Week 9 · Applied Statistics · HEG Genève

Does a higher price buy a better rating?

Week 1 warned you that the price–rating scatter had a lurking variable in it. This week you fit the line anyway — properly: the correlation coefficient r, the least-squares line, inference on its slope, the coefficient of determination r², and prediction with an honest interval. Then, with the tools in hand, the lurking variable comes back.

🏫 In class: 3 h · lesson ~1 h, then exercises ~2 h 📖 Saylor ch. 10 ▶ The Lecture button shows the slide outline

By the end of Week 9 you will be able to

Compute and interpret the linear correlation coefficient r.
Fit the least-squares regression line ŷ = b₁x + b₀ and interpret both coefficients in business terms.
Test whether the slope β₁ is zero and build a confidence interval for it.
Interpret r² as the share of variation explained.
Predict y for a given x with a prediction interval — and refuse to extrapolate.

Resources

✓Saylor §10.1–10.2 — Linear relationships and r ↗

✓Saylor §10.3–10.4 — The model and the least-squares line ↗

✓Saylor §10.5–10.6 — Inference about β₁ and r² ↗

✓Saylor §10.7–10.8 — Estimation, prediction, a complete example ↗

✓Saylor §10.9 — Formula list ↗

Homework for this week is written with the week itself, on the Week 1–2 pattern: a fresh dataset, hints and worked solutions.

Tools for this week

Exam cards c20–c23

← Course page

Section 9.1 · The hook

Price and rating

Planned · Hook

Guess r before you see the scatter

Slider from −1 to +1: "how strongly does price go with rating?" Lock it.

Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.

Section 9.2 · The scatter and r

How strong, which way

Planned · Correlation

r from the data (§10.1–10.2)

Widget: the 12-pizzeria price–rating scatter; drag a point and watch r change; four canned scatters to classify by r. Exam card c20.
Classify (6 rows): strong positive / weak / none / strong negative — from pictures.

Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.

Section 9.3 · The line

Least squares

Planned · Regression

ŷ = b₁x + b₀, residuals (§10.3–10.4)

Widget: draw your own line by hand, then reveal least squares and compare the sum of squared residuals.
Interpret b₁: "each extra franc buys __ rating points" — and b₀'s meaning, or lack of one. Exam card c21.

Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.

Section 9.4 · Inference

Is the slope real?

Planned · Inference

Test and CI for β₁; r² (§10.5–10.6)

Widget: the t test on the slope with df = n − 2; r² as a shaded share of the variation. Exam cards c22–c23.

Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.

Section 9.5 · Prediction — and the trap

What would a CHF 24 pizzeria score?

Planned · Prediction

Prediction intervals, extrapolation, the lurking variable (§10.7–10.8)

Widget: predict at x with a prediction interval that widens away from x̄; the extrapolation warning at CHF 40.
The Week 1 reveal returns: colour the points by neighbourhood. The line was right; the causal story was not.

Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.

Section 9.6 · Checkpoint

Prove it to yourself

Planned · Quiz

Self-check quiz & where this goes next

Ten questions: interpret r, interpret b₁, compute ŷ, the slope test, r², a prediction, extrapolation, and correlation ≠ causation.

Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.

Section 9.7 · Workshop

The pizzeria file · instalment nine

Planned · Exercise

Workbook fields

w9_model — one thing that might predict your takings, as ŷ = b₁x + b₀ with plausible numbers.
w9_lurking — the lurking variable that could explain that relationship without causation.

Status → this section is an outline. When the week is written it becomes an interactive screen on the Week 1–2 pattern: an earned completion, a classify exercise or lab where one is listed, and its own share of the progress bar.

Course page →

Part 2 · Exercises

8 exercises, worked together

Planned · ~105 min

The second half of the session

When this week is written, each exercise below becomes a form on this page and a slide in the deck, generated from one array so the two can never disagree — and its solution opens when the instructor reveals it in class. Same engine as Weeks 1–2 (exercises.js).

Exercise 1 · Guess r, then compute it 15 min
the price–rating scatter, by hand
Exercise 2 · Interpret r 10 min
four values of r, four sentences
Exercise 3 · The least-squares line 18 min
b₁ and b₀ from the sums
Exercise 4 · Interpret the slope in francs 10 min
and say what b₀ means — or does not
Exercise 5 · Is the slope real? 15 min
the t test on β₁, df = n − 2
Exercise 6 · r² — the share explained 12 min
compute it, then say what it does not tell you
Exercise 7 · Predict, and refuse to 15 min
ŷ at CHF 22, and why not at CHF 40
Exercise 8 · The lurking variable returns 10 min
the Week 1 scatter, coloured by neighbourhood

Status → outline only. Nothing here is interactive or counted yet.

Course page →