Question

The article Effect of Environmental Factors on Steel Plate Corrosion Under Marine Immersion Conditions (C. Soares. Y. Garbatov, and A. Zayed, Corrosion Engineering, Science and Technology, 2011 :524? 541 ) describes an experiment in which nine steel specimens were submerged in seawater at various temperatures, and the corrosion rates were measured. The result are presented in the following table (obtained by digitizing a graph).

Temperature (C) Corrosion (mm/y)
26.6 1.58
26.0 1.45
27.4 1.13
21.7 0.96
14.9 0.99
11.3 1.05
15.0 0.82

a. Construct a scatterplot of corrosion (y) versus temperature (x). Verify that a linear model is appropriate.
b. Compute the least-squares line for predicting corrosion from temperature.
c. Two steel specimens whose temperatures differ by 10◦ C are submerged in seawater. By how much would you predict their corrosion rates to differ?
d. Predict the corrosion rate for steel submerged in seawater at a temperature of 20◦ C.

Answer 1

Answer:

Check the explanation

Step-by-step explanation:

a) from the scatter plot in the attached image below, it appears that relationship is approximately linear

b) least square line: that =0.3940+0.0355x

c) for 10 C difference expected difference in corrosion rate =0.0355*10=0.355

d) for x=20 ; predicted temperature =0.3940+0.0355*20=1.1041

e) fitted values are:

X                      ŷ

26.600        1.3385

26.000        1.3172

27.400        1.3669

21.700         1.1645

14.900        0.9230

11.300          0.7952

15.000        0.9266

8.700          0.7029

8.200          0.6851