Statistics / Unit 4: Two-Variable Data
4.6 Cautions: Extrapolation and Causation
Notes
- Extrapolation is using the line to predict for $x$-values outside the range of the data. These predictions can be unreliable.
- Outliers and influential points (far from the others in the $x$-direction) can strongly change the line and $r$.
- Correlation does not imply causation. A lurking variable that affects both variables can create an association.
- Only a well-designed experiment (see Unit 5) can show that one variable causes a change in another.
- Example: Ice cream sales and drownings are positively associated. Hot weather is a lurking variable that raises both.
Practice
Ice cream sales and swimming-pool drownings are strongly positively correlated across months. The best explanation is:
Warm weather increases both ice cream sales and swimming.
A regression line is built from children aged 5 to 12 and then used to predict a person's height at age 40. This is a problem because it is:
Age 40 is far outside the data range, so the prediction is unreliable.
A survey finds $r = 0.9$ between hours of sleep and grades. Which conclusion is justified?
A survey shows association only, not cause and effect.
Ready for more? Take the Unit 4 test.