Abstract
Regression analysis is a cornerstone of predictive analytics, used extensively in science, engineering, and business to model relationships between variables. A fundamental challenge is finding parameter estimates that minimize the cost function, ensuring the best possible model fit. Gradient Descent (GD), a first-order iterative optimization algorithm, has emerged as a preferred approach for this purpose due to its simplicity, scalability, and effectiveness. This paper explores the principles of Gradient Descent, its advantages over traditional analytical solutions, its practical implementation in linear regression, and its performance in minimizing the Mean Squared Error (MSE). Experiments demonstrate how GD provides a robust, flexible approach to finding optimal regression parameters, especially for large and complex datasets where closed-form solutions may be impractical.