Regression Unfolded

Table of Contents

1. The Essence of Regression
- Understanding Data Relationships
- History and Evolution of Regression
- Major Types and Uses

2. Linear Regression in Depth
- Fundamentals of Linear Relationships
- Assumptions and Properties
- Practical Applications and Case Studies

3. Diving Into Logistic Regression
- From Linear to Logistic: The Transition
- Binary Outcomes and Odds Ratio
- Case Studies: Medical and Social Sciences

4. Polynomial Regression
- Beyond Linearity: Capturing Curvature
- Determining the Degree of Polynomials
- Polynomial Regression in the Wild

5. Ridge and Lasso Regression
- Tackling Multicollinearity
- Balance Between Fit and Complexity
- Ridge vs. Lasso: A Comparative Analysis

6. Elastic Net Regression
- Combining L1 and L2 Penalties
- Parameters Selection and Optimization
- Application in High-Dimensional Data

7. Quantile Regression
- Percentiles in Regression Analysis
- Advantages Over Ordinary Least Squares
- Applications in Economics and Finance

8. Generalized Linear Models
- Expanding Beyond Normality
- Link Functions and Exponential Families
- Model Selection and Evaluation

9. Non-Linear and Non-Parametric Regression
- When Linearity Fails
- Kernel Methods and Splines
- Case Studies: Complex Data Patterns

10. Survival and Hazard Regression
- Time-to-Event Data Analysis
- Cox Proportional-Hazards Model
- Predictive Modeling in Healthcare

11. Mixed Models and Hierarchical Data
- Random Effects and Nested Structures
- Application in Longitudinal Studies
- Software for Mixed Model Analysis

12. Machine Learning and Regression
- Regression Trees and Forests
- Support Vector Regression
- Neural Networks and Deep Learning