103. The presence of hard alloy carbides in high chromium white iron alloys results in excellent abrasion resistance, making them suitable for materials handling in the mining and materials processing industries. The accompanying data on x 

retained austenite content (%) and y  abrasive wear loss (mm3) in pin wear tests with garnet as the abrasive was read from a plot in the article Microstructure-Property Relationships in High Chromium White Iron Alloys (Internat. Materials Rev., 1996: 59—82).

x 4.6 17.0 17.4 18.0 18.5 22.4 26.5 30.0 34.0 y .66 .92 1.45 1.03 .70 .73 1.20 .80 .91 x 38.8 48.2 63.5 65.8 73.9 77.2 79.8 84.0 y 1.19 1.15 1.12 1.37 1.45 1.50 1.36 1.29 702 CHAPTER 12 Regression and Correlation Supplementary Exercises (103–119)

SAS output for Exercise 103 Dependent Variable: ABRLOSS Analysis of Variance Source DF Sum of Squares Mean Square F Value Prob F

Model 1 0.63690 0.63690 15.444 0.0013 Error 15 0.61860 0.04124 C Total 16 1.25551 Root MSE 0.20308 R-square 0.5073 Dep Mean 1.10765 Adj R-sq 0.4744 C.V. 18.33410 Parameter Estimates Parameter Standard T for H0:

Variable DF Estimate Error Parameter  0 Prob INTERCEP 1 0.787218 0.09525879 8.264 0.0001 AUSTCONT 1 0.007570 0.00192626 3.930 0.0013 0T 0

a. What proportion of observed variation in wear loss can be attributed to the simple linear regression model relationship?

b. What is the value of the sample correlation coef cient?

c. Test the utility of the simple linear regression model using a  .01.

d. Estimate the true average wear loss when content is 50% and do so in a way that conveys information about reliability and precision.

e. What value of wear loss would you predict when content is 30%, and what is the value of the corresponding residual?