Regression Analysis

  1. Multiple Linear Regression
    1. The Multiple Linear Regression Model
      1. Mathematical Formulation
        1. Matrix Notation and Representation
          1. Assumptions in Multiple Regression
            1. Extension from Simple Linear Regression
            2. OLS Estimation in Multiple Regression
              1. Matrix Formulation of OLS
                1. Normal Equations in Matrix Form
                  1. Estimation Procedure
                    1. Computational Aspects
                    2. Interpretation of Coefficients
                      1. Partial Regression Coefficients
                        1. Holding Other Variables Constant
                          1. Marginal Effects and Ceteris Paribus
                            1. Economic and Practical Interpretation
                            2. Assumptions of Multiple Linear Regression
                              1. Linear Relationship
                                1. Independence of Observations
                                  1. Homoscedasticity
                                    1. No Perfect Multicollinearity
                                      1. Normality of Residuals
                                        1. Additional Considerations in MLR
                                        2. Goodness-of-Fit in Multiple Regression
                                          1. Multiple R-squared
                                            1. Calculation and Interpretation
                                              1. Limitations of R-squared
                                              2. Adjusted R-squared
                                                1. Formula and Calculation
                                                  1. Penalty for Additional Variables
                                                    1. Comparison with R-squared
                                                    2. Standard Error of Regression
                                                    3. Statistical Inference in Multiple Regression
                                                      1. Individual Coefficient Testing
                                                        1. t-tests for Individual Coefficients
                                                          1. Standard Errors in Multiple Regression
                                                            1. Confidence Intervals for Coefficients
                                                            2. Joint Hypothesis Testing
                                                              1. F-test for Overall Significance
                                                                1. Testing Multiple Linear Restrictions
                                                                  1. Restricted vs Unrestricted Models
                                                                    1. F-statistic Calculation and Interpretation
                                                                    2. Testing Subsets of Coefficients
                                                                    3. The Gauss-Markov Theorem
                                                                      1. Statement of the Theorem
                                                                        1. BLUE Property
                                                                          1. Conditions for BLUE
                                                                            1. Implications for OLS Estimators
                                                                              1. Efficiency of OLS

                                                                            Previous

                                                                            2. Simple Linear Regression

                                                                            Go to top

                                                                            Next

                                                                            4. Model Specification and Diagnostics