## Lesson 9: Pearson Correlation Coefficient and R-Squared

September 26, 2018

Review:

**China****Travel**informational meeting**Thu, Sep 27 (tomorrow)****3:30p-5:30p****HSB 108**- Come and go as you please
- Scholarships and fundraising assistance available

- Linear Regression
- 2018 Colorado voter turnout
- Sample of turnout estimates

Presentation:

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

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

- Demonstrate in Sheets
- =PEARSON(y range, x range)
- =RSQ(y range, x range)

- 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

Assignment:

- Use 2013 MLB Team Stats and complete the following in Sheets
- Use Win % as the dependent/response (y) variable
- Use each of the other 6 variables (ERA, RBI, Slug, WS Mgr, BB, Payroll) as independent/explanatory (x) variables
- Calculate the Pearson Correlation Coefficient for each explanatory variable and Win % pair (ERA and Win%, RBI and Win%, etc) and characterize (describe) the nature of each correlation.
- Which independent/explanatory variable has the strongest relationship with Win %?