Lecture 6: Multivariate Regression

These flashcards aim to reinforce the key vocabulary and concepts associated with multivariate regression, its applications, and related statistical methods as discussed in Lecture 6.

Multivariate Regression

A statistical technique used to model the relationship between multiple independent variables and a dependent variable.

Difference-in-Differences (DiD)

A quasi-experimental design that compares the changes in outcomes over time between a treatment group and a control group.

Omitted Variable Bias (OVB)

A bias in regression analysis caused by the omission of one or more relevant variables.

Covariance

A measure of the degree to which two variables change together, indicating the direction of their linear relationship.

Control Group

A group separated from the rest of the experiment where the independent variable being tested is not applied.

Average Treatment Effect (ATT)

The average effect of a treatment (or intervention) on an outcome for those who receive the treatment.

Interaction Effects

Effects that occur when the effect of one variable on the dependent variable changes depending on the level of another variable.

Condition Expectation

The expected value of a random variable conditioned on the value of another variable.

Higher-dimensional Analog

An extension of a notion in lower dimensions (like linear regression) to higher dimensions involving multiple predictors.

SSE (Sum of Squared Errors)

A measure used in regression analysis to quantify the difference between observed and estimated values.

Binary Indicator Variable

A numerical variable that represents categorical data, in which the variable can take on one of two possible values.

Regression Coefficients

Parameters in a regression model that quantify the relationship between dependent and independent variables.

Gradient Descent

An optimization algorithm used to minimize the loss function in regression by iteratively adjusting the coefficients.

Randomized Control Trial (RCT)

An experimental study design that randomly assigns participants into either the treatment or control group.

Estimate

An approximation or calculation of a value, often derived from statistical analysis.

Variance

A statistical measurement of the spread between numbers in a dataset, indicating how far each number is from the mean.

Dependent Variable

The variable in a regression that you are trying to predict or explain.

Independent Variable

The variable in a regression that is manipulated or used to explain variations in the dependent variable.

Omitted Variable

A variable that should have been included in the analysis but was excluded, potentially biasing results.

Hypothesis Testing

A statistical method that uses sample data to evaluate a hypothesis about a population parameter.

Residuals

The difference between observed and predicted values in a regression model.

Significance Level

The probability of rejecting the null hypothesis when it is actually true.

Control Variables

Variables that are held constant or controlled to better assess the relationship of the principal variables.