Regression Analysis

  1. Model Specification and Diagnostics
    1. Model Specification Issues
      1. Omitted Variable Bias
        1. Causes and Sources
          1. Direction and Magnitude of Bias
            1. Consequences for Estimation
              1. Detection Methods
                1. Remedial Strategies
                2. Inclusion of Irrelevant Variables
                  1. Effects on Efficiency
                    1. Impact on Standard Errors
                      1. Model Parsimony Considerations
                      2. Functional Form Misspecification
                        1. Linear vs Nonlinear Relationships
                          1. Identifying Incorrect Functional Forms
                            1. Ramsey's RESET Test
                              1. Specification Testing
                            2. Violations of Classical Assumptions
                              1. Heteroscedasticity
                                1. Definition and Nature
                                  1. Consequences for OLS
                                    1. Unbiased but Inefficient Estimators
                                      1. Invalid Standard Errors
                                        1. Incorrect Inference
                                        2. Detection Methods
                                          1. Graphical Analysis
                                            1. Residual vs Fitted Plots
                                              1. Residual vs Predictor Plots
                                              2. Formal Statistical Tests
                                                1. Breusch-Pagan Test
                                                  1. White Test
                                                    1. Goldfeld-Quandt Test
                                                  2. Remedial Measures
                                                    1. Robust Standard Errors
                                                      1. White's Heteroscedasticity-Consistent Estimators
                                                        1. Weighted Least Squares
                                                          1. Transformation of Variables
                                                        2. Autocorrelation
                                                          1. Definition and Types
                                                            1. Consequences for OLS
                                                              1. Inefficient Estimators
                                                                1. Biased Standard Errors
                                                                  1. Invalid Test Statistics
                                                                  2. Detection Methods
                                                                    1. Graphical Analysis
                                                                      1. Time Series Plots of Residuals
                                                                        1. Autocorrelation Function Plots
                                                                        2. Statistical Tests
                                                                          1. Durbin-Watson Test
                                                                            1. Breusch-Godfrey LM Test
                                                                              1. Ljung-Box Test
                                                                            2. Remedial Measures
                                                                              1. Newey-West HAC Standard Errors
                                                                                1. Generalized Least Squares
                                                                                  1. Cochrane-Orcutt Procedure
                                                                                    1. Prais-Winsten Transformation
                                                                                  2. Multicollinearity
                                                                                    1. Perfect Multicollinearity
                                                                                      1. Near Multicollinearity
                                                                                        1. Consequences of Multicollinearity
                                                                                          1. Large Standard Errors
                                                                                            1. Unstable Coefficient Estimates
                                                                                              1. Difficulty in Interpretation
                                                                                              2. Detection Methods
                                                                                                1. High R-squared with Insignificant Coefficients
                                                                                                  1. High Pairwise Correlations
                                                                                                    1. Variance Inflation Factors
                                                                                                      1. Condition Number
                                                                                                        1. Eigenvalue Analysis
                                                                                                        2. Remedial Measures
                                                                                                          1. Variable Selection
                                                                                                            1. Ridge Regression
                                                                                                              1. Principal Component Analysis
                                                                                                                1. Combining Collinear Variables
                                                                                                            2. Residual Analysis and Diagnostics
                                                                                                              1. Properties of Residuals
                                                                                                                1. Standardized Residuals
                                                                                                                  1. Studentized Residuals
                                                                                                                    1. Checking Normality Assumptions
                                                                                                                      1. Histogram Analysis
                                                                                                                        1. Q-Q Plots
                                                                                                                          1. Shapiro-Wilk Test
                                                                                                                            1. Jarque-Bera Test
                                                                                                                              1. Kolmogorov-Smirnov Test
                                                                                                                              2. Outlier Detection
                                                                                                                                1. Definition of Outliers
                                                                                                                                  1. Leverage Points
                                                                                                                                    1. Influential Observations
                                                                                                                                      1. Studentized Deleted Residuals
                                                                                                                                      2. Influence Diagnostics
                                                                                                                                        1. Cook's Distance
                                                                                                                                          1. DFBETAS
                                                                                                                                            1. DFFITS
                                                                                                                                              1. Hat Matrix and Leverage Values

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                                                                                                                                          5. Advanced Linear Regression Topics