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# solution3 - Solution to Homework#3-Stat c151/c225 Winter...

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Solution to Homework #3 ----Stat c151/c225 Winter 2011 4.6 Because any non-zero estimated effects are significant the optimal setting corresponds to run 6 with percentage of non-cracked springs, the response Y=90. In the one-factor-at-a-time approach, suppose we start at run 1. The Y is 67. Now change only oil temperature. From run 5 we find Y=59, so the best level of oil temperature is 70. Now keeping oil temperature at 70, change percentage of carbon. From run no. 3, we see that Y=61, so the best level of percentage of carbon is 0.50. Then keeping oil temperature at 70 and percentage of carbon at 0.50, change the steel temperature. From run 2, Y=79. So the best level of steel temperature is 1600. Thus the best setting from the one-factor-at-a-time approach is run 2 with Y=79. Thus we miss the optimal setting. 4.10 This experiment has 3 factors, each at 3 levels. For two 3-level factors, we can break the 2- factor interaction into four components (for example, linear-by-linear, linear-by-quadratic, quadratic- by-linear, and quadratic-by-quadratic as in Section 2.3.3). Then, the design given in Table 3.14 is an

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