Extrapolation
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Extrapolation occurs when x-values or y-values fall outside the reasonable range of values that would occur.
Scenario: Crammer Nation University wants to develop a regression equation to predict the "Number of Recruits" a given fraternity will receive this rush season given the "Parties Thrown" by the fraternity last year. They take a random sample of 52 fraternities on campus, resulting in the regression output below.
y-hat = 85.8312 + 20.5313(x1)
This regression line assumes and infinite number of students at Crammer Nation University.
The fact of the matter is... a chapter can't get more recruits than the entire student population! The dotted portion of the red line represents this extrapolation of our linear regression!
Imagine a chapter threw 45 parties...
y-hat = 85.8312 + 20.5313(45)
y-hat = 85.8312 + 923.9085
y-hat = 1009.7397
The predicted value is 1009.7397 recruits... but the entire student population at Crammer Nation University is 750 students!