Question

extrapolating data
the regression calculator shows the relationship between the hours devin spent playing a video game, x, and the levels he achieved, y. which number of hours can be used to make an extrapolation of the level he could achieve?
2
3
4
5
linear regression
$y\approx 1.62x + 0.117$; $r\approx 0.92$
window: $0.14995\leq x\leq 4.35$
$0.39995\leq y\leq 7.6$

Explanation:

Step1: Understand extrapolation

Extrapolation is predicting values outside the range of the given data. The given \(x -\) values (hours) range from \(0.5\) to \(4\) (from the data table \(x = 0.5,1,1,1.5,2,2,2.5,3.5,3.5,4\)).

Step2: Check each option

• For \(x = 2\): \(2\) is within the range \(0.5\leq x\leq4\) (interpolation).
• For \(x = 3\): \(3\) is within the range \(0.5\leq x\leq4\) (interpolation).
• For \(x = 4\): \(4\) is at the upper - bound of the given data range (not extrapolation).
• For \(x = 5\): \(5>4\), which is outside the range of the given \(x -\) values.

Answer:

\(5\)