4.2 Cautions about Correlation and Regression
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4.2 Cautions about Correlation and Regression Correlation and regression are powerful tools for describing the relationship between two variables. When you use these tools, you must be aware of their limitations, beginning with the fact that correlation and regression describe only linear

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4 2 cautions about correlation and regression correlation and regression are powerful tools for

4.2 Cautions about Correlation and Regression

Correlation and regression are powerful tools for

describing the relationship between two variables.

When you use these tools, you must be aware of

their limitations, beginning with the fact that

correlation and regression describe only linear

relationships.

Also remember that the correlation r and the

least-squares regression line are not resistant.


4 2 cautions about correlation and regression correlation and regression are powerful tools for

Extrapolation

Extrapolation is the use of a regression line

prediction far outside the domain of values of

the explanatory variable x that you used to

obtain the line or curve. Such predictions are

often not accurate.

Example:

Deriving an equation for baby weight and

age where the age only goes up to 12 months.

Then trying to predict a baby weight at 16

months.


4 2 cautions about correlation and regression correlation and regression are powerful tools for

Lurking Variables

A lurking variables is a variable that is not

among the explanatory or response variables in a

study and yet may influence the interpretation

of relationship among those variables.

A lurking variable can falsely suggest a strong

relationship between x and y or it can hide a

relationship that is really there.


4 2 cautions about correlation and regression correlation and regression are powerful tools for

The question of Causation

In many studies of the relationship between two variables, the goal is to establish that changes in the explanatory variable cause changes in the response variable.

Even when a strong association is present, the

conclusion that this association is due to a causal link between the variables is often elusive.


4 2 cautions about correlation and regression correlation and regression are powerful tools for

Explaining Association: causation

X

Y

Causation: changes in x cause a change in y

x =

y =

Note: rarely will you find a direct causation

relationship. Just about every relationship has more

than one variable causing the change.


4 2 cautions about correlation and regression correlation and regression are powerful tools for

Common Response

Common Response: changes in both x and y are caused by changes in a lurking variable z.

X

Y

Z


4 2 cautions about correlation and regression correlation and regression are powerful tools for

Confounding

Confounding: The effects (if any) of x on y is

confounded with the effect of a lurking variable z.

?

X

Y

Z


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