Interactive Textbook Module Syllabus

Simple Linear Regression & Residual Diagnostics

Master the foundational predictive engine of business analytics. Learn Ordinary Least Squares derivation, slope and intercept interpretation, R-squared, hypothesis testing, and the core LINE residual diagnostic plots — with real applications in omnichannel ad saturation.

⏱️ ~26 min reading & interactives 📑 10 sections 🎓 Level: Core undergraduate 📐 Math: Formulas shown 📚 Courses: Intro Business Statistics, Marketing Analytics 🏷️ Topics: Regression, Descriptive statistics

Chapter Section Outline (10 Sections)

Topics and managerial frameworks covered in Simple Linear Regression & Residual Diagnostics:

1. Deterministic vs Probabilistic Relationships
2. The Simple Linear Regression Model and OLS Derivation
3. Managerial Interpretation: Slope, Intercept & Extrapolation
4. Goodness-of-Fit: Sum of Squares and R-Squared
5. Statistical Inference on the Slope
6. The LINE Assumptions of Ordinary Least Squares
7. Residual Diagnostics: The 4 Classic Plots
8. Flagship Marketing Case: Omnichannel Ad Spend Saturation
9. Guided Practice: Residual Diagnostics Studio
10. Auditing the AI Analyst: Catching Linear Extrapolation Hallucinations

Interactive Concept Mini-Widgets Embedded in This Chapter (2)

Students manipulate these interactive visual simulations directly inside the chapter reading before answering gated check-in questions:

By Hand vs. By Calculus

Students nudge a slope and intercept by hand, watch SSE respond, then press one button and see calculus land on the exact minimum instantly.

Linear Model

Pairs an equation with a picture so students see what each parameter *does* to the shape. Deliberately data-free: calibration against real observations is the job of the full Response Model Lab tool, not this widget.

Paired Browser-Based Analytics Calculators (3)

This chapter connects directly to these full MktPraxis analytical apps (with pre-loaded business case scenarios, CSV upload, and reproducible Python export):

🔬 Regression Residual Diagnostics

Audit the LINE assumptions of a simple or multiple regression (numeric and categorical predictors) with Residuals vs. Fitted, Normal Q-Q, Scale-Location, Cook's Distance and residuals-by-predictor plots, on a case study or your own CSV.

Pre-loaded Business Scenarios: Ad spend and sales revenue · Client size and B2B deal value · Influencer reach and orders · Weekly ad spend and sales · Store sales by ad spend and region · B2B deal value by headcount, industry and renewal

📉 Bivariate Regression (Simple)

Predict an outcome using one variable (e.g., Spend → Sales).

Pre-loaded Business Scenarios: Paid Social Spend vs. Weekly Revenue · Email Creative Themes vs. Average Order Value · Likert Reaction vs. Brand Favorability · D&D Character Level vs. Gold Earned

🔗 Pearson Correlation

Check if two continuous metrics move together (e.g., ad spend vs. revenue).

Pre-loaded Business Scenarios: Paid Social Spend vs Trial Signups · Awareness vs Consideration – Q3 Brand Tracker · Net Promoter Score vs Loyalty Retention · Full-Funnel KPI Matrix – Finding the Leak · Email Send Volume vs Revenue – and the Third Column