Lesson 10: Cautions about Correlation and Regression

October 1, 2018

Review:

• Pearson Correlation Coefficient
• R-Squared
• Exam 2 on Mon, Oct 8
• Sheets assignments due this Friday (10/5) by 5pm

Presentation:

• Cautions about Correlation and Regression
  • Influential Observations
    • Outliers
    • Diabetes and blood sugar (p. 129-130)
  • Lurking Variables
    • Explanatory variables not included
    • High School math and success in college (p. 132-133)
  • The Question of Causation
    • Correlation does not imply causation
    • Spurious Correlations
    • Retrospective study = looking back to find possible causes for an established outcome among a sample population
    • Prospective studies = following a sample population over time and studying behaviors possibly linked to likelihood of an outcome
    • Video
  • Extrapolation
    • Use of regression for prediction far outside the range of the explanatory variable
    • Predictions outside the range are unreliable
    • Further outside the range = less reliable predictions
  • Sensitivity Analysis Demonstration
    • Remove influential observations and recalculate regression equation and R-Squared
    • Use Pueblo Voter Turnout data

    • Midterm Election	Time Period	Ballots Cast
      2002	1	49,304
      2006	2	52,957
      2010	3	54,471
      2014	4	60,543

    • Produce a scatter plot with Time Period on the x axis and Ballots Cast on the y axis
    • Find the linear regression equation and the corresponding R-Squared value
    • Remove the 2002 data
    • Recalculate the linear regression equation and the corresponding R-Squared value
    • Remove the 2014 data
    • Recalculate the linear regression equation and the corresponding R-Squared value

Activity:

• CSU-Pueblo finished 5th in a recent Women’s golf tournament with individual results displayed below.
  

  Position	Player (seed)	Round 1	Round 2	Total
  T8	Jolene Kam (3)	72	73	145
  T23	Courtney Ewing (1)	75	75	150
  T34	Rachanok Rahulpan (4)	74	78	152
  T45	Orakorn Thirayatorn (2)	78	77	155
  T72	Amy Sutheran (5)	78	83	161

  • Produce a scatter plot with Round 1 scores on the x axis and Round 2 scores on the y axis
  • Find the linear regression equation and the corresponding R-Squared value
  • Identify the most influential observation
  • Omit the observation you think is most influential
  • Recalculate the linear regression equation and the corresponding R-Squared value

Assignment:

• Use Sheets and results from a recent Women’s golf tournament
  • Go to the “Team Results” worksheet
    • Plot the data with Round 1 scores on the x axis and Round 2 scores on the y axis
    • Find the linear regression equation and the corresponding R-Squared value
    • Identify the most influential observation(s)
    • Omit the observation(s) you think are most influential
    • Recalculate the linear regression equation and the corresponding R-Squared value
  • Go to the “Individual Results” worksheet
    • Plot the data with Round 1 scores on the x axis and Round 2 scores on the y axis
    • Find the linear regression equation and the corresponding R-Squared value
    • Identify the most influential observation(s)
    • Omit the observation(s) you think are most influential
    • Recalculate the linear regression equation and the corresponding R-Squared value