Question

use the line of fit, $hat{y} = 0.333x + 3.7$, to predict how many meets are won if the swimmer practices for 20 hours next week. explain whether this is an example of extrapolation.
10 360 this is not extrapolation because it is a reasonable prediction
10 300 this is extrapolation because it is far outside the domain of hours at practice
48 949 this is extrapolation because it is far outside the domain of hours at practice
48 949 this is not extrapolation because it is a reasonable prediction

Explanation:

Step1: Substitute \(x = 20\) into the line - of - fit equation

We have the line of fit \(\hat{y}=0.333x + 3.7\). Substitute \(x = 20\) into the equation: \(\hat{y}=0.333\times20+3.7\).
First, calculate \(0.333\times20 = 6.66\). Then, \(\hat{y}=6.66 + 3.7\).

Step2: Calculate the value of \(\hat{y}\)

\(\hat{y}=6.66+3.7=10.36\approx10.36\).
Looking at the \(x\) - axis (practice hours) in the scatter - plot, the maximum \(x\) value (from the data points) is much less than \(20\). Extrapolation is the process of estimating a value outside the range of the known data points. Since \(x = 20\) is far outside the domain (range of \(x\) values from the data points) of hours of practice in the scatter - plot.

Answer:

10.36; this is extrapolation because it is far outside the domain of hours of practice.