Quantitative Methods

  1. Correlation and Regression Analysis
    1. Correlation Analysis
      1. Bivariate Relationships
        1. Linear Relationships
          1. Non-linear Relationships
            1. Strength and Direction
            2. Pearson Correlation Coefficient
              1. Calculation
                1. Assumptions
                  1. Interpretation
                    1. Significance Testing
                    2. Spearman's Rank Correlation
                      1. Calculation
                        1. When to Use
                          1. Interpretation
                            1. Comparison with Pearson
                            2. Other Correlation Measures
                              1. Kendall's Tau
                                1. Point-Biserial Correlation
                                  1. Phi Coefficient
                                  2. Partial Correlation
                                    1. Calculation
                                    2. Correlation vs Causation
                                      1. Distinguishing Correlation from Causation
                                        1. Third Variable Problem
                                          1. Spurious Correlations
                                        2. Simple Linear Regression
                                          1. Model Specification
                                            1. Linear Relationship Assumption
                                              1. Model Equation
                                                1. Parameters
                                                2. Parameter Estimation
                                                  1. Least Squares Method
                                                    1. Normal Equations
                                                      1. Properties of Estimators
                                                      2. Model Interpretation
                                                        1. Slope Interpretation
                                                          1. Intercept Interpretation
                                                            1. Prediction
                                                            2. Goodness of Fit
                                                              1. Coefficient of Determination
                                                                1. Residual Analysis
                                                                  1. Standard Error of Estimate
                                                                  2. Inference in Regression
                                                                    1. Assumptions
                                                                      1. Linearity
                                                                        1. Independence
                                                                          1. Homoscedasticity
                                                                            1. Normality
                                                                            2. Hypothesis Tests
                                                                              1. Test for Slope
                                                                                1. Test for Intercept
                                                                                2. Confidence Intervals
                                                                                  1. For Parameters
                                                                                    1. For Predictions
                                                                                  2. Regression Diagnostics
                                                                                    1. Residual Plots
                                                                                      1. Normal Probability Plots
                                                                                        1. Outlier Detection
                                                                                          1. Influential Observations
                                                                                            1. Leverage
                                                                                              1. Cook's Distance
                                                                                                1. DFBETAS
                                                                                            2. Multiple Linear Regression
                                                                                              1. Model Specification
                                                                                                1. Multiple Predictor Variables
                                                                                                  1. Model Equation
                                                                                                    1. Matrix Notation
                                                                                                    2. Parameter Estimation
                                                                                                      1. Least Squares in Matrix Form
                                                                                                        1. Properties of Estimators
                                                                                                        2. Model Interpretation
                                                                                                          1. Partial Regression Coefficients
                                                                                                            1. Holding Other Variables Constant
                                                                                                            2. Goodness of Fit
                                                                                                              1. Multiple R-squared
                                                                                                                1. Adjusted R-squared
                                                                                                                  1. F-test for Overall Significance
                                                                                                                  2. Variable Selection
                                                                                                                    1. Forward Selection
                                                                                                                      1. Backward Elimination
                                                                                                                        1. Stepwise Selection
                                                                                                                          1. Best Subsets Regression
                                                                                                                          2. Multicollinearity
                                                                                                                            1. Detection
                                                                                                                              1. Correlation Matrix
                                                                                                                                1. Variance Inflation Factor
                                                                                                                                  1. Condition Index
                                                                                                                                  2. Consequences
                                                                                                                                    1. Remedies
                                                                                                                                      1. Ridge Regression
                                                                                                                                        1. Principal Components Regression
                                                                                                                                      2. Model Diagnostics
                                                                                                                                        1. Residual Analysis
                                                                                                                                          1. Assumption Checking
                                                                                                                                            1. Outlier and Influence Detection
                                                                                                                                          2. Logistic Regression
                                                                                                                                            1. Binary Logistic Regression
                                                                                                                                              1. Logistic Function
                                                                                                                                                1. Odds and Log-odds
                                                                                                                                                  1. Model Equation
                                                                                                                                                  2. Parameter Estimation
                                                                                                                                                    1. Maximum Likelihood Estimation
                                                                                                                                                      1. Iterative Procedures
                                                                                                                                                      2. Model Interpretation
                                                                                                                                                        1. Odds Ratios
                                                                                                                                                          1. Probability Interpretation
                                                                                                                                                            1. Marginal Effects
                                                                                                                                                            2. Model Assessment
                                                                                                                                                              1. Likelihood Ratio Test
                                                                                                                                                                1. Wald Test
                                                                                                                                                                  1. Goodness of Fit Tests
                                                                                                                                                                    1. Hosmer-Lemeshow Test
                                                                                                                                                                      1. Deviance
                                                                                                                                                                    2. Classification
                                                                                                                                                                      1. Predicted Probabilities
                                                                                                                                                                        1. Classification Rules
                                                                                                                                                                          1. Confusion Matrix
                                                                                                                                                                            1. ROC Curves
                                                                                                                                                                            2. Extensions
                                                                                                                                                                              1. Multinomial Logistic Regression
                                                                                                                                                                                1. Ordinal Logistic Regression

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                                                                                                                                                                            4. Advanced Statistical Methods