Course: Introduction to Statistics (MATH 11) · Silver Oak University (fictional sample) · Prof. Rivera
Module: Week 15 of 16 · Fall 2026 · in-person, two 75-minute sessions
Objective covered: Objective 8 — Fit and interpret a simple linear regression model, including inference for the slope.

This file holds two pieces: (A) the Module 15 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. Dates below assume a Tuesday/Thursday session pattern with Week 15 meeting Tue Dec 8 and Thu Dec 10, and end-of-week work due Sunday Dec 13, 11:59 p.m. Adjust the day-of-week and times to match your section.

(A) Module 15 Overview — Start Here

Welcome to Week 15: Linear Regression & Inference

This is your home base for the week. Read it first, then work the checklist below from top to bottom. Everything you need is linked inside the module.

This is our last regular week — the final is next week. Back in Week 4 we learned to measure a relationship with the correlation r, and we warned that correlation isn't causation. This week we go two giant steps further: we draw the actual line of best fit, use it to predict, and then make the grown-up move — we ask whether the line is real or whether we're being fooled by noise. By Friday you'll be able to take any "for every extra X, Y rises by…" headline and read its slope, its r², and its limits.

The week's big question

"Once two things move together, can we draw the line that turns the pattern into a prediction — and how do we know the line is real, and not just noise?"

By Friday you'll be able to do four things with any reported relationship: write its line (slope + intercept), predict with it (ŷ and residuals), measure how much it explains (r²), and test whether the trend is statistically real (compare a p-value to α).

By the end of this week, you can…

Use this as a checklist. If you can do all four out loud, you're ready for the quiz.

• [ ] Read a least-squares line ŷ = b₀ + b₁x and interpret its slope and intercept in context — the slope as a per-one-unit change in ŷ (with units!), the intercept as ŷ when x = 0.
• [ ] Predict ŷ for a given x and compute a residual (observed − predicted), knowing a positive residual sits above the line and a negative one below.
• [ ] Interpret r² as the share (percent) of the variation in y the line explains — and know it is not the slope.
• [ ] Explain inference for the slope — is it significantly different from 0? — by comparing a p-value to α (p < α → real; p ≥ α → could be noise), and read a residual plot (a patternless cloud means the line fits).

What's due this week, and when

Work these in order — each one gets you ready for the next.

Heads-up on the AI tutorial: you'll use a chatbot to draft, and then you judge its work against what we cover in class. Chatbots routinely slip here — hand one the line ŷ = 50 + 4x (fit on 1–6 hours of study) and ask if studying 40 hours means a score of 210, and whether it "proves" studying causes the scores. Watch whether it catches BOTH the extrapolation (40 is way outside the data) and the correlation-isn't-causation trap. Catching the model is the point.

Late policy reminder: 10% off per day late. If life happens, reach out before the deadline — I'd much rather hear from you early. (With the final next week, don't let Week 15 work slip.)

How to succeed this week

• Always interpret in context, with units. A slope isn't "4" — it's "4 points of exam score per extra hour studied." The number is half the answer; what it means is the other half.
• Memorize the tiny hooks. "Slope = per-one-x change in ŷ; intercept = ŷ when x = 0; ŷ wears a hat because it's predicted." "Residual = observed − predicted" (positive = above the line). "Slope = how much, r² = how well" — and r² is never the slope. And for inference: "H₀: slope = 0. Low p, slope's legit (p < α → reject)."
• Don't drive the line off the map. The line is only trustworthy inside the range of the data. Push x far past where the data lives and you're extrapolating — that's where regression lies.
• Remember the carry-over lesson: a line still isn't a cause. A significant slope and a high r² describe and predict — on observational data they're a link, not a cause. Ask the Week-4 questions: lurking variable? randomly assigned? (Ask me about coffee shops and home prices.)
• Treat the chatbot as a smart intern, not an oracle. It drafts; you check. That habit is the whole semester in miniature.

You don't need anything memorized in advance — just bring your curiosity and a willingness to question a trend line. Come to class ready to bet on a friend's exam score. See you Tuesday.

Looking ahead — the final is next week (Week 16). It's cumulative across all eight objectives. Your study guide, exam-prep tutorial, and practice exam live in the Week 16 module — start them this weekend if you can.

(B) Welcome Announcement — Module 15

Release setting: post on the module's start day (offset = 0 days), i.e., Tue Dec 8, 2026 — not before. If your platform won't preserve the scheduled date on import, post this as a draft labeled "Release: Tue Dec 8."

Subject: Week 15 — draw the line, then prove it's real 📈

Hi everyone,

Quick one before class: if I told you "for every extra hour a student studies, their exam score goes up about 4 points," and a friend says they're going to study 7 hours for the final — what score would you bet on? And how sure are you?

That's the whole week. In Week 4 we learned to measure a relationship with the correlation r. This week we go further: we draw the actual line of best fit, use it to predict (and measure how far off each prediction is — the residual), say how much the line explains (r²), and then make the grown-up move — we test whether the slope is real or just noise (inference for the slope: compare a p-value to α). And the Week-4 warning still stands: a line is not a cause.

This week — Linear Regression & Inference — is our last regular week. What's due (all close Sun Dec 13, 11:59 p.m., except the discussion's first post):
1. Lecture Tutorial 15 — the least-squares line, prediction & residuals, r², and inference for the slope, with one approved chatbot (Gemini, Claude, or ChatGPT); submit the share link.
2. Quiz 15 — the week's ideas, auto-graded.
3. Discussion 15 — "Read the headline's slope" — find a real "for every X, Y rises by…" trend and reason about its slope, r², and the extrapolation/causation pitfalls; initial post Fri Dec 11, replies by Sun Dec 13.
4. Assignment 15 — "Drawing & Testing the Line" — four problems, coached and graded by your chatbot; submit the report + chat link.

One promise, same as always: this is a course about thinking clearly, not about being a "math person." Lead with the plain-language meaning — what does the slope mean, how much does it explain, is it real, and where would it mislead? The notation comes second.

Heads-up: the final is next week (Week 16). It's cumulative, and your study guide, exam-prep tutorial, and practice exam are already waiting in the Week 16 module — give yourself a head start this weekend.

Open the Start Here / Module Overview page first — it lays out everything in order with due dates. Bring your curiosity (and an opinion about whether building coffee shops really raises home values) to class on Tuesday.

See you soon,
Prof. Rivera