Linear Models

  1. Simple Linear Regression
    1. The Simple Linear Regression Model
      1. Model Formulation
        1. Components of the Model
          1. Notation and Terminology
          2. The Error Term
            1. Definition and Role
              1. Sources of Error
              2. Assumptions of the Error Term
                1. Zero Mean
                  1. Constant Variance
                    1. Independence
                      1. Normality
                    2. Estimating Model Parameters
                      1. The Principle of Least Squares
                        1. Minimizing the Sum of Squared Errors
                          1. Geometric Interpretation
                          2. Ordinary Least Squares Estimation
                            1. OLS Objective Function
                              1. Steps in OLS Estimation
                              2. Derivation of OLS Estimators
                                1. Formula for Slope Estimator
                                  1. Formula for Intercept Estimator
                                    1. Properties of Estimators
                                  2. Interpreting Model Coefficients
                                    1. Interpretation of the Intercept
                                      1. Meaning in Context
                                        1. Limitations of Interpretation
                                        2. Interpretation of the Slope
                                          1. Change in Y per Unit Change in X
                                            1. Practical Examples
                                          2. Assessing Model Fit
                                            1. Residuals
                                              1. Definition of Residuals
                                                1. Calculating Residuals
                                                  1. Properties of Residuals
                                                  2. Sum of Squares Decomposition
                                                    1. Residual Sum of Squares
                                                      1. Total Sum of Squares
                                                        1. Regression Sum of Squares
                                                        2. Coefficient of Determination
                                                          1. Formula for R-squared
                                                            1. Interpretation of R-squared
                                                              1. Limitations of R-squared
                                                              2. Residual Standard Error
                                                                1. Calculation of RSE
                                                                  1. Interpretation of RSE

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                                                              1. Introduction to Linear Relationships

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                                                              3. Inference in Simple Linear Regression