Machine learning contains many different techniques for making predictions and classifications from data points. Linear regression and logistic regression stand as the two primary algorithms that people utilize within supervised learning approaches. The two models despite sharing the word “regression” within their titles demonstrate distinct application purposes. Linear regression functions to forecast continuous outputs but logistic regression serves classifications among categories.
What is Linear Regression?
Linear regression functions as a statistical technique to compute predictions regarding continuous responses derived from one or more input variables. A linear connection exists between features together with the output variable regarding this model framework.
Mathematical Representation
The fundamental principle of linear regression uses the following mathematical format for a straight line:
Y=β0​+β1​X+ϵ
Where:
- YYY = Predicted output (dependent variable)
- β0\beta_0β0​ = Intercept (value of YYY when X=0X = 0X=0)
- β1\beta_1β1​ = Coefficient (slope of the line)
- XXX = Input feature (independent variable)
- ϵ\epsilonϵ = Error term (random noise)
Example of Linear Regression
Some employees wish to understand how employee years of experience relate to their salary levels. A linear regression model would create an optimal regression line which predicts salary amounts from work experience data.
Types of Linear Regression
1. Simple Linear Regression – Uses one independent variable.
2. Multiple Linear Regression – Uses two or more independent variables.
3. Polynomial Regression – Uses a polynomial equation instead of a straight line.
Applications of Linear Regression
• House price prediction
• Stock market forecasting
• Sales and revenue prediction
• Medical cost estimation
Advantages of Linear Regression
– The interpretation remains straightforward because of its basic nature.
– Computationally efficient
– The method shows effectiveness when dealing with data sets which exhibit linear relationships.
Disadvantages of Linear Regression
– The technique depends on variables having a direct proportional relationship between them.
– Sensitive to outliers
– The model does not support analysing targets consisting of categorical categories.
What is Logistic Regression?
The classification method of logistic regression handles issues in which target outcomes take category-based forms (binary or multi-class categories). The model calculates class probabilities through sigmoid transformation of outputs.
Mathematical Representation
The logistic regression model utilizes a sigmoid function to adjust the basic linear regression expression:
P(Y=1) = 1/(1+e−(β0​+β1​X))
Where:
- P(Y=1) is the probability that the outcome is 1.
- e is Euler’s number (~2.718).
- β0​, β1​ are coefficients estimated from the data.
Example of Logistic Regression
A company desires to determine which customers will buy products (Yes/No) by studying their webpage activities. The model uses logistic regression to estimate purchase likelihood then determines whether the customer should be classified as (Yes or No).
Types of Logistic Regression
1. Binary Logistic Regression – Two possible outcomes (e.g., spam or not spam).
2. Multinomial Logistic Regression analyses three or more categories of unrelated outcomes such as different types of fruits.
3. The model can process Three or more ordered categories by using Ordinal Logistic Regression (for instance rating systems that have poor, average and excellent levels).
Applications of Logistic Regression
• Email spam detection
• Disease diagnosis (e.g., predicting diabetes)
• Credit card fraud detection
• Sentiment analysis
Advantages of Logistic Regression
– Works well for binary classification problems
– The model provides assessment results as probabilities which a reader can easily understand.
– The method works efficiently with computer systems while needing lower amounts of training information.
Disadvantages of Logistic Regression
– Assumes linear decision boundaries
– Struggles with highly complex data patterns
– Sensitive to imbalanced datasets
Key Differences Between Linear Regression and Logistic Regression
| Feature | Linear Regression | Logistic Regression |
|---|---|---|
| Type of Problem | Regression (Continuous Output) | Classification (Categorical Output) |
| Output Value | Any real number | Probability (0 to 1) |
| Equation Used | Y=β0+β1X | P(Y=1)=1/(1+e−(β0​+β1​X)) |
| Algorithm Used | Least Squares Method | Maximum Likelihood Estimation (MLE) |
| Use Case | Predicting numerical values | Predicting categories (labels) |
| Decision Boundary | A straight line | A curve (sigmoid function) |
Selecting between linear and logistic regression
- Your prediction of continuous values (sales revenue, temperature and price) should employ linear regression as your modelling technique.
- Logistic regression is suitable for categorical classifications such as the detection of diseases in patients.
Implementation of Linear and Logistic Regression in Python
Linear Regression using Scikit-learn
| from sklearn.linear_model import LinearRegressionimport numpy as np # Sample dataX = np.array([1, 2, 3, 4, 5]).reshape(-1, 1)Y = np.array([2, 4, 6, 8, 10]) # Create and train the modelmodel = LinearRegression()model.fit(X, Y) # Predicting valuespredicted = model.predict([[6]])print(“Predicted Value:”, predicted) |
Logistic Regression using Scikit-learn
| from sklearn.linear_model import LogisticRegressionimport numpy as np # Sample dataX = np.array([[1], [2], [3], [4], [5]])Y = np.array([0, 0, 1, 1, 1]) # Create and train the modelmodel = LogisticRegression()model.fit(X, Y) # Predicting probabilityprob = model.predict_proba([[3]])[:, 1]print(“Probability of Class 1:”, prob) |
Conclusion
Machine learning contains two core methods namely linear regression and logistic regression which operate for separate functional tasks. The optimal use of linear regression occurs for continuous value prediction but logistic regression proves most effective in classifying problems.
- The linear regression model detects direct proportional or inverse relationships between the variables within datasets.
- The output of logistic regression emerges as a probability because the sigmoid function converts it.