Regression analysis
Undergraduate · Statistics
Syllabus focus
Standard syllabus · STEM / applied
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Topics typically covered
Standard syllabus
Simple linear regression
- Least squares estimation of slope and intercept
- Interpretation of coefficients and R²
- Inference for regression parameters
- Prediction intervals and confidence bands
- Assumptions: linearity, homoscedasticity, normality of errors
Multiple regression
- Matrix formulation of the linear model
- Interpretation of partial coefficients
- F-tests for nested models
- Categorical predictors and dummy coding
- Interaction terms and effect modification
- Multicollinearity: detection and remedies
Model diagnostics
- Residual analysis and influence measures
- Leverage, Cook's distance, and outliers
- Transformations and weighted least squares (intro)
- Variable selection: stepwise and information criteria
STEM / applied
Applied modeling workflow
- Building models in R or Python (statsmodels, sklearn)
- Cross-validation for model assessment
- Regularization preview: ridge and lasso
- Logistic regression for binary outcomes
- Poisson regression for count data (introduction)
- Reporting regression results for applied audiences
Additional applied practice
- Reviewing assumptions with domain experts
- Documenting analysis choices for reproducibility
- Sensitivity analyses for key modeling decisions
- Connecting results to the original research or business question
Notes
Common capstone applied course for statistics and social-science majors. STEM sections emphasize diagnostics, software, and prediction; standard sections cover classical linear model theory.