Decoding Linear Regression vs. Logistic Regression

Linear Regression and Logistic Regression are two fundamental machine-learning algorithms used for predictive modeling. This article explores both techniques and highlights their key differences.

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Decoding Linear Regression vs. Logistic Regression

Linear Regression and Logistic Regression are two fundamental machine-learning algorithms used for predictive modeling. While they share certain similarities, their applications, methods, and outputs are distinctly different. This article explores both techniques and highlights their key differences.

What is Linear Regression?

Linear Regression is a supervised learning algorithm used for predicting a continuous numerical output based on one or more independent variables. It assumes a linear relationship between the dependent variable and the independent variables.

Linear Regression Formula

What is Logistic Regression?

Logistic Regression is also a supervised learning algorithm but is used for classification tasks. It predicts the probability of a categorical dependent variable, often binary (e.g., success/failure). It uses the logistic function to map predictions to a range between 0 and 1.

Logistic Regression Formula

Linear Regression vs. Logistic Regression

Here’s a detailed comparison table between Linear Regression and Logistic Regression:

Aspect	Linear Regression	Logistic Regression
Purpose	Predicts continuous outcomes (e.g., house prices, temperature).	Predicts categorical outcomes, typically binary (e.g., yes/no, 0/1).
Output	Produces a continuous value.	Produces a probability value between 0 and 1, interpreted as the likelihood of the outcome being 1.
Nature of Relationship	Models a linear relationship between independent and dependent variables.	Models a nonlinear (logistic/sigmoid) relationship between independent variables and probabilities.
Type of Dependent Variable	Continuous (e.g., salary, weight).	Categorical (binary or multinomial, e.g., spam or not spam, win/lose).
Error Metric	Minimizes the sum of squared residuals (Ordinary Least Squares - OLS).	Uses maximum likelihood estimation (MLE) to minimize error in predicted probabilities.
Assumptions	- Linearity of relationship between $x$ and $y$ . - Homoscedasticity (constant variance). - Normal distribution of errors.	- Linearity between $x$ and the log-odds of $y$ . - Independence of observations.
Interpretation of Coefficients	Change in $y$ for a one-unit change in $x$ , holding other variables constant.	Change in the log-odds of $y = 1$ for a one-unit change in $x$ , holding other variables constant.
Applications	- Predicting housing prices. - Estimating sales revenue. - Modeling energy consumption.	- Spam email detection. - Predicting customer churn. - Medical diagnosis (e.g., disease/no disease).
Output Range	Can range from $−∞-\infty$ to $+∞+\infty$ .	Restricted to the range [0, 1], representing probabilities.
Handling of Outliers	Sensitive to outliers, as they can significantly affect the model.	More robust to outliers, especially when they don’t affect the classification threshold much.
Best Fit Line	Produces a single straight line (or hyperplane for multiple features).	Produces an S-shaped curve (sigmoid) mapping probabilities.
Evaluation Metrics	Mean Squared Error (MSE), Root Mean Squared Error (RMSE), $R^2$ score.	Accuracy, Precision, Recall, F1 Score, ROC-AUC, Log-loss.
Algorithms Used	Ordinary Least Squares (OLS), Gradient Descent.	Gradient Descent, Newton-Raphson Method.
Handling Multicollinearity	Strong multicollinearity can distort results and reduce interpretability.	Multicollinearity can also affect results but is generally less impactful due to categorical outcomes.
Scalability	Can be applied to small and large datasets but may struggle with high-dimensional data without feature selection.	Scalable to large datasets but computationally intensive with many categorical outcomes.
Extensions	-Polynomial regression (to model nonlinear relationships). -Ridge/Lasso regression for regularization.	-Multinomial logistic regression for more than two categories. -Regularized logistic regression (L1/L2).
When to Use?	When the target variable is continuous, and the relationship between variables is linear.	When the target variable is categorical (binary or multinomial).

Also Read: Multiple Linear Regression: Formula, Steps, Applications

Conclusion

Linear Regression and Logistic Regression are both essential tools in machine learning but serve entirely different purposes. Linear Regression is best suited for predicting continuous outputs, while Logistic Regression excels in classification tasks. Choosing the right algorithm depends on the nature of the problem and the type of output required. Both techniques are foundational for data analysis and machine learning, forming the basis for more advanced models.

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Edited by

Shreeya Thakur

Content Team

I am a biotechnologist-turned-writer and try to add an element of science in my writings wherever possible. Apart from writing, I like to cook, read and travel.