Linear Regression Concepts

These flashcards cover key terms and concepts related to simple linear regression as outlined in the lecture.

Simple Linear Regression

A method for modeling the relationship between a dependent variable and an independent variable using a linear equation.

Dependent Variable

The variable being predicted or estimated in a regression model; typically denoted as y.

Independent Variable

The variable that is being manipulated or changed in the model to observe its effect on the dependent variable; typically denoted as x.

Covariance

A measure of the degree to which two random variables change together; it indicates the direction of the linear relationship between the variables.

Variance

A measure of how much values in a dataset differ from the mean value; in regression, used to assess the spread of the independent and dependent variables.

Error Term (Epsilon)

The component of the regression model that accounts for the variability in the dependent variable not explained by the independent variable.

Regression Equation

An equation that expresses the relationship between the independent variable and dependent variable in the form: $y = \beta_0 + \beta_1 x + \epsilon$.

Coefficient of Determination (R²)

A statistical measure that indicates the proportion of variance in the dependent variable that can be explained by the independent variable.

Residuals

The differences between the observed values and the predicted values in a regression model; used to assess the accuracy of the model's predictions.

Population vs. Sample

In statistics, a population refers to the entire group of individuals or instances, while a sample is a subset of the population used to infer conclusions about the population.

Maximization Theory

A principle that suggests finding the maximum output (e.g., profit) from a given input (e.g., advertising) within constraints.

Multilinear Regression

An extension of linear regression that uses multiple independent variables to predict a dependent variable.

Slope

In a linear equation, the slope (denoted as $\beta_1$) represents the change in the dependent variable for a one-unit change in the independent variable.

Intercept

The y-intercept (denoted as $\beta_0$) is the value of the dependent variable when the independent variable is zero.

Linear Relationship

A relationship between two variables that can be represented by a straight line on a graph, where the change in one variable corresponds to a constant change in the other variable.