Cautions About Correlation Cautions About Correlation and Regressionand Regression

Section 4.2Section 4.2

CAUTIONS … to keep in mind …CAUTIONS … to keep in mind …

ExtrapolationExtrapolation – – A prediction made based on a regression line for a A prediction made based on a regression line for a

value of x that is outside of the domain of values for value of x that is outside of the domain of values for the explanatory variable. Such predictions are often the explanatory variable. Such predictions are often inaccurate. (Example … Mile Run far in the future)inaccurate. (Example … Mile Run far in the future)

Lurking VariablesLurking Variables – – A variable that is NOT among the explanatory or A variable that is NOT among the explanatory or

response variables, that may influence the response variables, that may influence the interpretation of the relationship among those interpretation of the relationship among those variables. (Example …Men, Women, Heart Disease variables. (Example …Men, Women, Heart Disease Treatment)Treatment)

More Cautions …More Cautions …

Using Averaged DataUsing Averaged Data – – When studies use averages from large numbers of When studies use averages from large numbers of

people, resist the urge to apply the findings to the people, resist the urge to apply the findings to the individuals.individuals.

Averages will smooth out the deviations from the Averages will smooth out the deviations from the LSRL.LSRL.

CAUSATIONCAUSATION – – A correlation does not imply a causation.A correlation does not imply a causation. Other explanations exist regarding the Association – Other explanations exist regarding the Association –

Common Response & ConfoundingCommon Response & Confounding

Explaining AssociationExplaining Association

CausationCausation: A strong association may in : A strong association may in fact be a result of a true causation.fact be a result of a true causation. Sometimes there are more factors as well. Sometimes there are more factors as well.

(Ex: BMI Mom, BMI daughter – genetic IS the (Ex: BMI Mom, BMI daughter – genetic IS the cause, but Diet, Exercise are also relevant)cause, but Diet, Exercise are also relevant)

EXPERIMENTS are what we use to hold as EXPERIMENTS are what we use to hold as many factors constant as possible.many factors constant as possible.

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

Explaining AssociationExplaining Association

Common ResponseCommon Response – – ““Beware the Lurking Variable”Beware the Lurking Variable” The strong association between The strong association between xx and and yy might might

be a common response to some other be a common response to some other variable variable zz..

Ex: High SATs and High College Grades – z = the Ex: High SATs and High College Grades – z = the students ability and knowledge.students ability and knowledge.Ex: Amount of Money individuals invest, and how Ex: Amount of Money individuals invest, and how well the market does – z = underlying investor well the market does – z = underlying investor sentiment.sentiment.

Explaining AssociationExplaining AssociationConfoundingConfounding – Two variables are confounded – Two variables are confounded when their effects cannot be distinguished from when their effects cannot be distinguished from each other.each other.Mixing in many different causes together at the Mixing in many different causes together at the same time (Ex: Heredity, Diet, Exercise, same time (Ex: Heredity, Diet, Exercise, Modeled Behavior, Couch Potato).Modeled Behavior, Couch Potato). EX: Religious people live longer. It might not be the EX: Religious people live longer. It might not be the

religion, it might be that hey also take better care of religion, it might be that hey also take better care of themselves – less likely to smoke, drink, live themselves – less likely to smoke, drink, live excessively.excessively.

EX: More education and higher income. It might be EX: More education and higher income. It might be the initial affluence that drives the ability to get the the initial affluence that drives the ability to get the education.education.

CAUSATIONCAUSATIONCarefully Designed ExperimentsCarefully Designed ExperimentsControl the Lurking VariablesControl the Lurking VariablesDoes Gun Control Reduce Violent Crime?Does Gun Control Reduce Violent Crime?Do Power Lines Cause Cancer?Do Power Lines Cause Cancer?Ethical and Practical Constraints!Ethical and Practical Constraints!

Smoking & Lung CancerSmoking & Lung CancerIn the absence of and experiment, what is needed In the absence of and experiment, what is needed to establish “Causation”: to establish “Causation”: Strong AssociationStrong Association (How strong is the association to (How strong is the association to

start with – for smoking and lung cancer, it is very start with – for smoking and lung cancer, it is very strong); strong);

Consistent AssociationConsistent Association (Many studies, many countries, (Many studies, many countries, many different kinds of people); many different kinds of people);

Higher Doses have Stronger ResponsesHigher Doses have Stronger Responses (People who (People who smoke more, have greater incidents of cancer); smoke more, have greater incidents of cancer);

Alleged Cause is Chronologically before the EffectAlleged Cause is Chronologically before the Effect (Deaths today are related to smoking from 30 years ago);(Deaths today are related to smoking from 30 years ago);

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