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 3.5, 2.3, 1.1, negative 2.2, negative 4.1. The third column is labeled predicted with entries 4.06, 2.09, 0.12, negative 1.85, negative 3.82. 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?

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.

Answer 1

Calculate residual = (given) − (predicted):

- x=1: 3.5 − 4.06 = −0.56
- x=2: 2.3 − 2.09 = 0.21
- x=3: 1.1 − 0.12 = 0.98
- x=4: −2.2 − (−1.85) = −0.35
- x=5: −4.1 − (−3.82) = −0.28

So the residuals are: −0.56, 0.21, 0.98, −0.35, −0.28.

Residual-plot description: plotting residual (y) vs x gives negative at x=1, positive peak at x=2–3, then negative at x=4–5 — a curved (concave-down) pattern. Because the residuals show a clear curved pattern, a straight-line model is not appropriate.

How to make the plot on a graphing calculator: enter x-values in L1, residuals in L2 (or compute L2 = L_given − L_predicted), turn on Stat Plot 1 (scatter, xlist=L1, ylist=L2), set an appropriate window, and graph.