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?
yes, because the points have no clear pattern
no, the points have no pattern.
no, the points are in a linear pattern.
yes, the points are in a curved pattern.

Explanation:

Step1: Calculate residual for \(x = 1\)

Residual formula: \(Residual=Given - Predicted\)
For \(x = 1\): \(3.5-4.06=- 0.56\)

Step2: Calculate residual for \(x = 2\)

For \(x = 2\): \(2.3 - 2.09=0.21\)

Step3: Calculate residual for \(x = 3\)

For \(x = 3\): \(1.1-0.12 = 0.98\)

Step4: Calculate residual for \(x = 4\)

For \(x = 4\): \(-2.2-(-1.85)=-2.2 + 1.85=-0.35\)

Step5: Calculate residual for \(x = 5\)

For \(x = 5\): \(-4.1-(-3.82)=-4.1 + 3.82=-0.28\)

Now, for the second part:
A residual plot is used to assess the appropriateness of a linear regression model. If the points in a residual plot have no clear pattern (randomly scattered), then the line of best - fit is appropriate for the data.

Answer:

The residual values are \(-0.56\), \(0.21\), \(0.98\), \(-0.35\), \(-0.28\)
Yes, because the points have no clear pattern.