Directed Acyclic Graph and Advanced Statistical Visualization

Accreditation-ready visual pedagogy: layered DAG semantics, topological flow, and regression analysis with diagnostics.

Directed Acyclic Graph (DAG): Pipeline and Dependency Semantics

Topological ordering, edge classification, and level annotations

Standard dependency

Critical path edge

Weighted/optional edge

This DAG encodes a strict partial order over tasks. The absence of cycles supports valid topological sorting, enabling deterministic scheduling and critical-path analysis for throughput forecasting.

Advanced Regression with Residual Diagnostics and Confidence Bands

OLS fit, R², residual distribution, and 95% confidence interval

The model estimates a linear relationship y = β₀ + β₁x with Gaussian noise. We annotate R², visualize residuals, and render a 95% confidence band for the mean prediction. This supports academic assessment of fit quality and model assumptions.

Academic Summary and Learning Objectives

Key takeaways and assessment-ready notes

• Topology: DAG organizes tasks into layers; critical path determines latency lower bound.
• Scheduling: Topological sort permits parallel execution within levels, respecting dependency constraints.
• Estimation: OLS regression provides parameter estimates and interpretable uncertainty via confidence bands.
• Diagnostics: Residual distribution and heteroscedasticity hints inform model suitability and next-step modeling.