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education/statistics/Correlation and Regression.md
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@@ -64,6 +64,11 @@ https://www.thoughtco.com/how-to-calculate-the-correlation-coefficient-3126228
# Regression # Regression
(Chapter 10, STAT 1040) (Chapter 10, STAT 1040)
## Notes ## Notes
### Explanatory and Response Variables
- Regression uses values of one variable to predict values for a related value. - Regression uses values of one variable to predict values for a related value.
- The variable you are trying to predict is called the *response variable*. It is graphed along the *y-axis*. - The variable you are trying to predict is called the *response variable*. It is graphed along the *y-axis*. This is the thing being predicted/measured.
The variable you have information about that you are using to make the prediction is called the *explanatory variable*. It is graphed along the *x-axis*. - The variable you have information about that you are using to make the prediction is called the *explanatory variable*. It is graphed along the *x-axis*. This is the treatment.
- Just because a relationship exists between $x$ and $y$ *does not* mean that changes in $x$ *cause* changes in $y$.
- If the graph is given to you already set up, you already know the response and explanatory variables.
- The $\sigma$ line will always always have a slope of:
$$\frac{\sigma_x}{\sigma_y}$$