Question

Find the residual values, and use the graphing calculator tool to make a residual plot.

A 4-column table with 5 rows. The first column is labeled x with entries 1, 2, 3, 4, 5. The second column is labeled given with entries negative 2.7, negative 0.9, 1.1, 3.2, 5.4. The third column is labeled predicted with entries negative 2.84, negative 0.81, 1.22, 3.25, 5.28. The fourth column is labeled residual value with all entries blank.
Does the residual plot show that the line of best fit is appropriate for the data?

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.

Answer 1

Residuals = observed − predicted:

- x = 1: −2.70 − (−2.84) = 0.14
- x = 2: −0.90 − (−0.81) = −0.09
- x = 3: 1.10 − 1.22 = −0.12
- x = 4: 3.20 − 3.25 = −0.05
- x = 5: 5.40 − 5.28 = 0.12

Residual plot points: (1, 0.14), (2, −0.09), (3, −0.12), (4, −0.05), (5, 0.12).

The residuals are small and show no clear pattern (they are scattered about zero), so the line of best fit is appropriate. Answer: "Yes, the points have no pattern."