Regression Diagnostics: Identifying and Fixing Model Violations

Linear regression is a powerful predictive tool, but its validity relies on strict mathematical assumptions that are frequently violated by noisy, real-world data. When these assumptions fail, your model's predictions become unreliable and its coefficients misleading. This text-based course provides a systematic approach to diagnosing regression vulnerabilities and applying precise mathematical and programmatic remedies. You will transition from simply fitting models to critically evaluating their health, ensuring your data insights are statistically sound and defensible. What you'll learn: - Understand the core assumptions of linear regression, including linearity, homoscedasticity, independence, and normality. - Identify outliers, high-leverage points, and influential observations using residual analysis and Cook's distance. - Detect multicollinearity using Variance Inflation Factors and resolve it using modern regularization techniques. - Apply mathematical transformations, such as the Box-Cox method, to correct non-linear patterns and unequal error variance. - Implement robust regression methods and weighted least squares to handle non-normal error distributions. This course begins with foundational regression theory and assumption definitions, guiding you step-by-step through diagnostic tests and practical correction strategies. It is designed for aspiring data scientists, analysts, and technical professionals who have a basic familiarity with statistics and want to build highly reliable models. Start mastering diagnostic workflows to ensure your statistical models deliver accurate, real-world value.