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 ≈ 1.14x + 3.805; r ≈ 0.946
-1 ≤ x ≤ 19.3
-1 ≤ y ≤ 26
which point is an approximate extrapolation for x = 30 from the line of best fit?
○ (23, 30)
○ (30, 38)
○ (44, 30)
○ (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 \( y \) when \( x = 30 \).

Step2: Substitute \( x = 30 \)

Substitute \( x = 30 \) into the equation: \( y \approx 1.14(30) + 3.805 \).
Calculate \( 1.14\times30 = 34.2 \), then add \( 3.805 \): \( 34.2 + 3.805 = 38.005 \approx 38 \).
So the point should be \( (30, 38) \).

Answer:

(30, 38)