Cautions About Correlation and Regression Section 4.2

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Cautions About Correlation and RegressionSection
4.2
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CAUTIONS to keep in mind

• Extrapolation
• A prediction made based on a regression line for
  a value of x that is outside of the domain of
  values for the explanatory variable. Such
  predictions are often inaccurate. (Example Mile
  Run far in the future)
• Lurking Variables
• A variable that is NOT among the explanatory or
  response variables, that may influence the
  interpretation of the relationship among those
  variables. (Example Men, Women, Heart Disease
  Treatment)

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More Cautions

• Using Averaged Data
• When studies use averages from large numbers of
  people, resist the urge to apply the findings to
  the individuals.
• Averages will smooth out the deviations from the
  LSRL.
• CAUSATION
• A correlation does not imply a causation.
• Other explanations exist regarding the
  Association
• Common Response Confounding

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Explaining Association

• Causation A strong association may in fact be a
  result of a true causation.
• Sometimes there are more factors as well. (Ex
  BMI Mom, BMI daughter genetic IS the cause, but
  Diet, Exercise are also relevant)
• EXPERIMENTS are what we use to hold as many
  factors constant as possible.
• Yet, the finding might not generalize to other
  settings. (Ex Rats, Saccharin, Bladder Tumors)

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Explaining Association

• Common Response
• Beware the Lurking Variable
• The strong association between x and y might be a
  common response to some other variable z.
• Ex High SATs and High College Grades z the
  students ability and knowledge.
• Ex Amount of Money individuals invest, and how
  well the market does z underlying investor
  sentiment.

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Explaining Association

• Confounding Two variables are confounded when
  their effects cannot be distinguished from each
  other.
• Mixing in many different causes together at the
  same time (Ex Heredity, Diet, Exercise, Modeled
  Behavior, Couch Potato).
• EX Religious people live longer. It might not
  be the religion, it might be that hey also take
  better care of themselves less likely to smoke,
  drink, live excessively.
• EX More education and higher income. It might
  be the initial affluence that drives the ability
  to get the education.

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CAUSATION

• Carefully Designed Experiments
• Control the Lurking Variables
• Does Gun Control Reduce Violent Crime?
• Do Power Lines Cause Cancer?
• Ethical and Practical Constraints!

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Smoking Lung Cancer

• In the absence of and experiment, what is needed
  to establish Causation
• Strong Association (How strong is the association
  to start with for smoking and lung cancer, it
  is very strong)
• Consistent Association (Many studies, many
  countries, many different kinds of people)
• Higher Doses have Stronger Responses (People who
  smoke more, have greater incidents of cancer)
• Alleged Cause is Chronologically before the
  Effect (Deaths today are related to smoking from
  30 years ago)
• The Alleged Cause is Plausible (Animal Research)
• The evidence that Smoking Causes Lung cancer is
  OVERWHELMING but nothing beats a
  well-designed Experiment.