Index

A

ANOVA (Analysis of Variance) — Ch. 3: Model Fit: R², Correlation, and ANOVA

Authoritarianism — Ch. 5: Dummy Variables and Categorical Predictors

Autocorrelation (see Independent errors) — Ch. 6: Gauss-Markov Assumptions

B

Best Linear Unbiased Estimator (BLUE) — Ch. 2: The Gauss-Markov Theorem

Bias (see Unbiasedness) — Ch. 2: Unbiasedness

Breusch-Pagan test — Ch. 6: Formal Tests for Heteroskedasticity

C

Causation vs. correlation — Ch. 1: Important Considerations

Cholesky decomposition — Ch. 6: Modeling Variation (rho decomposition)

Coefficient of determination (see R-squared) — Ch. 3: R²: The Coefficient of Determination

Coefficients, interpretation of — Ch. 1: Anatomy of lm

Coefficients, multiple regression — Ch. 5: Interpretation of Coefficients in Multiple Regression

Collinearity (see Multicollinearity) — Ch. 5: From Bivariate to Multiple Regression

Confidence intervals — Ch. 1: confint() — Confidence Intervals

Confounding — Ch. 1: Important Considerations

Cook-Weisberg test — Ch. 6: Formal Tests for Heteroskedasticity

Cook’s distance — Ch. 1: Plot 4: Influence

Correlation coefficient — Ch. 3, 4: The Relationship Between R² and Correlation; Similarity and Vector Products

Covariance — Ch. 2, 4: Gauss-Markov Assumptions; Covariance and Correlation

Covariance, vectors — Ch. 4: Similarity and Vector Products

Cronbach’s alpha — Ch. 5: Dummy Variables and Categorical Predictors

Cross product — Ch. 4: Looking Forward: The Cross Product

D

Data Generating Process (DGP) — Ch. 3: Data Generating Process (DGP)

Degrees of freedom — Ch. 1, 3: Components of lm; The F-statistic and ANOVA

Dependent variable — Ch. 1: Understanding Linear Regression

Deterministic vs. stochastic — Ch. 1: Deterministic versus Stochastic

Diagnostic plots — Ch. 1: Diagnostic Plots

Dot product (see Inner product) — Ch. 4: Similarity and Vector Products

dplyr (mutate, filter, select, group_by, summarize) — Ch. 6: Data and Setup (dplyr refresher callout)

Dummy variables — Ch. 5: Dummy Variables and Categorical Predictors

E

Endogenous variable — Ch. 1: Understanding Linear Regression

Error term — Ch. 1, 2: Types of Data; Gauss-Markov Assumptions

Euclidean distance — Ch. 4: The Norm of a Vector

Exogeneity assumption — Ch. 2: Gauss-Markov Assumptions

Exogenous variable — Ch. 1: Understanding Linear Regression

F

F-distribution — Ch. 3: The F-statistic and ANOVA

F-statistic — Ch. 3: The F-statistic and ANOVA

Fitted values — Ch. 1: Fitted Values ($fitted.values)

Frequency weights — Ch. 6: Common Weighting Schemes

G

Gauss-Markov assumptions — Ch. 2, 6: Gauss-Markov Assumptions; Recall the G-M Theorem

Gauss-Markov theorem — Ch. 2, 6: The Gauss-Markov Theorem; Recall the G-M Theorem

Generalized Least Squares (GLS) — Ch. 6: GLS/WLS

Gini index — Ch. 6: Data and Setup

glm() vs. gls() vs. lm() — Ch. 6: glm() vs. gls() vs. lm() (callout)

Goldfeld-Quandt test — Ch. 6: Formal Tests for Heteroskedasticity

H

Heteroskedasticity — Ch. 6: Heteroskedasticity and Weighted Least Squares

Heteroskedasticity, consequences of — Ch. 6: Building the Case / Consequences

Heteroskedasticity, detection — Ch. 6: Visual Diagnostics; Formal Tests

Heteroskedasticity, examples of — Ch. 6: When Does Heteroskedasticity Arise?

Homoskedasticity assumption — Ch. 2, 6: Gauss-Markov Assumptions; Recall the G-M Theorem

Horvitz-Thompson principle — Ch. 6: Common Weighting Schemes

I

Identity matrix — Ch. 4: Matrix Properties and Types

Independent errors assumption — Ch. 2: Gauss-Markov Assumptions

Independent variable — Ch. 1: Understanding Linear Regression

Inference — Ch. 5: Model Fit, Uncertainty, and Inference

Inner product — Ch. 4: The Inner Product

Institutional trust — Ch. 5: Dummy Variables and Categorical Predictors

Interaction effects — Ch. 5: Interaction effects

Intercept — Ch. 1: Deriving the OLS Estimator; Anatomy of lm

Intercept shifts (dummy variables) — Ch. 5: Intercept Shifts

Inverse probability of treatment weighting (IPTW) — Ch. 6: Common Weighting Schemes

Iteratively Reweighted Least Squares (IRLS) — Ch. 6: glm() vs. gls() vs. lm() (callout)

K

k weights (OLS) — Ch. 2: Properties of k_i

L

Law of cosines — Ch. 4: The Law of Cosines

Leverage — Ch. 1: Plot 4: Influence

Linear algebra — Ch. 4: Introduction; Vectors

Linear regression, assumptions — Ch. 2, 6: Gauss-Markov Assumptions; Recall the G-M Theorem

Linearity assumption — Ch. 2: Gauss-Markov Assumptions

lm() function — Ch. 1: lm; An Example with Spotify Data

lm() object components — Ch. 1: Anatomy of lm

M

Matrix algebra — Ch. 4: Matrices

Matrix multiplication — Ch. 4: Matrix Multiplication

Matrix, design (X) — Ch. 4: Matrices

Matrix, identity — Ch. 4: Matrix Properties and Types

Matrix, inverse — Ch. 4: Matrix Properties and Types

Matrix, symmetric — Ch. 4: Matrix Properties and Types

Matrix, transpose — Ch. 4: Matrix Properties and Types

Matrix, variance-covariance — Ch. 2, 6: Gauss-Markov Theorem; Recall the G-M Theorem

Mean centering — Ch. 6: Data and Setup (rescaling)

Mean squared error — Ch. 3: The F-statistic and ANOVA

Meta-analysis weights — Ch. 6: Common Weighting Schemes

Minimum variance — Ch. 2, 6: Minimum Variance; GLS/WLS

Model fit — Ch. 3: Model Fit and Prediction

Model specification assumption — Ch. 2: Gauss-Markov Assumptions

Monte Carlo simulation — Ch. 3: Data Generating Process (DGP)

Multicollinearity — Ch. 5: From Bivariate to Multiple Regression

Multiple regression — Ch. 5: From Bivariate to Multiple Regression

N

Norm of a vector — Ch. 4: The Norm of a Vector

Normal distribution — Ch. 1, 2: Types of Data; Gauss-Markov Assumptions

Normal Q-Q plot — Ch. 1: Plot 2: Normal Q-Q

Normality assumption — Ch. 2: Gauss-Markov Assumptions

O

OLS estimator, derivation (matrix) — Ch. 4, 5: Linear Algebra; Deriving Multiple Regression Coefficients

OLS estimator, derivation (scalar) — Ch. 1: Deriving the OLS Estimator

OLS estimator, properties — Ch. 2: Properties of k_i; Unbiasedness; Minimum Variance

Omega matrix — Ch. 6: GLS/WLS

Orthogonal vectors — Ch. 4: Similarity and Vector Products

Outer product — Ch. 4: Looking Forward: The Outer Product

P

p-value — Ch. 1: summary() — Comprehensive Model Summary

Partial effect — Ch. 5: Interpretation of Coefficients in Multiple Regression

Party identification — Ch. 5: Dummy Variables and Categorical Predictors

Population Regression Function (PRF) — Ch. 2, 3: SRF vs. PRF; Data Generating Process

Prediction — Ch. 1, 3: predict() — Generate Predictions; Estimation

Probability weights (survey) — Ch. 6: Common Weighting Schemes

Propensity score weights — Ch. 6: Common Weighting Schemes

R

R-squared — Ch. 3: R²: The Coefficient of Determination

R-squared, relationship to correlation — Ch. 3: The Relationship Between R² and Correlation

Reference category — Ch. 5: Dummy Variables and Categorical Predictors

Regression Sum of Squares (RegSS) — Ch. 3: Decomposing the Variance

Residual Sum of Squares (RSS) — Ch. 3: Decomposing the Variance

Residuals — Ch. 1: Residuals ($residuals)

Residuals vs. fitted plot — Ch. 1, 6: Diagnostic Plots; Visual Diagnostics

Rho matrix (GLS transformation) — Ch. 6: Modeling Variation (rho decomposition)

Robust standard errors (HC1, HC3) — Ch. 6: Robust Standard Errors

S

Sample Regression Function (SRF) — Ch. 2, 3: SRF vs. PRF; Data Generating Process

Sampling distribution — Ch. 2: Simulation: Demonstrating Unbiasedness

Sampling weights (see Probability weights) — Ch. 6: Common Weighting Schemes

Scale-Location plot — Ch. 1: Plot 3: Scale-Location

Slope coefficient — Ch. 1: Deriving the OLS Estimator

Spotify data example — Ch. 1: An Example with Spotify Data

Standard error — Ch. 1, 2: summary(); Gauss-Markov Assumptions

Sum of squared residuals — Ch. 1: Deriving the OLS Estimator

Survey weights — Ch. 6: Common Weighting Schemes

T

t-statistic — Ch. 1: summary() — Comprehensive Model Summary

Total Sum of Squares (TSS) — Ch. 3: Decomposing the Variance

Transpose — Ch. 4: Matrix Properties and Types

Trump-Harris margin (Arizona data) — Ch. 5, 6: Data and Setup; Predicted Margins

U

Unbiasedness — Ch. 2: Unbiasedness

Unbiasedness, simulation — Ch. 2: Simulation: Demonstrating Unbiasedness

V

Variance — Ch. 1, 2: Types of Data; Gauss-Markov Assumptions

Variance function estimation — Ch. 6: WLS Correction (variance function estimation)

Variance Inflation Factor (VIF) — Ch. 5, 6: Interpretation of Coefficients; Recall the G-M Theorem

Variance-covariance matrix — Ch. 2, 6: Gauss-Markov Theorem; Recall the G-M Theorem

Variance-covariance matrix (OLS) — Ch. 2, 6: Gauss-Markov Theorem; Recall the G-M Theorem

Vectors — Ch. 4: Vectors

W

Weighted Least Squares (WLS) — Ch. 6: GLS/WLS; Modeling Variation

Weighted Least Squares, implementation — Ch. 6: WLS Correction

Western States Survey (WSS) — Ch. 5: Dummy Variables and Categorical Predictors

White’s robust standard errors — Ch. 6: Robust Standard Errors

White’s test — Ch. 6: Formal Tests for Heteroskedasticity

Z

Zero mean error assumption — Ch. 2: Gauss-Markov Assumptions