Lesson 18: Cautions about Correlation and Regression

October 31, 2024

Review:

• Tuesday activity data
• Pearson Correlation Coefficient
• R-Squared
• Schedule
  • Week of Nov 4 – Residuals (and maybe some election data)
  • Week of Nov 11 – Review and Exam 3 (Thu Nov 14)
  • Week of Nov 18 – Return Exam 3, portfolio check and Make Up Exam (Thu Nov 21)
  • Week of Nov 25 – Thanksgiving
  • Week of Dec 2 – Review for Final Exam (Tue Dec 10 at 10:30)

Presentation:

• Cautions about Correlation and Regression
  • Influential Observations
    • Outliers
    • Diabetes and blood sugar (p. 129-130)
    • Use Tuesday activity data
  • Lurking Variables
    • Explanatory variables not included
    • Beyond scope
• • 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 glucose level data

Presidential Election Year	Time Period	Ballots Cast (thousands)
2004	1	68.4
2008	2	73.9
2012	3	77.7
2016	4	78.7

• 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 2004 data
• Recalculate the linear regression equation and the corresponding R-Squared value
• Remove the 2016 data
• Recalculate the linear regression equation and the corresponding R-Squared value

Activity:

Price of Coffee ($ per pound)	Deforestation (%)
0.29	0.49
0.40	1.59
0.54	1.69
0.55	1.82
0.72	3.10

• Produce a scatter plot with Price of Coffee on the x axis and Deforestation on the y axis
• Find the linear regression equation and the corresponding R-Squared value
• Estimate Deforestation % assuming Price of Coffee is $0.90 per pound.
• Sensitivity Analysis
  • Identify and remove the most influential observation (use scatter plot)
  • Recalculate the linear regression equation and the corresponding R-Squared value
  • Recalculate Deforestation % assuming Price of Coffee is $0.90 per pound.

• Go back to Lesson 15 and use the data from the Activity section
• Follow the same process, i.e., look for outliers, remove and recalculate.