LESSON: Extrapolation & Predicted Values

Extrapolation & Interpolation

When we use a regression line (linear or nonlinear) to make a prediction about are data set, there are two types of predictions that can be made:

Extrapolation

Extrapolated predictions are those that are made outside of the known data points. Trends in the known data can often be used to make accurate extrapolated predictions; however, this is not always the case. That's why it's best to avoid making extrapolated predictions. 

For example, a young man's parents kept track of his height through the years, as shown in the graph below. Extrapolation shows that Bryan will be about 10 feet tall when he's 30 years old. What faulty assumption was made in this extrapolation?

Data on Bryan's height was only tracked from his birth through 17 years. This data shows a very strong linear regression. However, we all know as people age they stop growing taller. So after 17 years, we would expect the regression line to flatten. Since the regression line only tracks to age 17, we can't accurately predict what will happen after that. That's why a predicted height of 10 feet tall when Bryan is 30 years old is inaccurate. It was an extrapolated prediction.

Interpolation

Interpolated predictions are those that are made between known data points. An interpolation of this data would lead one to the prediction that Bryan was about 4.5 ft tall at the age of 14. Is this a reasonable prediction?

Was your interpolated prediction more or less accurate than your extrapolated prediction? Typically, interpolated predictions are more accurate. Why do you think this is so?