Correlation & Regression Vocabulary

Vocabulary flashcards covering key terms from the Business Statistics lecture on Correlation and Regression.

Correlation

A statistical measure that describes the strength and direction of a linear relationship between two quantitative variables.

Regression

The process of modeling and analyzing the relationship between a dependent variable and one or more independent variables, primarily for explanation or prediction.

Scatter Plot (Scatter Diagram)

A graph of paired (x, y) data points used to visually assess the relationship between two variables.

Simple Correlation Coefficient (r)

A unit-free statistic ranging from –1 to +1 that estimates the population correlation (ρ) and indicates both strength and direction of a linear relationship.

Population Correlation Coefficient (ρ, rho)

The true but usually unknown correlation value that quantifies the linear association between two variables in an entire population.

Positive Correlation

A relationship in which high values of one variable are associated with high values of the other; r is close to +1.

Negative Correlation

A relationship in which high values of one variable are associated with low values of the other; r is close to –1.

No (Zero) Correlation

A situation where r is near 0, indicating no linear association between variables.

Coefficient of Determination (R²)

The proportion of total variation in the dependent variable that is explained by the regression model; ranges from 0 to 1.

Dependent Variable (y)

The outcome or response variable a model seeks to explain or predict.

Independent Variable (x)

The predictor or explanatory variable used to account for variation in the dependent variable.

Simple Linear Regression Model

A model of the form ŷ = b₀ + b₁x that relates one dependent variable to a single independent variable via a straight line.

Slope (b₁)

The estimated change in the average value of y for a one-unit increase in x in a linear regression equation.

Intercept (b₀)

The estimated average value of y when x equals zero (within the observed data range).

Least Squares Criterion

The method of estimating b₀ and b₁ by minimizing the sum of squared residuals between observed and predicted y values.

Residual (Error Term, ε or e)

The difference between an observed y value and its corresponding predicted value ŷ in a regression model.

Total Sum of Squares (SST)

The total variability in the dependent variable; calculated as Σ(yi – ȳ)².

Regression Sum of Squares (SSR)

The part of SST explained by the regression model; Σ(ŷi – ȳ)².

Error Sum of Squares (SSE)

The unexplained portion of variation; Σ(yi – ŷi)².

Explained Variation

Variation in y accounted for by the regression model, quantified by SSR.

Unexplained Variation

Variation in y not accounted for by the model, quantified by SSE.

Bivariate Analysis

Statistical examination of the relationship between exactly two variables.

Multivariate Analysis

Analysis involving more than two variables, such as studying the effect of advertising and price on sales simultaneously.

Linear Regression Assumptions

Conditions including linearity, independent errors, normally distributed errors, and constant error variance necessary for valid inference.

Curvilinear Relationship

A non-linear association between variables where data points follow a curved pattern rather than a straight line.

Strength of Relationship

The degree to which two variables are linearly related, indicated by the absolute value of r.

Direction of Relationship

Indicates whether the relationship is positive or negative, reflected by the sign of r.

Prediction (Forecasting)

Using a regression equation to estimate the value of the dependent variable for given independent variable values.

Causation in Regression

The concept that changes in independent variables may cause changes in the dependent variable when model assumptions hold.

Unit-Free Measure

A statistic—like r—that has no physical units, enabling comparison across different data sets or scales.