Chapter 13.1, Problem 5E

As the air temperature drops, river water becomes supercooled and ice crystals form. Such ice can significantly affect the hydraulics of a river. The article “Laboratory Study of Anchor Ice Growth” (J. of Cold Regions Engr., 2001: 60–66) described an experiment in which ice thickness (mm) was studied as a function of elapsed time (hr) under specified conditions. The following data was read from a graph in the article: n = 33; x = .17, .33, .50, .67,…, 5.50; y = .50, 1.25, 1.50, 2.75, 3.50, 4.75, 5.75, 5.60, 7.00, 8.00, 8.25, 9.50, 10.50, 11.00, 10.75, 12.50, 12.25, 13.25, 15.50, 15.00, 15.25, 16.25, 17.25, 18.00, 18.25, 18.15, 20.25, 19.50, 20.00, 20.50, 20.60, 20.50, 19.80.

a. The r2 value resulting from a least squares fit is .977. Interpret this value and comment on the appropriateness of assuming an approximate linear relationship.

b. The residuals, listed in the same order as the x values, are

-1.03	-0.92	-1.35	-0.78	-0.68	-0.11	0.21
-0.59	0.13	0.45	0.06	0.62	0.94	0.80
-0.14	0.93	0.04	0.36	1.92	0.78	0.35
0.67	1.02	1.09	0.66	-0.09	1.33	-0.10
-0.24	-0.43	-1.01	-1.75	-3.14

Plot the residuals against elapsed time. What does the plot suggest?