Course: Introduction to Statistics (18-week generic edition)
Module: Week 17 of 18 · planned around two ~75-minute sessions
Objective covered: Objective 8 — Fit and interpret a simple linear regression and carry out inference for the slope (plus the synthesis review of the whole inference toolkit).

This file holds two pieces: (A) the Module 17 Overview page ("Start Here") and (B) the Welcome Announcement that drips out when the module opens. All timing is relative — "start of Week 17," "end of Week 17" — and maps onto real dates when the adopting instructor sets the term calendar.

(A) Module 17 Overview — Start Here

Welcome to Week 17: Linear Regression with Inference + Course Synthesis

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 the last week of new material — and it's the week the course shakes hands with itself. You've been able to see a two-variable relationship since Week 4 (scatterplots, the correlation r). This week you finally get to use one: fit the least-squares line, read its slope like a professional, and then put that slope on trial with the same t-machinery you've run since Week 11. Then we zoom out: with every tool now on the table, the final skill is choosing the right one — which is exactly what next week's cumulative final rewards.

The week's big question

"When can a line drawn through yesterday's data be trusted to predict tomorrow — and how do we tell a real slope from a lucky tilt?"

By the end of the week you'll ask three questions of any fitted line you meet: What does the slope say, in units? How much does the line explain (r²)? And where does the data's range end — because beyond it, the line is fiction.

By the end of this week, you can…

Use this as a checklist. If you can do all five out loud, you're ready for the quiz — and most of the way ready for the final.

• [ ] Interpret a slope and intercept in context — the full four-part sentence: per one unit of x, predicted, on average, in y's units (and know when an intercept deserves no interpretation at all).
• [ ] Read r² as a share of variation explained (never an accuracy rate) and a residual as actual − predicted.
• [ ] Judge a residual plot (patternless = good; curve or fan = trouble) and refuse to extrapolate beyond the fitted range.
• [ ] Run the t-test and confidence interval for the slope from computer output — t = b ⁄ SE(b), df = n − 2, H₀: β = 0 ("the flat line") — and use the interval-contains-zero duality.
• [ ] Choose the right procedure for any scenario from Weeks 11–17: mean, proportion, counts, or a line?

What to do this week, in order

The table below lists the week's items in working order, with what each is worth and when it's due.

Heads-up on the AI work: in this course the chatbot drafts, and you judge. Regression is where chatbots bluff hardest — they'll call r² "the correlation," read a meaningless intercept with a straight face, and extrapolate to a 300 mm flipper without blinking. This week's lab bait is designed to make yours do exactly that — catching it is graded.

Late policy reminder: 10% off per day late. If life happens, reach out to your instructor before the deadline — early is always easier.

How to succeed this week

• Memorize the four-part slope sentence. Per one unit of x · predicted · on average · in context units. Every slope question on the quiz, the lab, and the final is this sentence wearing different clothes.
• Keep r² humble. It's a share of variation explained — a share, not a grade — and never "percent accurate."
• Respect the data's range. Inside it, the line predicts; outside it, the line is fiction (ask the lab's 300 mm penguin).
• Reuse your t-skills. The slope test is Week 14 with a new df rule: t = b ⁄ SE(b), df = n − 2, same table, same duality (interval contains 0 ⇔ fail to reject).
• Drill the decision map. Mean, proportion, counts, or a line? Name the answer's shape and the procedure names itself — that one habit is most of the final.
• A word about Week 18: the final is cumulative, 60 multiple-choice, worth 5% — a low-stakes checkpoint, exactly like the midterm. Its study guide, practice exam, and exam-prep tutorial are all in the Week 18 module, waiting. Nothing to fear; everything to review.

Seventeen weeks ago, a statistic was a number someone told you. This week it becomes a claim you can interrogate from every side. Finish strong.

(B) Welcome Announcement — Module 17

Release setting: drips at the start of Week 17 (offset = 0 days from module start) — not before. If your platform won't preserve the scheduled release on import, post it as a draft labeled "Release: start of Week 17."

Subject: Welcome to Week 17 — the last new tool, and the whole toolkit

Hi everyone,

Last week you put whole categorical tables on trial with chi-square. This week — the final week of new material — you get the tool everyone's been waiting for: regression. Your energy bill arrives, and you mutter "it was a cold month" — that's a regression running in your head. This week the hunch gets a formula (a line with a slope you can read out loud), a report card (r²), and a trial (the t-test for the slope — the same t-machinery you've used since Week 11).

This week — Linear Regression with Inference + Course Synthesis — we tackle the big question: When can a line drawn through yesterday's data be trusted to predict tomorrow — and how do we tell a real slope from a lucky tilt? And then we zoom out and assemble every tool from the course into one decision map: mean, proportion, counts, or a line?

Three things not to miss:
1. Chapter 17 is your primary reading — start there. The extrapolation trap alone (a line that confidently predicts negative energy use) is worth the read.
2. Data Lab 17 comes full circle: you'll fit a real regression — flipper length predicting body mass — on the same Antarctic penguins you met in Week 1. Three spreadsheet cells, one capstone. Due at the end of Week 17.
3. Discussion 17 — "The Tool You'll Keep" — is the course's last discussion: which tool will you actually use after this course? Initial post two days before the week ends, so classmates can argue with you.

And a calm word about what's next: Week 18 is Final Exam Week. The final is cumulative, 60 multiple-choice, closed to AI, and worth 5% — a low-stakes checkpoint, just like the midterm was. Its study guide, practice exam, and exam-prep tutorial are already in the Week 18 module. Steady weekly work has carried your grade all term; next week is the victory lap.

Open the Start Here / Module Overview page first — it lays out everything in order with due points. Eighteen weeks ago a statistic was a number someone told you. The last chapter of the story is yours.

See you in the course!