Question

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 = 1.62x + 0.117; r ≈ 0.92 0.14906 ≤ x ≤ 4.35 0.30906 ≤ y ≤ 7.6

Explanation:

Step1: Understand Extrapolation

Extrapolation uses a model (here, linear regression \( y = 1.62x + 0.117 \)) to predict values outside the original data range. The original \( x \)-values (hours) in the data are from \( 0.5 \) to \( 4 \) (from the table: \( 0.5, 1, 1, 1.5, 2, 2, 2.5, 3.5, 3.5, 4 \)).

Step2: Analyze Options

• Option 2: \( x = 2 \) is within the original \( x \)-range (\( 0.5 \leq x \leq 4 \)) → this is interpolation, not extrapolation.
• Option 3: \( x = 3 \) is within the original \( x \)-range → interpolation.
• Option 4: \( x = 4 \) is at the upper limit of the original \( x \)-range (data includes \( x = 4 \)) → not extrapolation.
• Option 5: \( x = 5 \) is outside the original \( x \)-range (\( 0.5 \leq x \leq 4 \)) → this is extrapolation (using the model to predict beyond the observed data).

Answer:

\( \boldsymbol{5} \) (corresponding to the option: 5)