Question: Case hardening. An experiment involving the case hardening of lightweight shafts machined from bars of an alloy was run to study the effects of the amount of a chemical agent added t the alloy in a molten state (factor $A$ ), the temperature of the hardening process (factor $B$ ), and the time duration of the hardening process (factor $C$ ) on the outside hardness of the shaft. A factors were at two levels (1: low, 2: high), and the number of rods tested for each treatment was $n=3 .$ The data on hardness (in Brinell units) follow.

1. Obtain the residuals for ANOVA model (24.14) and prepare aligned residual dot plots for each level of factor \(A\). Do the same for each of the other two factors. What information do these plots provide about the appropriateness of ANOVA model (24.14)?
2. Prepare a normal probability plot of the residuals. Also obtain the coefficient of correlation between the ordered residuals and their expected values under normality. Does the normality assumption appear to be reasonable here?

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