Linear Regression
Linear regression is a supervised learning algorithm used to model the relationship between a dependent variable (output) and one or more independent variables (inputs) by fitting a straight line (in one dimension) or a hyperplane (in multiple dimensions). In artificial intelligence and machine learning, it is one of the most fundamental algorithms for prediction and data analysis.
Background and origins
The roots of linear regression go back to the 19th century, with statisticians like Francis Galton and Karl Pearson developing methods to study relationships between variables. Initially a statistical tool, regression became one of the earliest algorithms applied in machine learning due to its simplicity, interpretability, and efficiency. Today, linear regression is often taught as a baseline model against which more complex algorithms are compared.
Practical applications
- Economics and finance: predicting housing prices or stock market trends based on explanatory factors.
- Healthcare: modeling the relationship between risk factors (e.g., smoking, exercise) and health outcomes.
- AI systems: as a simple predictive baseline, often compared against neural networks or ensemble models.
- Marketing and business: estimating the impact of advertising spend on sales.
Challenges and debates
Linear regression assumes a linear relationship between variables, which is often too simplistic for real-world AI problems. It also assumes independence of errors, constant variance (homoscedasticity), and no multicollinearity—conditions frequently violated in practice. Despite these limits, it remains valuable for its interpretability and as a foundation for advanced models (e.g., logistic regression, generalized linear models).
References
- Wikipedia – Linear regression
- James, G. et al. (2013). An Introduction to Statistical Learning.
- Hastie, T., Tibshirani, R., Friedman, J. (2009). The Elements of Statistical Learning.
