Example 11

EXAMPLE 11 Identifying when extrapolation occurs

Using the regression equation from Example 10, estimate the high temperature for the following low temperatures. If the estimate represents extrapolation, indicate so.

50°F
60°F

Solution

From Table 3, the smallest value of $x$ is 30°F and the largest is 50°F, so estimates for any value of $x$ between 30°F and 50°F, inclusive, would not represent extrapolation.

$\hat{y} = 1.4 (50) + 8 = 78 ° F$ . Because $x = 50 ° F$ lies between 30°F and 50°F, inclusive, this estimate does not represent extrapolation.
$\hat{y} = 1.4 (60) + 8 = 92 ° F$ . Because $x = 60 ° F$ does not lie between 30°F and 50°F, this estimate represents extrapolation.

NOW YOU CAN DO

Exercises 25c–36c.