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Cautions About Correlation and Regression Section 4.2

Cautions About Correlation and Regression Section 4.2. CAUTIONS … to keep in mind …. Extrapolation –

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Cautions About Correlation and Regression Section 4.2

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  1. Cautions About Correlation and RegressionSection 4.2

  2. 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)

  3. 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

  4. 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)

  5. 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.

  6. 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.

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

  8. 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.

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