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 1 -2.7 -2.84 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 the points randomly scattered (no pattern). If the points are in a curved pattern, it indicates that a non - linear model may be more appropriate. If the points are evenly distributed about the \(x\) - axis but in a pattern (not random), the linear model is not appropriate. If the points are in a linear pattern, it means there is some underlying structure that the current linear model is not capturing well.
Since a good residual plot has points with no pattern, the answer is:

Answer:

\(x\)	Residual
2	\(-0.09\)
3	\(-0.12\)
4	\(-0.05\)
5	\(0.12\)

Yes, the points have no pattern.