Untitled Flashcards Set

Population Mean (μ)

The true average of a variable in the entire population.

Sample Mean (X̄)

The average computed from a sample, used to estimate the population mean.

Conditional Expectation (E(Y|X))

The expected value of a variable Y given a certain value of X.

Regression Equation

Y = β0 + β1X + u, where Y is the dependent variable, X is the independent variable, u is the error term, β0 is the intercept, and β1 is the slope.

Residual (u^\hat{})

The difference between observed and predicted values (Y − Ŷ).

Ordinary Least Squares (OLS)

A method to estimate regression parameters by minimizing the sum of squared residuals.

Standard Error of Regression (SER)

Measures the average size of the residuals.

R-Squared (R2)

Measures the proportion of variance in Y explained by X.

Sum of Squared Residuals (SSR)

The sum of squared differences between observed and predicted values.

Total Sum of Squares (TSS)

The total variation in the dependent variable (Y).

Explained Sum of Squares (ESS)

The portion of TSS explained by the regression model.

R-Squared Calculation

R2 = ESS / TSS = 1 - SSR / TSS.

Goodness of Fit (R2 close to 1)

Indicates a high proportion of the variance in Y is explained by X, meaning a good model fit.

Goodness of Fit (R2 close to 0)

Indicates the model explains very little of the variance in Y.

Best Regression Line Criterion

The one that minimizes the sum of squared residuals (OLS method).