How many pushups someone can do can be correlated to the distance they run. The regression equation for this is pushups = 0.72 +
7.62 miles. When you used the equation to determine how many miles someone should be able to run if that person does 24 push-ups, was that an example of interpolation or extrapolation?
Determining the Number of miles a person who does 24 push-ups should be able to run is an example of extrapolation, this is because we are making a prediction into the the future or outside our data based on the available information. Regression equations are used for extrapolation (making future predictions). Interpolation on the other hand makes estimation within the limit of the data usually between two known values.
