Cautions About Correlation and Regression Section 4.2

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) 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) 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)

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

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) 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. 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) Yet, the finding might not generalize to other settings. (Ex: Rats, Saccharin, Bladder Tumors)

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.

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.

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

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); 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); 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); 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); 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 Alleged Cause is Plausible (Animal Research) The evidence that Smoking Causes Lung cancer is OVERWHELMING … but nothing “beats” a well- designed Experiment.