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" (Intl. Materials Reviews, 1996: 59-82).

Use the data and the SAS output above to answer the following questions.
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 coefficient?
c. Test the utility of the simple linear regression model using a 5 .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?

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x4.6 17.0 174 18.0 18.5 22.4 26.5 30.0 34.0 y66.92 145 103 70 73 1.20 80 91 x 38.8 48.2 63.5 65.8 73.9 77.2 79.8 84.0 1.19 1.15 1.12 1.37 1.45 1.50 1.36 1.29