Flashcards: Regression Analysis Fundamentals — 20 cards

Unit goals — main aim?

Framework for statistical analyses using GLM.

Assessment tasks — components?

Data-analysis task, practical project, final exam.

Regression — definition?

Predicts a numeric outcome y from predictors x.

Residual — what?

Difference between observed y and predicted $\hat{y}\

R2 — meaning?

Proportion of y variance explained by the model.

Simple linear regression — equation?

$\hat{y} = ext{intercept} + ext{slope} imes x$.

Model fit — goal?

Minimize residual variation, maximize explained variation.

Regression assumptions — key?

Linearity, independence, normal residuals, homoscedasticity.

Multiple regression — workflow step?

Univariate summaries, bivariate plots, fit full then reduced model.

Data screening — purpose?

Check distributions, outliers, collinearity.

Collinearity — indicator?

High correlation ($|r| > 0.7$ or $>0.8$) among predictors.

VIF — what?

Variance inflation factor; measures multicollinearity.

Residual independence — check?

Residuals should show no systematic pattern over observations.

Normal residuals — check?

Normal probability plot and Shapiro-Wilk test.

Homoscedasticity — meaning?

Constant residual spread across predicted values.

Linearity — assessment?

Residuals vs predicted plot and residuals vs each predictor.

Sample size rule — minimum?

n > 5p; preferably n > 10p.

Collinearity heuristics — when?

$|r| > 0.7$ possible, $|r| > 0.8$ definite.

Tolerance — relation?

Tolerance = 1 / VIF; <0.1 indicates concern.

Regression diagnostics — purpose?

Check residual independence, normality, homoscedasticity, linearity.