Linear Regression Analysis and Causality Concepts

Vocabulary flashcards covering key econometric, statistical, and causal inference concepts from Chapters 1 and 4-7.

Simple Linear Regression

A regression model that involves one outcome of interest (dependent variable) and one regressor (independent variable).

Ordinary Least Squares (OLS)

A mathematical optimization method that determines the intercept and slope of the line that best fits data by minimizing the sum of squared errors.

Multiple Regression Model

A linear regression model that includes more than one regressor to explain a single dependent variable.

Indicator Variable

A binary variable (also called a dummy variable) that takes on only two values, $0$ or $1$, to categorize observations into groups.

Reference Group

The excluded category when converting a categorical variable with more than two categories into a set of indicator variables in a regression model.

Standard Error (SE)

A statistic measuring the estimation error or uncertainty associated with an estimated parameter in a regression model.

Statistical Significance

A determination of whether an estimated coefficient is statistically different from zero, evaluated at conventional significance levels such as $10\%$, $5\%$, or $1\%$.

t-value

A test statistic calculated as $t_j = \frac{\hat{\beta}_j}{SE(\hat{\beta}_j)}$, used to evaluate the statistical significance of a regression coefficient.

Star System

A reporting convention in regression tables where asterisks ($*$, $**$, $***$) signal statistical significance at the $10\%$, $5\%$, and $1\%$ levels, respectively.

P-value

A statistic between $0$ and $1$ that indicates the precise level of statistical significance for an estimated regression coefficient.

Confidence Interval

A calculated range around a parameter estimate, constructed as $\hat{\beta}_j \pm \text{critical value} \times SE(\hat{\beta}_j)$, within which the true parameter value is expected to lie with a specified probability.

Homoskedasticity

The condition where the variance of the regression error term is constant regardless of the value of the regressor $X$.

Heteroskedasticity

The condition where the variance of the regression error term is not constant and depends on the value of the regressor $X$.

Robust Standard Errors

Standard error calculations that are specifically corrected to remain valid in the presence of heteroskedasticity.

Adjusted R-Squared

A statistic indicating the percentage of variation in the dependent variable explained by the regressors, adjusted for the number of predictors in the model.

Omitted Variable Bias (OVB)

The bias in estimated regression coefficients created when a relevant variable that determines the outcome is left out of the model and is correlated with an included regressor.

Empirical Analysis

Data-driven analysis used to evaluate competing theoretical predictions and quantify the magnitude of real-world effects.

A/B Testing

A causal evaluation method in business applications that compares customer performance across two different design packages or variations.

Rubin Causal Model

A framework defining a causal effect as the difference between potential outcomes under treatment versus non-treatment states ($\delta_i = Sales_{i, U_1} - Sales_{i, U_0}$).

Counterfactual

The unobserved potential outcome for a given unit under the treatment condition it did not actually experience.

Fundamental Problem of Causal Inference

The impossibility of directly observing both potential outcomes for a single unit, making individual causal effect calculations impossible.

Average Treatment Effect (ATE)

The average causal effect of a treatment estimated across an entire sample or population.

Cross-Sectional Data

Data consisting of multiple entities observed at a single period in time.

Time Series Data

Data consisting of a single entity observed across multiple periods in time.

Panel Data

Data consisting of multiple entities where each entity is observed across two or more periods in time (also known as longitudinal data).