Question

a line of best fit is drawn for the set of points shown on the graph.
data
x | y
5 | 8.9
6 | 11.4
8 | 13.6
8 | 14
10 | 15.3
11 | 12.25
14 | 22.1
15 | 21.8
16 | 20.8
18 | 24.5
(linear regression: $y \approx 1.14x + 3.805; r \approx 0.946$)
which point is an approximate extrapolation for $x = 30$ from the line of best fit?
$\circ$ $(23, 30)$
$\circ$ $(30, 38)$
$\circ$ $(44, 30)$
$\circ$ $(30, 72)$

Explanation:

Step1: Use the line equation

The line of best fit is given by \( y \approx 1.14x + 3.805 \). We need to find the \( y \)-value when \( x = 30 \).

Step2: Substitute \( x = 30 \) into the equation

Substitute \( x = 30 \) into \( y = 1.14x + 3.805 \):
\( y \approx 1.14(30) + 3.805 \)
Calculate \( 1.14 \times 30 = 34.2 \), then \( 34.2 + 3.805 = 38.005 \), which is approximately 38. So the point is \( (30, 38) \).

Answer:

(30, 38)