Question

question 7 of 10
which regression equation best fits these data?

x	y
-4	15
-3	17
-1	17
1	15
2	11
3	9
4	6

a. $y=11.73\cdot0.94^{x}$
b. $y=-0.32x^{2}-1.26x+15.81$
c. $y=-0.67x+12.41$
d. $y=0.32x^{2}+1.26x+15.81$

Explanation:

Step1: Analyze data trend

Plot shows a curved (non-linear) downward trend, ruling out linear option C. Exponential option A decays but does not match the symmetric-like curve. Option D is upward-opening parabola, conflicting with downward trend.

Step2: Verify quadratic fit

Check option B: $y=-0.32x^2 -1.26x +15.81$. For $x=-6$:
$y=-0.32(-6)^2 -1.26(-6)+15.81=-0.32(36)+7.56+15.81=-11.52+23.37=11.85\approx12$.
For $x=4$:
$y=-0.32(4)^2 -1.26(4)+15.81=-0.32(16)-5.04+15.81=-5.12+10.77=5.65\approx6$. Values match the dataset closely.

Answer:

B. $y=-0.32x^2 -1.26x+15.81$