Regression analysis
Undergraduate · Math
Syllabus focus
Topics typically covered
Click a topic for the full text and related unit practice.
Undergraduate Regression analysis — outline derived from course README sections and typical US statistics syllabi (OpenIntro / standard OER where applicable).
Simple linear regression
- Least squares estimation of slope — Least squares estimation of slope
- Intercept — Intercept
- Interpretation of coefficients and R² — Interpretation of coefficients and R²
- Inference for regression parameters — Inference for regression parameters
- Prediction intervals — Prediction intervals
- Confidence bands — Confidence bands
- Assumptions: linearity, homoscedasticity, normality of errors — Assumptions: linearity, homoscedasticity, normality of errors
Multiple regression
- Matrix formulation of the linear model — Matrix formulation of the linear model
- Interpretation of partial coefficients — Interpretation of partial coefficients
- F-tests for nested models — F-tests for nested models
- Categorical predictors — Categorical predictors
- Dummy coding — Dummy coding
- Interaction terms — Interaction terms
- Effect modification — Effect modification
- Multicollinearity: detection — Multicollinearity: detection
- Remedies — Remedies
Model diagnostics
- Residual analysis — Residual analysis
- Influence measures — Influence measures
- Leverage and Cook's distance — Leverage and Cook's distance
- Outliers — Outliers
- Transformations — Transformations
- Weighted least squares (intro) — Weighted least squares (intro)
- Variable selection: stepwise — Variable selection: stepwise
- Information criteria — Information criteria
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Simple linear regression
Least squares estimation of slope
Coming soon - Multiple regression
Matrix formulation of the linear model
Coming soon - Model diagnostics
Residual analysis
Coming soon
Notes
Undergraduate Regression analysis — outline derived from course README sections and typical US statistics syllabi (OpenIntro / standard OER where applicable). Topic outline: `content/topics/undergraduate/regression.json`.