**Learning objectives**

- Distinguish between a linear and a nonlinear model
- Create vectors from functions by sampling
- Convert a linear modeling problem to a linear algebra problem, probably with no solutions
- Use projections to find a least squares fit
- Discuss the difference between a model and the real world phenomenon it models.

**Before class**

- Build a linear model and at least one nonlinear model of the Mauna Loa CO2 data. Make nice graphs of your models with the data superimposed. Be sure to label axes and include a title. Produce scatter plots of the residuals for both models.
- Read introduction to linear models
- Start reading Chapter 5 of the Linear Algebra Reader.
- Consult the main points of the lesson.

**In class**

- Answer questions about CO2 project
- Work through Chapter 5 of the Linear Algebra Reader
- Activity: which terms in a 2-variable quadratic are needed in a model?
- QUIZ 5 (vectors)

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