Social Statistics

12.

Bivariate Correlation and Regression

12.1.

Correlation Analysis

12.1.1.

Concept of Correlation

12.1.2.

12.1.2.1.

Creating and Interpreting Scatterplots

12.1.2.2.

Identifying Patterns and Outliers

12.1.2.3.

Linear vs. Non-linear Relationships

12.1.3.

Pearson's Correlation Coefficient

12.1.3.1.

12.1.3.2.

Calculation Methods

12.1.3.3.

Interpretation of r Values

12.1.3.4.

Statistical Significance Testing

12.1.3.5.

Confidence Intervals for Correlations

12.1.4.

Coefficient of Determination

12.1.4.1.

r-squared Interpretation

12.1.4.2.

Explained vs. Unexplained Variance

12.1.5.

Spearman's Rank Correlation

12.1.5.1.

12.1.5.2.

Calculation and Interpretation

12.1.6.

Point-Biserial Correlation

12.1.6.1.

Correlation with Dichotomous Variables

12.1.7.

Partial Correlation

12.1.7.1.

Controlling for Third Variables

12.1.8.

Correlation vs. Causation

12.1.8.1.

Common Misconceptions

12.1.8.2.

Third Variable Problem

12.1.8.3.

Spurious Correlations

12.2.

Simple Linear Regression

12.2.1.

The Regression Model

12.2.1.1.

Population vs. Sample Regression

12.2.1.2.

Linear Relationship Assumption

12.2.2.

Least Squares Method

12.2.2.1.

Minimizing Sum of Squared Errors

12.2.2.2.

Calculating Slope and Intercept

12.2.3.

The Regression Equation

12.2.3.1.

Interpreting the Intercept

12.2.3.2.

Interpreting the Slope

12.2.3.3.

Making Predictions

12.2.4.

Assessing Model Fit

12.2.4.1.

12.2.4.2.

Standard Error of Estimate

12.2.4.3.

Residual Analysis

12.2.5.

Assumptions of Linear Regression

12.2.5.1.

12.2.5.2.

12.2.5.3.

Homoscedasticity

12.2.5.4.

Normality of Residuals

12.2.6.

Inference in Regression

12.2.6.1.

Testing Significance of Slope

12.2.6.2.

Confidence Intervals for Parameters

12.2.6.3.

Prediction Intervals

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13. Multivariate Regression