Lesson 16: Linear Regression

October 24, 2024

Review:

• Exam 2 review
• Scatterplots
• Sum of Squares

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)
  • 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
    • Download the Beer Party Regression Example
  • Video: Fitting Lines to Data

Demonstrate in Sheets:

• Forecast 2020 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 forecast Ballots Cast in 2020
    • Hints
      • Use Time Period (rather than year) as the independent (x) variable
      • Use Ballots Cast as the dependent (y) variable
      • To forecast 2020 turnout, solve for y-hat when x = 5
      • To forecast 2024 turnout, solve for y-hat when x = 6

Presidential Election Year	Time Period	Ballots Cast
2004	1	68,371
2008	2	73,881
2012	3	77,671
2016	4	78,652

Assignment in Sheets:

• Download the Snowpack and Runoff in the Arkansas River Basin
• Generate a scatter plot
  • x-axis = Column B “Freemont Pass Snow H2O Equiv (in) on March 1” and
  • y-axis = Column C: Arkansas R at Pueblo Streamvolume Observed (ac_ft) in May”
• Add a Trendline and display the linear Equation
• Create a function in Sheets to estimate runoff based on snowpack
• Generate runoff estimates assuming x=5, 10, 15, 20 and 25 inches snowpack (produce 5 forecasts)