Biostatistics

12.

Correlation and Simple Regression

12.1.

Correlation Analysis

12.1.1.

Pearson Correlation Coefficient

12.1.1.1.

Definition and Calculation

12.1.1.2.

Assumptions and Limitations

12.1.1.3.

Interpretation Guidelines

12.1.1.4.

Significance Testing

12.1.2.

Spearman Rank Correlation

12.1.2.1.

Definition and Calculation

12.1.2.2.

12.1.2.3.

Comparison to Pearson

12.1.3.

Correlation vs Causation

12.1.3.1.

Common Misconceptions

12.1.3.2.

Third Variable Problem

12.1.3.3.

Temporal Relationships

12.1.4.

Factors Affecting Correlation

12.1.4.1.

Outliers and Influential Points

12.1.4.2.

Restriction of Range

12.1.4.3.

Non-Linear Relationships

12.2.

Simple Linear Regression

12.2.1.

Model Specification

12.2.1.1.

Linear Relationship Assumption

12.2.1.2.

Regression Equation

12.2.1.3.

Parameters and Interpretation

12.2.2.

Least Squares Estimation

12.2.2.1.

Minimizing Sum of Squared Errors

12.2.2.2.

Normal Equations

12.2.2.3.

Properties of Estimates

12.2.3.

Model Assessment

12.2.3.1.

Coefficient of Determination (R²)

12.2.3.2.

Residual Standard Error

12.2.3.3.

Standard Errors of Coefficients

12.2.4.

Inference for Regression

12.2.4.1.

Hypothesis Tests for Slope

12.2.4.2.

Confidence Intervals for Coefficients

12.2.4.3.

Prediction Intervals

12.2.5.

Assumptions and Diagnostics

12.2.5.1.

12.2.5.2.

12.2.5.3.

Homoscedasticity

12.2.5.4.

Normality of Residuals

12.2.5.5.

Residual Analysis

12.2.5.5.1.

12.2.5.5.2.

Normal Probability Plots

12.2.5.5.3.

Identifying Outliers

12.2.5.5.4.

Influential Observations

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11. Analysis of Variance (ANOVA)

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13. Multiple Regression Analysis