Analyzing Regression Models: Observed, Fitted, and Residual Values

Understanding what happens after you run a regression model is the key to making accurate, data-driven decisions. Simply generating a model is not enough; you must know how to evaluate its predictions and diagnose potential issues. This course guides you through the essential concepts of observed values, fitted values, and residuals so you can confidently interpret your statistical results. By reading through clear explanations and practical examples, you will learn how to assess the accuracy of your models and validate their underlying assumptions. We start with foundational definitions, ensuring you grasp the core terminology before moving on to diagnostics and interpretation. What you'll learn: - Understand the fundamental differences between observed data and model-fitted predictions - Calculate and interpret residuals to assess how well your multiple regression model performs - Identify patterns in residual plots to detect common issues like heteroscedasticity and non-linearity - Apply statistical metrics to quantify model fit and prediction error - Evaluate the impact of multiple input variables on your final model predictions You will begin with basic definitions of regression components, progress to interpreting real-world model outputs, and finish with diagnostic techniques to ensure your models are reliable and valid. This text-only course is designed for beginners who want to understand the mechanics of regression analysis without getting lost in overly dense mathematical jargon. No advanced programming or statistical background is required to start.