Video Notes: Simple Linear Regression Vocabulary

Vocabulary flashcards covering key terms and definitions from the lecture notes on simple linear regression, model assumptions, testing, and ANOVA.

Simple Linear Regression (SLR) model

A population model relating y to x: y = β0 + β1 x + ε, where ε is a random error term; used to predict the mean response of y given x.

True mean response (μ_y|x)

The expected value of y for a given x in the population: μ_y|x.

Predicted mean (y-hat, ŷ)

The estimated mean response for a given x, computed from sample data: ŷ = a + b x.

Residual (e)

The difference between an observed y and its predicted mean: e = y − ŷ.

Error term (ε)

The stochastic error term for observation i; εi = yi − μy|xi, assumed to be N(0, σ^2) and independent.

Normal distribution

The assumed distribution for the error term: ε ∼ N(0, σ^2).

Independently and identically distributed (iid)

Errors are independent and come from the same distribution (same variance and shape).

Homoskedasticity

Constant variance of the error terms across all levels of x.

Confidence interval for β

An interval estimate for the population slope β based on β̂; uses the t distribution: β̂ ± t* SE(β̂).

t-test for β

Hypothesis test for β = 0 (or other value) using a t statistic with df = n − 2 in simple linear regression.

ANOVA in SLR

Analysis of variance for regression; partitions total variation into SSR and SSE; uses F-statistic to test model significance.

R-squared (R²)

Proportion of the total variation in y explained by the regression: R² = SSR / SST.

Total Sum of Squares (SST)

Sum of squared deviations of y from its mean; SST = SSR + SSE.

Regression Sum of Squares (SSR)

Sum of squared deviations explained by the regression.

Error Sum of Squares (SSE)

Sum of squared residuals; SSE = Σ (yi − ŷi)².

Mean Square for Regression (MSR)

SSR divided by its degrees of freedom; MSR = SSR / dfRegression.

Mean Square Error (MSE)

SSE divided by its degrees of freedom; MSE = SSE / dfError.

F-statistic

Ratio MSR/MSE used to test the overall significance of the regression.

Slope (β1)

The coefficient of x in the regression; represents the change in y for a one-unit change in x.

Intercept (β0)

The expected value of y when x = 0; where the regression line crosses the y-axis.