Download 4.2 Correlation Cautions

Cautions About Correlation
and Regression
Section 4.2
CAUTIONS … to keep in mind …
Extrapolation –
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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 –
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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 –
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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 –
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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.
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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)
Explaining Association
Common Response –
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“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.
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).
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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”:
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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 welldesigned Experiment.