## Cautions about Regression and Correlation

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.

■ Correlation and regression lines describe only linear relationships. You can do the calculations for any relationship between two quantitative variables, but the results are useful only if the scatterplot shows a linear pattern.
■ Correlation and least-squares regression lines are not resistant. Always plot your data and look for observations that may be influential.
Extrapolation. Suppose that you have data on a child’s growth between 3 and 8 years of age. You find a strong linear relationship between age x and height y. If you fit a regression line to these data and use it to predict height at age 25 years, you will predict that the child will be 8 feet tall. Growth slows down and
then stops at maturity, so extending the straight line to adult ages is foolish. Few relationships are linear for all values of x. Don’t make predictions far outside the range of x that actually appears in your data.
Lurking variable. the relationship between two variables can often be understood only by taking other variables into account. Lurking variables can make a correlation or regression misleading.
You should always think about possible lurking variables before you draw conclusions based on correlation or regression.

E X T R A P O L AT I O N
Extrapolation is the use of a regression line for prediction far outside the range of values of the explanatory variable x that you used to obtain the line. Such predictions are often not accurate.

L U R K I N G V A R I A B L E
A lurking variable is a variable that is not among the explanatory or response variables in a study and yet may influence the interpretation of relationships among those variables.