Linear Regression
Linear regression is one of the simplest and most widely used techniques in statistics and machine learning for modeling the relationship between a dependent variable and one or more independent variables. It assumes a linear relationship between the variables, expressed mathematically as \( Y = \beta_0 + \beta_1X + \epsilon \), where \( \beta_0 \) is the intercept, \( \beta_1 \) is the slope, and \( \epsilon \) represents the error term. The goal is to minimize the sum of squared errors (SSE) to find the best-fitting line through the data points. Introduced formally in the early 19th century, linear regression remains a cornerstone of predictive modeling due to its interpretability and simplicity.
https://en.wikipedia.org/wiki/Linear_regression
Linear regression finds extensive applications in fields like economics, finance, and social sciences. For example, it is used to predict sales revenue based on advertising spend or to estimate the relationship between income and education level. With the advent of computational tools like scikit-learn, introduced in 2007, and TensorFlow, launched in 2015, implementing linear regression models has become highly accessible. These tools allow users to efficiently handle large datasets, automatically calculate performance metrics like the R-squared value, and perform cross-validation to ensure model robustness.
https://scikit-learn.org/stable/
Despite its simplicity, linear regression has limitations, such as its inability to model non-linear relationships and sensitivity to multicollinearity among predictors. Extensions like multiple linear regression and polynomial regression address some of these challenges by incorporating additional predictors or transforming variables. Additionally, regularization techniques like ridge regression and lasso regression are employed to manage overfitting and improve generalization. Linear regression continues to evolve with advanced computational methods, making it a foundational tool in data analytics and predictive modeling.
https://en.wikipedia.org/wiki/Ridge_regression
https://en.wikipedia.org/wiki/Lasso_(statistics)