Regression Analysis

Regression analysis is a powerful and widely used statistical method for estimating the relationships between a dependent variable and one or more independent variables. The core objective is to model the relationship between these variables to understand how the value of the dependent variable changes when any of the independent variables are varied. By establishing a mathematical equation, regression analysis allows for prediction and forecasting, as well as quantifying the strength of the relationship between the variables, making it a fundamental tool for drawing conclusions from data.

1. Foundations of Regression Analysis
   1. Core Concepts and Definitions
      1. Definition of Regression Analysis
      2. Purpose and Objectives of Regression
      3. Applications Across Disciplines
      4. Variables in Regression
         1. Dependent Variables
         2. Independent Variables
         3. Explanatory Variables
         4. Response Variables
      5. The Regression Model Framework
         1. Deterministic Models
         2. Stochastic Models
         3. Linear Models
         4. Nonlinear Models
      6. Population vs Sample Relationships
         1. Population Regression Function
         2. Sample Regression Function
         3. Estimation vs True Parameters
   2. Correlation and Causation
      1. Understanding Correlation
      2. Distinguishing Correlation from Causality
      3. Spurious Correlation
      4. Confounding Variables
      5. Establishing Causal Relationships
   3. The Error Term
      1. Definition and Role of the Error Term
      2. Sources of Randomness in Regression
      3. Interpretation of the Error Term
      4. Assumptions about the Error Term
      5. Unobserved Heterogeneity
   4. Types of Data in Regression
      1. Cross-Sectional Data
         1. Characteristics and Structure
         2. Examples and Applications
         3. Specific Issues and Challenges
      2. Time Series Data
         1. Characteristics and Structure
         2. Temporal Ordering
         3. Trends and Seasonality
         4. Examples and Applications
      3. Panel Data
         1. Structure and Dimensions
         2. Balanced vs Unbalanced Panels
         3. Advantages of Panel Data
         4. Challenges in Panel Data Analysis
      4. Pooled Cross-Sectional Data
         1. Definition and Structure
         2. Use Cases and Applications