## Lesson 8: Linear Regression

September 24, 2018

Review:

- Scatterplots
- Sum of Squares
**China****Travel**informational meeting**Thu, Sep 27****3:30p-5:30p****HSB 108**- Come and go as you please
- Scholarships and fundraising assistance available

Presentation:

- Linear regression (simple, bivariate)
- Calculate equation of the regression line
- y-hat = b1*x + bo
- b1 = “slope” of the line
- b0 = “y-intercept”

- Calculate Sum of Squares: SSxx, SSyy, SSxy
- b1 = SSxy/SSxx
- b0 = (∑y/n) – b1*(∑x/n)

- y-hat = b1*x + bo
- Example
- Beer party data: {(60,10), (70,12), (80,20), (90,40)}
- Calculate slope (b1) and y-intercept (b0) for linear equation
- Estimate Beer consumption when temperature is 75 degrees
- Solve for y-hat when x = 75, x = 85, x = 100 (be careful!)

- Video

- Calculate equation of the regression line

Activity:

- Estimate 2018 voter turnout in Pueblo County using the data below
- Create a Scatterplot
- Calculate Sum of Squares: SSxx, SSyy, SSxy
- Calculate slope and intercept for the regression line and write the linear equation
- Use the regression equation to estimate turnout in 2018
- Solve for y-hat when x = 5

Midterm Election | Time Period | Ballots Cast |

2002 | 1 | 49,304 |

2006 | 2 | 52,957 |

2010 | 3 | 54,471 |

2014 | 4 | 60,543 |

Assignment:

- Estimate voter turnout for the State of Colorado and bring to class on Wed
- Gather data from the Colorado Secretary of State Election Results website
- Use linear regression to estimate turnout, like we did in the activity

- Read pp. 101-105, Correlation and pp. 108-115, Least Squares Regression