Week 6 · Simple and multiple regression. Bias. Linearity
Recap of the t-test, then the regression line, OLS, multiple regression, bias and efficiency, the six assumptions and linearity
The longest deck of the programme. It opens with an exam-style t-test assignment, then introduces simple linear regression on farmland prices, extends it to multiple regression, and discusses what the estimates mean, when they are biased and efficient, and which assumptions guarantee that. The first assumption, linearity, is worked through in detail. A self-study section on the origins of regression closes the deck.
Slides
| Material | WS 2024/25 | WS 2023/24 |
|---|---|---|
| 🖥 Interactive slides | Week 06. Recap. Simple Linear Regression. Multiple Regression. Bias. Regression assumptions. Linearity | not rendered (sources were revised for 2024/25) |
| 🖥 Standalone part | t-test recap: example of an exam assignment | |
| 📄 PDF from Ilias | Week 06 (version 1).pdf · 92 pages · added 19 Nov 2024 Week 06 (version 2).pdf · 93 pages · added 27 Nov 2024 |
Week 06. Recap. Simple Linear Regression. Multiple Regression. Bias. Regression assumptions. Linearity.pdf · 95 pages · added 23 Jan 2024 |
| 💻 Source | mk68-06-slides.qmd, which includes t-test-recap.qmd, very-simple-regression.qmd, MLR.qmd, mk68-07-Bias-Efficiency.qmd and linearity-simple.qmd |
mk68-06-slides.qmd |
What the deck covers
- Example of an exam assignment (the t-test recap): a definition question, problem introduction, descriptive analysis, checks and balances, the effect of technology and of variety on rice yields, how to measure the effect of nitrogen fertiliser, and a framework for interpreting any statistical test.
- (Very) simple linear regression: regression on population and sample; plot size and farmland prices; the regression line; coefficients and their interpretation; the OLS algorithm; the population regression function and random sampling; sample variation; inference; goodness of fit; key takeaways and self-study examples, including CFC-11 in the stratosphere.
- Multiple regression: vocabulary, motivation and interpretation; examples (the wage equation, test scores and spending, CEO salary); mechanics; a full example on the effect of fuel taxes on petrol consumption, from problem formulation and exploratory analysis to estimating simple and multiple regressions and interpreting each coefficient.
- Bias and efficiency: sampling from the population; unbiased and efficient, unbiased but inefficient, biased but efficient, biased and inefficient estimates.
- Assumptions of the MLR: the six assumptions and what each group of them guarantees (unbiased; BLUE; classical linear model).
- Assumption 1, linearity: can we draw a straight line through the dots; detection with residual plots; resolutions; common linear transformations; the Anscombe quartet.
- Key concepts checklist and a self-study section on the cradle of regression analysis: Galton, Yule and the dark past of statistics.
Data used
- 📊 CFC-11 daily means at Mauna Loa (
CATS_mlo_F11_Day.dat), for the self-study ozone example. fuel2001(US fuel consumption by state) from the alr4 R package.gomez.splitsplit(rice yields by technology and variety) from the agridat R package, in the t-test recap.- A simulated population of farmland plots, generated by
01-simple-reg-plots.R.
Where the course goes next
← Week 5 · Central Limit Theorem. t-distribution. Confidence intervals · → Week 7 · Multiple linear regression. Practice