Quantitative Methods

3.

Correlation and Regression Analysis

3.1.

Correlation Analysis

3.1.1.

Bivariate Relationships

3.1.1.1.

Linear Relationships

3.1.1.2.

Non-linear Relationships

3.1.1.3.

Strength and Direction

3.1.2.

Pearson Correlation Coefficient

3.1.2.1.

3.1.2.2.

3.1.2.3.

3.1.2.4.

Significance Testing

3.1.3.

Spearman's Rank Correlation

3.1.3.1.

3.1.3.2.

3.1.3.3.

3.1.3.4.

Comparison with Pearson

3.1.4.

Other Correlation Measures

3.1.4.1.

3.1.4.2.

Point-Biserial Correlation

3.1.4.3.

Phi Coefficient

3.1.5.

Partial Correlation

3.1.5.1.

3.1.6.

Correlation vs Causation

3.1.6.1.

Distinguishing Correlation from Causation

3.1.6.2.

Third Variable Problem

3.1.6.3.

Spurious Correlations

3.2.

Simple Linear Regression

3.2.1.

Model Specification

3.2.1.1.

Linear Relationship Assumption

3.2.1.2.

3.2.1.3.

3.2.2.

Parameter Estimation

3.2.2.1.

Least Squares Method

3.2.2.2.

Normal Equations

3.2.2.3.

Properties of Estimators

3.2.3.

Model Interpretation

3.2.3.1.

Slope Interpretation

3.2.3.2.

Intercept Interpretation

3.2.3.3.

3.2.4.

Goodness of Fit

3.2.4.1.

Coefficient of Determination

3.2.4.2.

Residual Analysis

3.2.4.3.

Standard Error of Estimate

3.2.5.

Inference in Regression

3.2.5.1.

3.2.5.1.1.

3.2.5.1.2.

3.2.5.1.3.

Homoscedasticity

3.2.5.1.4.

3.2.5.2.

Hypothesis Tests

3.2.5.2.1.

3.2.5.2.2.

Test for Intercept

3.2.5.3.

Confidence Intervals

3.2.5.3.1.

3.2.5.3.2.

For Predictions

3.2.6.

Regression Diagnostics

3.2.6.1.

3.2.6.2.

Normal Probability Plots

3.2.6.3.

Outlier Detection

3.2.6.4.

Influential Observations

3.2.6.4.1.

3.2.6.4.2.

Cook's Distance

3.2.6.4.3.

3.3.

Multiple Linear Regression

3.3.1.

Model Specification

3.3.1.1.

Multiple Predictor Variables

3.3.1.2.

3.3.1.3.

Matrix Notation

3.3.2.

Parameter Estimation

3.3.2.1.

Least Squares in Matrix Form

3.3.2.2.

Properties of Estimators

3.3.3.

Model Interpretation

3.3.3.1.

Partial Regression Coefficients

3.3.3.2.

Holding Other Variables Constant

3.3.4.

Goodness of Fit

3.3.4.1.

Multiple R-squared

3.3.4.2.

Adjusted R-squared

3.3.4.3.

F-test for Overall Significance

3.3.5.

Variable Selection

3.3.5.1.

Forward Selection

3.3.5.2.

Backward Elimination

3.3.5.3.

Stepwise Selection

3.3.5.4.

Best Subsets Regression

3.3.6.

Multicollinearity

3.3.6.1.

3.3.6.1.1.

Correlation Matrix

3.3.6.1.2.

Variance Inflation Factor

3.3.6.1.3.

Condition Index

3.3.6.2.

3.3.6.3.

3.3.6.3.1.

Ridge Regression

3.3.6.3.2.

Principal Components Regression

3.3.7.

Model Diagnostics

3.3.7.1.

Residual Analysis

3.3.7.2.

Assumption Checking

3.3.7.3.

Outlier and Influence Detection

3.4.

Logistic Regression

3.4.1.

Binary Logistic Regression

3.4.1.1.

Logistic Function

3.4.1.2.

Odds and Log-odds

3.4.1.3.

3.4.2.

Parameter Estimation

3.4.2.1.

Maximum Likelihood Estimation

3.4.2.2.

Iterative Procedures

3.4.3.

Model Interpretation

3.4.3.1.

3.4.3.2.

Probability Interpretation

3.4.3.3.

Marginal Effects

3.4.4.

Model Assessment

3.4.4.1.

Likelihood Ratio Test

3.4.4.2.

3.4.4.3.

Goodness of Fit Tests

3.4.4.3.1.

Hosmer-Lemeshow Test

3.4.4.3.2.

3.4.5.

3.4.5.1.

Predicted Probabilities

3.4.5.2.

Classification Rules

3.4.5.3.

Confusion Matrix

3.4.5.4.

3.4.6.

3.4.6.1.

Multinomial Logistic Regression

3.4.6.2.

Ordinal Logistic Regression

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