Statistical Inference

  1. Simple Linear Regression Inference
    1. The Simple Linear Regression Model
      1. Model Specification
        1. Population Regression Line
          1. Random Error Component
            1. Assumptions of the Model
              1. Linearity
                1. Independence
                  1. Homoscedasticity
                    1. Normality of Errors
                  2. Least Squares Estimation
                    1. Principle of Least Squares
                      1. Estimating Slope and Intercept
                        1. Properties of Least Squares Estimators
                          1. Residuals and Fitted Values
                          2. Sampling Distributions of Estimators
                            1. Distribution of Slope Estimator
                              1. Distribution of Intercept Estimator
                                1. Standard Errors
                                  1. Correlation Between Estimators
                                  2. Inference for Regression Coefficients
                                    1. Inference for the Slope
                                      1. Confidence Interval for Slope
                                        1. Hypothesis Test for Slope
                                          1. Testing for No Linear Relationship
                                          2. Inference for the Intercept
                                            1. Confidence Interval for Intercept
                                              1. Hypothesis Test for Intercept
                                                1. Practical Interpretation
                                              2. Inference for Correlation
                                                1. Population Correlation Coefficient
                                                  1. Sample Correlation Coefficient
                                                    1. Testing for Linear Association
                                                      1. Confidence Interval for Correlation
                                                        1. Fisher's Z-Transformation
                                                        2. Prediction and Confidence Intervals
                                                          1. Confidence Interval for Mean Response
                                                            1. Formula and Interpretation
                                                              1. Confidence Band
                                                              2. Prediction Interval for Individual Response
                                                                1. Formula and Interpretation
                                                                  1. Prediction vs Confidence Intervals
                                                                  2. Extrapolation Concerns
                                                                  3. Model Adequacy and Diagnostics
                                                                    1. Residual Analysis
                                                                      1. Checking Model Assumptions
                                                                        1. Outliers and Influential Points
                                                                          1. Goodness of Fit Measures
                                                                            1. Coefficient of Determination
                                                                              1. Standard Error of Regression

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                                                                          9. Analysis of Variance (ANOVA)

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                                                                          11. Introduction to Bayesian Inference