## Lesson 17: Pearson Correlation Coefficient and R-Squared

October 29, 2024

Review:

- Linear Regression
- Pueblo County 2020 voter turnout estimates

Presentation:

- Correlation and R-Squared
- Pearson Correlation Coefficient
- r = SSxy/√(SSxx*SSyy)
- -1 < r < 1

- R-Squared
- Calculate r and then square the result, i.e., =r^2
- 0 < r^2 < 1

- Example
- Use Beer Party
- Sample data: {(2,3), (4,6), (7,9), (11,12)}
- Calculate Pearson Correlation Coefficient (r)
- Calculate R-Squared

- Pearson Correlation Coefficient

Activity:

x | y |

10 | -30 |

3 | -2 |

5 | -10 |

1 | 6 |

6 | -14 |

- Use the data above
- Make a scatterplot
- Calculate the Sum of Squares
- Calculate the linear regression equation
- Calculate the Pearson Correlation Coefficient
- Calculate R-Squared

Femur (cm) | Humerus (cm) |

38 | 41 |

56 | 63 |

59 | 70 |

64 | 72 |

74 | 84 |

- Use the data above
- Make a scatterplot
- Calculate the Sum of Squares
- Calculate the linear regression equation
- Calculate the Pearson Correlation Coefficient
- Calculate R-Squared