Question

make a scatterplot of the data and graph the function on the same coordinate grid. calculate the residuals and make a residual plot. describe the fit of the function to the data.
$f(x)=3x^2 - x + 1$

x	y
-1	10
0	6
1	12
2	17

make a residual plot. choose the correct answer below.
a.
image of a coordinate grid
b.
image of a coordinate grid
c.
image of a coordinate grid
d.
image of a coordinate grid

Explanation:

Step1: Calculate predicted y-values

For each $x$, compute $\hat{y}=3x^2 - x + 1$:

• $x=-2$: $\hat{y}=3(-2)^2 - (-2) + 1=12+2+1=15$
• $x=-1$: $\hat{y}=3(-1)^2 - (-1) + 1=3+1+1=5$
• $x=0$: $\hat{y}=3(0)^2 - 0 + 1=1$
• $x=1$: $\hat{y}=3(1)^2 - 1 + 1=3-1+1=3$
• $x=2$: $\hat{y}=3(2)^2 - 2 + 1=12-2+1=11$

Step2: Calculate residuals ($y-\hat{y}$)

Residual = observed $y$ - predicted $\hat{y}$:

• $x=-2$: $18-15=3$
• $x=-1$: $10-5=5$
• $x=0$: $6-1=5$
• $x=1$: $12-3=9$
• $x=2$: $17-11=6$

Step3: Match to residual plot

Residual points are $(-2,3), (-1,5), (0,5), (1,9), (2,6)$, which matches option C.

Answer:

C