Teacher guide — Grade 11, Unit 5: Regression with interpretation¶

Time: 3 lessons + project (about 5 periods). Track: B (code).

#	Lesson	Time
1	Simple regression revisited	40–45 min
2	Multiple regression	40–45 min
3	Checking the model	40–45 min
P	Unit project: Explain it, don't just fit it	2 periods

Before you start¶

Materials: Notebook notebooks/regression.ipynb.
Read docs/pedagogy/lesson-anatomy.md and docs/pedagogy/ai-use-policy.md.

If you have no computers / no internet¶

Use a printed scatter of birth weight vs visits; draw a line; read its slope.

Common misconceptions¶

Coefficient = causal effect. It is an association given the other variables.
High R² means a good model.

Differentiation¶

Support: give a partially filled table / sentence starters; pair with a data-steward role.
Stretch: ask "what would change your conclusion?" and "who is missing?"

Answer key (check questions)¶

Lesson 1: Simple regression revisited 1. Slope 0.04 kg per visit means…
Answer: Each extra visit goes with about 0.04 kg higher birth weight on average. 2. What does the intercept mean?
Answer: The predicted y when x = 0 (may not make sense). 3. What is minimised?
Answer: The sum of squared residuals.

Lesson 2: Multiple regression 1. 'Holding visits fixed' means…
Answer: Comparing mothers with the same number of visits. 2. Why might a coefficient shrink when adding a predictor?
Answer: Predictors share information. 3. Does a coefficient show cause?
Answer: Not by itself.

Lesson 3: Checking the model 1. What does R² = 0.4 mean?
Answer: 40% of the variation in y is explained by the model. 2. What pattern in residuals is a warning?
Answer: A curve or funnel shape. 3. Is high R² always good?
Answer: No: it depends on purpose and can reflect overfitting.

Assessment¶

Starter quiz each lesson (3 questions, one recalling the previous lesson); unit quiz in quiz.yml; project marked with the rubric in docs/pedagogy/assessment.md; 2-minute oral check per group.

Alignment¶

Enrichment aligned to NEB Grade 11–12 Computer Science (databases, programming) and Maths/Statistics.

Answers: practice exercises¶

Each extra bag of fertiliser is associated with about 15 kg more rice per ropani on average; 120 kg per ropani is the predicted yield with no fertiliser (meaningful only if such plots are in the data).
With k dummies plus an intercept the columns add up to the intercept column (perfect collinearity); one category must be the reference that the others are compared with.
"…75% of the variation in the outcome; 25% is left unexplained."
Quintile 2, 4 visits: 2.544 + 0.124 + 0.208 ≈ 2.88 kg; quintile 5: ≈ 3.06 kg. Difference 0.186 kg = 3 × 0.062 (the wealth coefficient, visits held fixed).
Coefficients: intercept 0.150, visits +0.074, wealth +0.022 → each extra visit goes with about 7 percentage points higher probability of facility delivery, wealth held fixed. Predictions here range 0.17–0.81, but in general a linear model can predict below 0 or above 1 (impossible probabilities) — logistic regression (Grade 12) fixes this.
Mean residual by wealth: quintile 1 −0.09, 2 −0.06, 3 0.00, 4 +0.02, 5 +0.14 kg — the visits-only model systematically under-predicts rich mothers' babies and over-predicts poor ones: wealth is a missing predictor.
Students who study more also tend to take more tuition; a model with both cannot tell which one matters, and the coefficients swing between samples.
Who the workers were (sample), what else differs between more- and less-schooled workers (family wealth, location, ability — confounders), whether it is an experiment or observational, the interval for the coefficient, whether the relationship is linear.
fake correlates 0.98 with wealth: coefficients split arbitrarily (wealth 0.053, fake 0.026) and their bootstrap intervals become wide and include 0 (≈ −0.02 to 0.12 and −0.05 to 0.10) although wealth clearly matters.
Yes: bootstrap R² ≈ 0.06 to 0.12.

Lesson 3: bootstrap 95% intervals (1,000 resamples, seed 0) — visits 0.033 to 0.068 kg; wealth 0.046 to 0.079 kg.

Real-data exercises: notes¶

R1 Flipper coefficient shrinks once species is included (species differ in both size and flipper length).
R2 The income coefficient usually shrinks when a health-system variable is added — those variables are partly how income works.
R3 Expect −0.5 to −0.6 °C per 100 m; adding latitude changes it little within Nepal's narrow latitude range.