72. As the air temperature drops, river water becomes supercooled and ice crystals form. Such ice can signi cantly affect the hydraulics of a river. The article Laboratory Study of Anchor Ice Growth (J.

Cold Regions Engrg., 2001: 60—66) described an experiment in which ice thickness (mm) was studied as a function of elapsed time (hr) under speci ed 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 r 2 value resulting from a least squares t is .977. Given the high r 2, does it seem appropriate to assume 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 x, and reconsider the question in (a). What does the plot suggest?