Adjusted R-squared (Ch 4)A modified version of R-squared that penalizes the inclusion of additional independent variables. Adjusted R² = 1 − (1 − R²)(n−1)/(n−k−1).
AIC (Akaike Information Criterion) (Ch 9)A model selection criterion that balances goodness-of-fit with model complexity. AIC = 2k − 2ln(L). Lower values indicate better models.
Alternative Hypothesis (H₁) (Ch 2)The hypothesis that contradicts the null hypothesis. It is what the researcher wants to prove or find evidence for.
ARIMA Model (Ch 9)Autoregressive Integrated Moving Average model. A general class of time series models with parameters p (AR order), d (differencing degree), and q (MA order).
Autocorrelation (Ch 7)Correlation between a variable and its lagged values. Also called serial correlation. Common in time series data.
Autoregressive (AR) Model (Ch 9)A time series model where the current value depends on its own past values: Yt = δ + φ₁Yt-1 + ⋯ + φpYt-p + εt.
B
Baseline Category (Ch 10)In multinomial models, the reference category against which all other categories are compared.
BIC (Bayesian Information Criterion) (Ch 9)A model selection criterion similar to AIC but with a stronger penalty for complexity. BIC = kln(n) − 2ln(L). Lower values indicate better models.
Binary Choice Model (Ch 10)A model where the dependent variable takes only two values (0/1), such as Logit or Probit.
Breusch-Pagan Test (Ch 7)A test for heteroskedasticity that regresses squared residuals on the independent variables. LM statistic follows χ²(k).
C
Causal Inference (Ch 8)The process of drawing conclusions about causal relationships from observational or experimental data.
Ceteris Paribus (Ch 4)"All else equal" — the assumption that all other relevant factors are held constant when interpreting the effect of one variable on another.
Chi-squared Distribution (χ²) (Ch 2)A distribution used in hypothesis tests for variance, goodness-of-fit, and in tests like the White test. Defined by degrees of freedom.
Coefficient (Ch 1)The estimated parameter in a regression model. It represents the change in the dependent variable for a one-unit change in the independent variable.
Confidence Interval (Ch 2)A range of values that, with a specified level of confidence (e.g., 95%), contains the true population parameter.
Control Group (Ch 8)In experimental and quasi-experimental designs, the group that does not receive the treatment. Used as a benchmark for comparison.
Correlation (Ch 2)A measure of the linear association between two variables, ranging from -1 to +1. Correlation does not imply causation.
Counterfactual (Ch 8)The hypothetical outcome that would have occurred in the absence of treatment. Central to causal inference.
Covariance (Ch 2)A measure of how two variables move together. Positive covariance means variables move in the same direction; negative means they move in opposite directions.
Cut Points / Thresholds (Ch 10)In ordered models, the boundaries between ordered categories. Estimated as part of the ordered Logit/Probit model.
D
Dependent Variable (Ch 1)The variable being explained or predicted in a regression model. Also called the explained variable, outcome variable, or Y variable.
Differencing (Ch 9)A transformation of a time series where each observation is replaced by the difference between consecutive observations (Yt − Yt-1). Used to achieve stationarity.
Difference-in-Differences (DiD) (Ch 8)A quasi-experimental method that compares the change in outcomes between a treatment group and a control group before and after an intervention.
Dummy Variable (Ch 6)A binary variable (0 or 1) that represents categorical data, such as gender, region, or treatment status.
Dummy Variable Trap (Ch 6)The problem of perfect collinearity that arises when all dummy variables for a categorical variable are included in the regression along with an intercept.
Durbin-Watson Test (Ch 7)A test for first-order serial correlation in the residuals of a regression model. DW ≈ 2(1 − ρ̂). Values near 2 indicate no autocorrelation.
E
Econometrics (Ch 1)The application of statistical methods to economic data for the purpose of testing economic theories and forecasting economic phenomena.
Endogeneity (Ch 7)A situation where an independent variable is correlated with the error term, often caused by omitted variables, measurement error, or simultaneity (reverse causality).
Error Term (u) (Ch 3)The unobserved factors that affect the dependent variable. Also called the disturbance term.
Exogeneity (Ch 7)The assumption that an instrument is uncorrelated with the error term. One of the two key conditions for a valid instrument (along with relevance).
Expected Value (Ch 2)The long-run average of a random variable. Also called the mean or expectation, denoted E[X] or μ.
F
F-Distribution (Ch 2)A distribution used for testing multiple hypotheses simultaneously (e.g., F-test for overall significance, or testing exclusion restrictions). Defined by two degrees of freedom (df₁, df₂).
Fixed Effects (FE) (Ch 8)A panel data method that allows each individual to have its own intercept (αi), capturing time-invariant unobserved heterogeneity. Also called the within estimator.
G
Gauss-Markov Theorem (Ch 3)Under assumptions of linearity, random sampling, sample variation, zero conditional mean, and homoskedasticity, OLS is the Best Linear Unbiased Estimator (BLUE).
Granger Causality (Ch 9)A statistical concept where past values of one variable help predict another variable. Does not imply true causality.
H
Hausman Test (Ch 8)A test to decide between Fixed Effects and Random Effects in panel data. A significant p-value suggests FE is appropriate.
Heteroskedasticity (Ch 7)A violation of the assumption of constant error variance. The variance of the error term varies across observations.
Homoskedasticity (Ch 3)The assumption that the error term has a constant variance: Var(u|X) = σ².
I
Impulse Response (Ch 9)In VAR models, the response of a variable to a one-time shock to another variable over time.
Independent Variable (Ch 1)The variable used to explain or predict the dependent variable. Also called the explanatory variable, predictor, or X variable.
Indicator Variable (Ch 6)A binary variable (0 or 1) that indicates the presence or absence of a characteristic. Also called a dummy variable.
Instrumental Variable (IV) (Ch 7)A variable used to address endogeneity by satisfying two conditions: relevance (correlated with the endogenous X) and exogeneity (uncorrelated with the error term).
Interaction Term (Ch 6)A variable created by multiplying two or more independent variables. Allows the effect of one variable to depend on the value of another.
Intercept (β₀) (Ch 3)The value of the dependent variable when all independent variables are zero. Also called the constant term.
J
Jarque-Bera Test (Ch 7)A test for normality of residuals based on skewness and kurtosis. Significant p-value indicates non-normality.
Joint Hypothesis (Ch 5)A hypothesis involving multiple coefficients simultaneously, e.g., β₁ = 0 and β₂ = 0. Tested using an F-test.
L
Latent Variable (Ch 10)An unobserved (latent) variable that underlies observed outcomes. In binary choice models, Y* represents utility or propensity.
Limited Dependent Variable (Ch 10)A dependent variable that is restricted in some way, such as binary (0/1), multinomial, ordered, or censored.
Logarithmic Model (Ch 6)A regression model where variables are transformed using logarithms. Common forms include log-log (elasticity), log-linear (semi-elasticity), and linear-log.
Logistic Function (Ch 10)The sigmoid function used in the Logit model: Λ(z) = ez / (1 + ez). Maps any real number to (0,1).
Logit Model (Ch 10)A binary choice model where the probability of Y = 1 is given by the logistic function: P(Y=1) = Λ(Xβ).
Longitudinal Data (Ch 8)Another name for panel data – data that follows the same individuals/units over time.
M
MAE (Mean Absolute Error) (Ch 9)A forecast evaluation metric: Σ|Yt − Ŷt| / n. Lower values indicate better forecasting accuracy.
Marginal Effect (Ch 10)In Logit/Probit models, the effect of a one-unit change in X on the predicted probability of Y = 1. Depends on where it is evaluated.
Maximum Likelihood (ML) (Ch 10)A method of estimating the parameters of a statistical model by maximizing the likelihood function. Used for Logit and Probit models.
Moving Average (MA) Model (Ch 9)A time series model where the current value depends on past errors: Yt = μ + εt + θ₁εt-1 + ⋯ + θqεt-q.
Multicollinearity (Ch 4)High correlation between independent variables, which can lead to large standard errors and imprecise coefficient estimates.
Multinomial Logit (Ch 10)An extension of binary Logit to multiple unordered categories. Estimates coefficients for each category relative to a baseline.
Multiple Regression (Ch 4)A regression model with more than one independent variable: Y = β₀ + β₁X₁ + β₂X₂ + ⋯ + βkXk + u.
N
Newey-West Standard Errors (Ch 7)Standard errors that are robust to both heteroskedasticity and autocorrelation. Also called HAC (Heteroskedasticity and Autocorrelation Consistent) standard errors.
Normal Distribution (Ch 2)A symmetric, bell-shaped distribution defined by its mean (μ) and variance (σ²). Often denoted N(μ, σ²).
Null Hypothesis (H₀) (Ch 2)The hypothesis that is assumed to be true (e.g., β = 0). The researcher tries to find evidence against it.
O
Odds Ratio (Ch 10)In Logit models, the odds ratio is eβ. It represents the change in odds for a one-unit increase in X. Odds = P/(1−P).
OLS (Ordinary Least Squares) (Ch 1)The standard estimation method in linear regression that minimizes the sum of squared residuals.
Omitted Variable Bias (Ch 4)Bias that arises when a relevant variable is omitted from the model. The omitted variable must be correlated with both the dependent variable and the included independent variable.
Ordered Logit (Ch 10)A model for ordered categorical outcomes (e.g., Poor/Good/Excellent). Estimates cut points between categories.
Ordered Probit (Ch 10)The Probit version of ordered models. Similar to ordered Logit but uses the normal CDF.
Overall Significance (Ch 5)A test of whether all slope coefficients are zero: H₀: β₁ = β₂ = ⋯ = βk = 0. Tested using an F-test.
P
p-value (Ch 1)The probability of observing a test statistic as extreme or more extreme than the one calculated, assuming the null hypothesis is true. A small p-value (e.g., <0.05) provides evidence against H₀.
Panel Data (Ch 8)Data that combines cross-sectional and time series dimensions, following the same individuals/units over multiple time periods.
Parallel Trends Assumption (Ch 8)The key assumption of DiD: in the absence of treatment, the treatment and control groups would have followed parallel trends over time.
Partialling Out (Ch 4)The interpretation of multiple regression coefficients as the effect of one variable after removing the effects of all other variables.
Perfect Collinearity (Ch 4)A situation where one independent variable is a perfect linear function of one or more other independent variables. Prevents OLS estimation.
Pooled OLS (Ch 8)A panel data method that ignores the panel structure and treats all observations as independent.
Probit Model (Ch 10)A binary choice model where the probability of Y = 1 is given by the standard normal CDF: P(Y=1) = Φ(Xβ).
Q
Quadratic Model (Ch 6)A regression model that includes a squared term (X²) to capture non-linear relationships. Y = β₀ + β₁X + β₂X² + u.
R
R-squared (R²) (Ch 1)The proportion of the variation in the dependent variable that is explained by the independent variables. R² = SSR/SST = 1 − SSE/SST.
Random Effects (RE) (Ch 8)A panel data method where individual-specific effects (νi) are treated as random and uncorrelated with the independent variables.
Random Variable (Ch 2)A variable whose value is determined by the outcome of a random phenomenon. Can be discrete or continuous.
Relevance (Ch 7)One of the two key conditions for a valid instrument: the instrument must be correlated with the endogenous independent variable.
Residual (û) (Ch 3)The difference between the observed and predicted values of the dependent variable: û = Y − Ŷ.
Restricted Model (Ch 5)A model that imposes restrictions on the coefficients, such as setting some coefficients to zero. Used in F-tests.
Robust Standard Errors (Ch 7)Standard errors that are corrected for heteroskedasticity (White standard errors). Also called heteroskedasticity-consistent standard errors.
S
Seasonality (Ch 9)A regular, repeating pattern in a time series that occurs within a year (e.g., Christmas sales, summer tourism).
Serial Correlation (Ch 7)Correlation between the error terms of a regression model across time periods. Also called autocorrelation.
Significance Level (α) (Ch 2)The probability of rejecting the null hypothesis when it is true (Type I error). Common values: 0.01, 0.05, 0.10.
Simple Linear Regression (Ch 3)A regression model with a single independent variable: Y = β₀ + β₁X + u.
Slope (β₁) (Ch 3)The change in the dependent variable for a one-unit change in the independent variable.
Standard Deviation (Ch 2)The square root of the variance. A measure of the spread of a distribution around its mean.
Standard Error (Ch 1)A measure of the sampling variability of an estimator. The standard deviation of the sampling distribution of a statistic.
Stationarity (Ch 9)A time series is stationary if its statistical properties (mean, variance, autocorrelation) do not change over time.
T
t-Distribution (Ch 2)A distribution used for hypothesis testing when the population variance is unknown. Similar to the normal distribution but with heavier tails. Defined by degrees of freedom.
t-statistic (Ch 1)The test statistic used to test the significance of an individual coefficient: t = β̂ / SE(β̂). Used to test H₀: β = 0.
Time Series (Ch 9)Data collected over time at regular intervals, such as daily, monthly, quarterly, or yearly.
Treatment Group (Ch 8)In experimental and quasi-experimental designs, the group that receives the treatment or intervention.
Trend (Ch 9)The long-term movement in a time series. Can be upward, downward, or flat.
Two-Stage Least Squares (2SLS) (Ch 7)An instrumental variables estimation method. Stage 1: Regress X on instruments. Stage 2: Regress Y on fitted X̂.
U
Unit Root (Ch 9)A characteristic of a non-stationary time series where shocks have a permanent effect. Tested using the Augmented Dickey-Fuller (ADF) test.
Unrestricted Model (Ch 5)A model with no restrictions on the coefficients. The full model used in F-tests.
V
Variance (Ch 2)A measure of the spread of a distribution around its mean: Var(X) = E[(X − μ)²].
Vector Autoregression (VAR) (Ch 9)A model where each variable is a function of its own lags and lags of other variables. Used for forecasting and impulse response analysis.
W
Weighted Least Squares (WLS) (Ch 7)A method for addressing heteroskedasticity by weighting observations by 1/σᵢ when the form of heteroskedasticity is known.
White Test (Ch 7)A general test for heteroskedasticity that regresses squared residuals on X, X², and cross-products of X. LM statistic follows χ²(k).
Within Estimator (Ch 8)Another name for Fixed Effects estimation, which uses variation within each individual over time.
Z
Zero Conditional Mean (Ch 3)The assumption that the expected value of the error term is zero for any value of the independent variables: E(u|X) = 0. This is the key assumption for the causal interpretation of OLS coefficients.