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)

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 %?