. Health Care: Forecasting Illnesses
Diseases including diabetes, heart disease, and cancer can be predicted using logistic regression.
2. Banking Fraud Detection
Based on trends in transaction history, banks employ logistic regression to identify fraudulent transactions.
3. Marketing: Retaining Customers
Based on demographics and engagement levels, businesses forecast whether customers are likely to churn, or stop using a service.
4. Email Spam Detection
Using keywords, sender information, and other metadata, logistic regression determines if an email is spam or not.
Example: Predicting Loan Approval
Let's say a bank wishes to forecast a customer's likelihood of being granted a loan by looking at the following characteristics:
Revenue (in US dollars)
Score for credit (out of 850)
Requested Loan Amount (in dollars)
The bank is able to determine the likelihood of approval by employing logistic regression. The loan is accepted if the probability is greater than 0.5; if not, it is denied.
Conclusion
A strong yet straightforward technique for classification issues, logistic regression finds application in a wide range of sectors, including healthcare and finance. Although it is extensively used, interpretable, and economical, it has certain drawbacks, especially when working with high-dimensional datasets and nonlinear interactions.
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