3.3.8: Extrapolation

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When using the model to make predictions, care must be taken to only choose values of \(X\) that are in the range of \(X\) values of the data. In the rainfall/sales example, the values of \(X\) range from 10 to 40 inches of rainfall. Choosing a value of \(X\) outside this range is called extrapolation and could lead to invalid results. For example, if we use the model to predict sales for a city with 80 inches of rainfall, we get an impossible negative result for sales:

\(\hat{Y}=45.647-.767 X\)

\(\hat{Y}_{80}=45.647-.767(80)=-15.7\)