Linear Models

  1. Multiple Linear Regression
    1. The Multiple Linear Regression Model
      1. Model Formulation with Multiple Predictors
        1. General Form
          1. Notation for Multiple Predictors
          2. Matrix Notation for MLR
            1. Design Matrix
              1. Parameter Vector
                1. Error Vector
              2. Estimation in Multiple Linear Regression
                1. OLS Estimation in Matrix Form
                  1. Matrix Algebra for OLS
                    1. Solution for Parameter Vector
                    2. Fitted Values and Residuals in Matrix Form
                      1. Calculating Fitted Values
                        1. Calculating Residuals
                      2. Interpretation of Coefficients
                        1. Partial Effects
                          1. Holding Other Variables Constant
                            1. Interpretation in Context
                            2. Comparing Magnitudes of Coefficients
                              1. Standardized Coefficients
                                1. Cautions in Interpretation
                              2. Assessing Overall Model Significance
                                1. The F-statistic
                                  1. Formula for F-statistic
                                    1. Interpretation
                                    2. The F-test for Overall Significance
                                      1. Hypotheses for F-test
                                        1. Decision Criteria
                                        2. Relationship between F-statistic and t-statistics
                                        3. Measures of Fit in Multiple Regression
                                          1. R-squared in Multiple Regression
                                            1. Calculation
                                              1. Interpretation
                                              2. The Problem of Increasing R-squared
                                                1. Overfitting
                                                  1. Spurious Improvement
                                                  2. Adjusted R-squared
                                                    1. Formula for Adjusted R-squared
                                                      1. Advantages over R-squared

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                                                  3. Inference in Simple Linear Regression

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                                                  5. Model Diagnostics and Assumption Checking