John's parents recorded his height at various ages up to 66 months. Following is a record of their results:
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?
$$\begin{array} { | l | l | l | l | l | l | }
\hline \text { Age (months) } & 36 & 48 & 54 & 60 & 66 \
\hline \text { Height (inches) } & 35 & 38 & 41 & 43 & 45 \
\hline
\end{array}$$ John's parents decide to use the least-squares regression line of John's height (y) on age (x) based on these data to predict his height at age 21 years. What can we conclude based on this information?

Question

John's parents recorded his height at various ages up to 66 months. Following is a record of their results:
?
?
$$\begin{array} { | l | l | l | l | l | l | } 
\hline \text { Age (months) } & 36 & 48 & 54 & 60 & 66 \
\hline \text { Height (inches) } & 35 & 38 & 41 & 43 & 45 \
\hline
\end{array}$$ John's parents decide to use the least-squares regression line of John's height (y) on age (x) based on these data to predict his height at age 21 years. What can we conclude based on this information?

Quizplus · Accepted Answer

Extrapolation involves using data to make predictions outside the range of data that was used to make the model. In this case, John's parents are trying to predict his height at age 21 years, which is far outside the range of data they have collected. This means that the prediction is an extrapolation and therefore may not be accurate. While the data are clearly correlated and a regression line can be calculated, this does not ensure the accuracy of predictions outside the range of data.

John's Parents Recorded His Height at Various Ages Up to 66