Question

find the residual values, and use the graphing calculator tool to make a residual plot. does the residual plot show that the line of best fit is appropriate for the data?

x	given	predicted	residual
2	-0.9	-0.81
3	1.1	1.22
4	3.2	3.25
5	5.4	5.28

no, the points are in a curved pattern.
no, the points are evenly distributed about the x - axis.
yes, the points are in a linear pattern.
yes, the points have no pattern.

Explanation:

Step1: Recall residual formula

Residual = Given - Predicted

Step2: Calculate residual for \(x = 1\)

Residual \(=-2.7-(-2.84)=-2.7 + 2.84 = 0.14\)

Step3: Calculate residual for \(x = 2\)

Residual \(=-0.9-(-0.81)=-0.9 + 0.81=-0.09\)

Step4: Calculate residual for \(x = 3\)

Residual \(=1.1 - 1.22=-0.12\)

Step5: Calculate residual for \(x = 4\)

Residual \(=3.2-3.25=-0.05\)

Step6: Calculate residual for \(x = 5\)

Residual \(=5.4 - 5.28 = 0.12\)

For the second - part, a good residual plot for a linear regression has points that have no pattern. When the points in a residual plot have no pattern, the line of best - fit is appropriate for the data.

Answer:

\(x\)	Given	Predicted	Residual
2	-0.9	-0.81	-0.09
3	1.1	1.22	-0.12
4	3.2	3.25	-0.05
5	5.4	5.28	0.12

Yes, the points have no pattern.