Linear Models

  1. Inference in Simple Linear Regression
    1. Properties of OLS Estimators
      1. Unbiasedness
        1. Definition of Unbiasedness
          1. Conditions for Unbiasedness
          2. Variance of Estimators
            1. Formula for Variance of Slope
              1. Formula for Variance of Intercept
                1. Factors Affecting Variance
                2. Gauss-Markov Theorem
                  1. Statement of the Theorem
                    1. Best Linear Unbiased Estimators
                  2. Hypothesis Testing for Coefficients
                    1. Null and Alternative Hypotheses
                      1. Formulating Hypotheses for Slope
                        1. Formulating Hypotheses for Intercept
                          1. One-sided vs. Two-sided Tests
                          2. The t-statistic
                            1. Formula for t-statistic
                              1. Degrees of Freedom
                                1. t-distribution Properties
                                2. p-values and Statistical Significance
                                  1. Definition of p-value
                                    1. Interpreting p-values
                                      1. Significance Levels
                                    2. Confidence Intervals
                                      1. Confidence Interval for the Slope
                                        1. Formula for Confidence Interval
                                          1. Interpretation
                                          2. Confidence Interval for the Intercept
                                            1. Formula for Confidence Interval
                                              1. Interpretation
                                            2. Prediction and Prediction Intervals
                                              1. Point Prediction for New Observations
                                                1. Confidence Interval for Mean Response
                                                  1. Calculation and Interpretation
                                                  2. Prediction Interval for Individual Response
                                                    1. Calculation and Interpretation
                                                    2. Distinguishing Between Confidence and Prediction Intervals

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                                                  2. Simple Linear Regression

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                                                  4. Multiple Linear Regression