08/31/2020

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The following topics will be covered in this lecture:

- Linear models
- Simple linear regression
- Basic regression assumptions
- The process of creating a regression model

- In past mathematics courses, we have seen many examples of linear models.
- Suppose that we wish to model a relationship between two variables, \( x \) and \( y \) to the left.
- We will call \( y \) a
**dependent variable**, or the**response variable**. - On the other hand, we will call \( x \) an
**independent variable**, an**explanatory variable**or a**predictor variable**for the response. **Q:**can you propose a valid linear model for the relationship between the response and the predictor?

**A:**actually, any line that passes through the point is a valid linear model.- Particularly, this relationship is underconstrained and there exists infinitely many choices of linear models;
- given the current data, any choice is as valid as any other.

**Q:**given the data on the left, can you propose a valid linear model for the relationship between \( x \) and \( y \)?