# Simple linear regression – part 1

08/31/2020

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## Outline

• The following topics will be covered in this lecture:

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

## Introducing linear models

• 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?

### Introducing linear models – continued

• 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.

### Introducing linear models – continued

• Q: given the data on the left, can you propose a valid linear model for the relationship between $$x$$ and $$y$$?