Statistics

  1. Correlation and Regression
    1. Correlation Analysis
      1. Purpose
        1. Measuring Linear Relationships
          1. Strength and Direction
          2. Pearson Correlation Coefficient (r)
            1. Formula
              1. Calculation
                1. Interpretation of r Values
                  1. Perfect Correlation
                    1. Strong Correlation
                      1. Moderate Correlation
                        1. Weak Correlation
                          1. No Correlation
                        2. Properties of Correlation
                          1. Unitless Measure
                            1. Symmetry
                              1. Linear Relationships Only
                              2. Interpreting Correlation
                                1. Strength and Direction
                                  1. Scatter Plot Analysis
                                    1. Linear Patterns
                                      1. Curved Patterns
                                        1. Outlier Effects
                                      2. Correlation vs. Causation
                                        1. Third Variable Problem
                                          1. Spurious Correlation
                                            1. Confounding Variables
                                              1. Establishing Causation
                                              2. Other Correlation Measures
                                                1. Spearman's Rank Correlation
                                                  1. Point-Biserial Correlation
                                                2. Simple Linear Regression
                                                  1. Purpose
                                                    1. Prediction
                                                      1. Modeling Relationships
                                                      2. The Regression Model
                                                        1. Population Regression Line
                                                          1. Sample Regression Line
                                                            1. Dependent and Independent Variables
                                                              1. Error Term
                                                              2. The Method of Least Squares
                                                                1. Minimizing Sum of Squared Errors
                                                                  1. Calculation of Slope and Intercept
                                                                    1. Normal Equations
                                                                    2. The Equation of the Regression Line
                                                                      1. Slope Interpretation
                                                                        1. Y-intercept Interpretation
                                                                          1. Prediction Equation
                                                                          2. Assumptions of Linear Regression
                                                                            1. Linearity
                                                                              1. Scatter Plot Examination
                                                                                1. Residual Plots
                                                                                2. Independence
                                                                                  1. Random Sampling
                                                                                    1. No Autocorrelation
                                                                                    2. Homoscedasticity
                                                                                      1. Constant Variance
                                                                                        1. Residual Plot Analysis
                                                                                        2. Normality of Residuals
                                                                                          1. Normal Probability Plots
                                                                                            1. Histogram of Residuals
                                                                                          2. Coefficient of Determination (R²)
                                                                                            1. Interpretation
                                                                                              1. Explained vs. Unexplained Variation
                                                                                                1. Limitations
                                                                                                2. Standard Error of the Estimate
                                                                                                  1. Calculation
                                                                                                    1. Interpretation
                                                                                                      1. Prediction Accuracy
                                                                                                      2. Residual Analysis
                                                                                                        1. Residual Calculation
                                                                                                          1. Residual Plots
                                                                                                            1. Outlier Detection
                                                                                                              1. Influential Points
                                                                                                              2. Inference about the Slope
                                                                                                                1. Hypothesis Testing
                                                                                                                  1. Testing Significance
                                                                                                                    1. t-test for Slope
                                                                                                                    2. Confidence Intervals
                                                                                                                      1. Slope Confidence Interval
                                                                                                                        1. Mean Response Confidence Interval
                                                                                                                          1. Prediction Intervals
                                                                                                                      2. Multiple Linear Regression
                                                                                                                        1. Purpose
                                                                                                                          1. Multiple Predictors
                                                                                                                            1. Complex Relationships
                                                                                                                            2. The Multiple Regression Model
                                                                                                                              1. Model Specification
                                                                                                                                1. Matrix Notation
                                                                                                                                  1. Interpretation of Coefficients
                                                                                                                                    1. Partial Slopes
                                                                                                                                      1. Holding Other Variables Constant
                                                                                                                                    2. Assumptions
                                                                                                                                      1. Same as Simple Regression
                                                                                                                                        1. No Perfect Multicollinearity
                                                                                                                                        2. Model Estimation
                                                                                                                                          1. Least Squares Method
                                                                                                                                            1. Normal Equations
                                                                                                                                            2. Model Evaluation
                                                                                                                                              1. R-squared
                                                                                                                                                1. Adjusted R-squared
                                                                                                                                                  1. Purpose
                                                                                                                                                    1. Penalty for Additional Variables
                                                                                                                                                      1. Interpretation
                                                                                                                                                      2. F-test for Overall Significance
                                                                                                                                                      3. Individual Coefficient Testing
                                                                                                                                                        1. t-tests for Each Coefficient
                                                                                                                                                          1. Confidence Intervals
                                                                                                                                                          2. Multicollinearity
                                                                                                                                                            1. Detection
                                                                                                                                                              1. Correlation Matrix
                                                                                                                                                                1. Variance Inflation Factor (VIF)
                                                                                                                                                                  1. Tolerance
                                                                                                                                                                  2. Consequences
                                                                                                                                                                    1. Remedies
                                                                                                                                                                      1. Variable Selection
                                                                                                                                                                        1. Ridge Regression
                                                                                                                                                                      2. Model Building and Selection
                                                                                                                                                                        1. Forward Selection
                                                                                                                                                                          1. Backward Elimination
                                                                                                                                                                            1. Stepwise Regression
                                                                                                                                                                              1. Model Comparison Criteria
                                                                                                                                                                                1. AIC (Akaike Information Criterion)
                                                                                                                                                                                  1. BIC (Bayesian Information Criterion)
                                                                                                                                                                                    1. Adjusted R-squared

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                                                                                                                                                                              9. Analysis of Variance (ANOVA)

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                                                                                                                                                                              11. Chi-Square Tests