2 Linear Models

Learning Objectives

By the end of this chapter, you will be able to:

Write a linear model in matrix form and build X for a given design
Compare parameterizations and show they give identical fitted values
Solve (X’X)⁻X’y by hand and reproduce it with lm()
Explain estimability and why individual solutions need not be unique
Interpret residuals and estimate σ²e

Assumes Ch 1.

Chapter in progress

This chapter has not been written yet. The objectives above are the contract it will be written against — they are taken from CHAPTERS.md, which is the outline for the whole book.

Purpose. Fixed effects only. Build X, solve the normal equations, confront non-full-rank.

---
title: "Linear Models"
---

::: {.callout-note icon=false}
## Learning Objectives

By the end of this chapter, you will be able to:

1. **Write** a linear model in matrix form and build **X** for a given design
2. **Compare** parameterizations and show they give identical fitted values
3. **Solve** (X'X)⁻X'y by hand and reproduce it with `lm()`
4. **Explain** estimability and why individual solutions need not be unique
5. **Interpret** residuals and estimate σ²e
:::

*Assumes Ch 1.*

::: {.callout-warning}
## Chapter in progress

This chapter has not been written yet. The objectives above are the contract it will be written
against — they are taken from `CHAPTERS.md`, which is the outline for the whole book.

**Purpose.** Fixed effects only. Build **X**, solve the normal equations, confront non-full-rank.
:::