This is the graded finale for the whole course. It pulls every thread together — the signal-plus-noise machinery, Galton and the birth of the word “regression”, the regression fallacy and its control-group cure, the praise-and-punishment illusion, and the razor-thin line between regression and the gambler’s fallacy. Read each question twice: several look easy until you notice a hidden regression trap hiding in the wording, and the tempting answer is usually the one the whole course was built to inoculate you against.
How this exam works
Questions appear one at a time. Once you submit an answer it LOCKS — there is no going back, no retry, and no restart, so commit before you click. Your score stays hidden until the very end, when you find out whether you cleared the bar. The pass mark is 70 percent. A few questions ask you to select ALL correct options, not just the single best one — read the prompt carefully.
A test has reliability 0.5, and its scores have a mean of 50. A student scores 90 on the first sitting. Using expected retest = mean + reliability×(observed − mean), what score should you expect on their retest?
Select an answer to continue.
Course Recap
Big picture
Regression to the Mean — the whole course on one map
- Regression to the Mean
- 01 · Signal + Noise
- The core mechanic
- Every observation is a stable signal plus transient noise. Selecting on an extreme observation preferentially selects for extreme noise, which by definition does not repeat, so the next measurement drifts back toward the signal. Reliability is the signal’s share of the variation, and the best forecast is expected retest = mean + reliability×(observed − mean): a value of 90 on a mean-50, reliability-0.5 test predicts a 70, moving partway back but not all the way to the mean.
- The core mechanic
- 02 · Galton’s Discovery
- Where the word comes from
- Galton found that tall parents have tall-but-shorter children and short parents have short-but-taller children — children of extreme parents land closer to the population mean. He named it "regression toward mediocrity", the literal origin of the term. It is not humanity converging on one height and not a reversal: regression is symmetric, works both directions, describes only selected extremes, and the population keeps its full spread because average parents scatter widely.
- Where the word comes from
- 03 · The Regression Fallacy
- Crediting reversion to an intervention
- The fallacy is claiming an intervention caused an improvement that regression would have delivered anyway. It powers the Sports Illustrated cover curse (covers pick peaks that regress down), speed cameras at the worst intersections (worst-sites-first selection regresses down), and feeling better after the doctor (you visit at a symptom trough of a self-limiting illness). The fix is a control group selected the same way: it measures how much pure regression produces, so the treatment effect is the difference in differences.
- Crediting reversion to an intervention
- 04 · Praise, Punishment & Superstition
- The feedback illusion
- Kahneman’s flight instructors praised after peaks (which regress down) and punished after troughs (which regress up), then concluded praise hurts and punishment works. It is pure timing: punishment fires right before inevitable upward reversion, so it steals the credit and falsely appears effective, while praise appears to backfire. The same engine drives superstition, quack cures, and managerial over-reaction — people intervene at extremes, regression delivers a bounce, and the ritual gets miscredited.
- The feedback illusion
- 05 · Telling It Apart & Defending
- Regression vs. trends vs. the gambler’s fallacy
- Regression is a one-time move back toward the mean after an extreme; a real trend is a sustained drift that persists across many measurements. The gambler’s fallacy differs on independence: roulette spins have no memory so nothing is "due", whereas a retest is correlated through a shared signal so conditioning on an extreme legitimately predicts reversion. Neither involves a compensating force. The toolkit: expect reversion, run control groups, use bigger samples and multiple periods, and apply shrinkage — pull extreme estimates toward the mean by the noise share before acting.
- Regression vs. trends vs. the gambler’s fallacy
- 01 · Signal + Noise
Key takeaways
Regression to the mean is not a force, a curse, or a compensating hand — it is the statistical shadow of imperfect correlation. Whenever you select cases for being extreme, some of that extremeness was lucky (or unlucky) noise that will not repeat, so the next measurement drifts back toward the signal. That single fact explains Galton’s shrinking-toward-mediocrity children, the cover curse, the worst-sites-first camera “success”, the doctor who cures self-limiting illness, and the flight instructor who wrongly learns that punishment beats praise. Your defenses are always the same: expect reversion after any extreme, demand a control group before crediting an intervention, prefer larger samples and multiple time periods, and shrink noisy estimates toward the mean. And never confuse regression with the gambler’s fallacy — one conditions on a shared signal, the other invents a memory that independent events simply do not have.