Linear Models

  1. Model Building and Variable Selection
    1. Handling Categorical Predictors
      1. Dummy Variables
        1. Creating Dummy Variables
          1. Coding Schemes
          2. Choosing a Reference Category
            1. Interpretation of Reference Category
              1. Impact on Coefficient Interpretation
              2. Interpretation of Coefficients for Dummy Variables
                1. Comparing Categories
                  1. Cautions in Interpretation
                2. Interaction Terms
                  1. Concept of Interaction
                    1. Definition and Examples
                      1. Synergy and Antagonism
                      2. Modeling Interactions between Predictors
                        1. Creating Interaction Terms
                          1. Centering Predictors
                          2. Interpretation of Models with Interactions
                            1. Main Effects vs. Interaction Effects
                              1. Visualization of Interactions
                            2. Non-linear Relationships
                              1. Polynomial Regression
                                1. Adding Polynomial Terms
                                  1. Interpretation of Polynomial Coefficients
                                  2. Transformations
                                    1. Log Transformation
                                      1. Reciprocal Transformation
                                        1. Box-Cox Transformation
                                      2. Addressing Multicollinearity
                                        1. Definition and Consequences
                                          1. Impact on Coefficient Estimates
                                            1. Impact on Model Stability
                                            2. Detection of Multicollinearity
                                              1. Correlation Matrix
                                                1. Variance Inflation Factor
                                                  1. Condition Number
                                                  2. Mitigation Strategies
                                                    1. Variable Removal
                                                      1. Variable Combination
                                                        1. Ridge Regression
                                                          1. Principal Component Regression
                                                        2. Variable Selection Methods
                                                          1. Best Subset Selection
                                                            1. Exhaustive Search
                                                              1. Computational Considerations
                                                              2. Stepwise Selection Methods
                                                                1. Forward Selection
                                                                  1. Backward Elimination
                                                                    1. Bidirectional Selection
                                                                  2. Model Selection Criteria
                                                                    1. Mallows' Cp
                                                                      1. Calculation and Interpretation
                                                                      2. Information Criteria
                                                                        1. Akaike Information Criterion
                                                                          1. Bayesian Information Criterion
                                                                          2. Cross-Validation
                                                                            1. k-Fold Cross-Validation
                                                                              1. Leave-One-Out Cross-Validation
                                                                                1. Interpreting Cross-Validation Results

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                                                                            5. Model Diagnostics and Assumption Checking

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                                                                            7. Extensions and Advanced Topics