DYESTUFF (Yield of dyestuff by batch) Data: Dyestuff: Batch Yield 1 A 1545 2 A 1440 3 A 1440 4 A 1520 5 A 1580 6 B 1540 7 B 1555 8 B 1490 9 B 1560 10 B 1495 11 C 1595 12 C 1550 13 C 1605 14 C 1510 15 C 1560 16 D 1445 17 D 1440 18 D 1595 19 D 1465 20 D 1545 21 E 1595 22 E 1630 23 E 1515 24 E 1635 25 E 1625 26 F 1520 27 F 1455 28 F 1450 29 F 1480 30 F 1445 Dyestuff2: Batch Yield 1 A 7.298 2 A 3.846 3 A 2.434 4 A 9.566 5 A 7.990 6 B 5.220 7 B 6.556 8 B 0.608 9 B 11.788 10 B -0.892 11 C 0.110 12 C 10.386 13 C 13.434 14 C 5.510 15 C 8.166 16 D 2.212 17 D 4.852 18 D 7.092 19 D 9.288 20 D 4.980 21 E 0.282 22 E 9.014 23 E 4.458 24 E 9.446 25 E 7.198 26 F 1.722 27 F 4.782 28 F 8.106 29 F 0.758 30 F 3.758 Description: The Dyestuff data frame provides the yield of dyestuff (Naphthalene Black 12B) from 5 different preparations from each of 6 different batchs of an intermediate product (H-acid). Format: Data frames, each with 30 observations on the following 2 variables. Batch - a factor indicating the batch of the intermediate product from which the preparation was created. Yield - the yield of dyestuff from the preparation (grams of standard color). Details: The Dyestuff data are described in Davies and Goldsmith (1972) as coming from β€œan investigation to find out how much the variation from batch to batch in the quality of an intermediate product (H-acid) contributes to the variation in the yield of the dyestuff (Naphthalene Black 12B) made from it. In the experiment six samples of the intermediate, representing different batches of works manufacture, were obtained, and five preparations of the dyestuff were made in the laboratory from each sample. The equivalent yield of each preparation as grams of standard colour was determined by dye-trial.” The Dyestuff2 data are described in Box and Tiao (1973) as illustrating β€œ the case where between-batches mean square is less than the within-batches mean square. These data had to be constructed for although examples of this sort undoubtably occur in practice, they seem to be rarely published.” Source: O.L. Davies and P.L. Goldsmith (eds), Statistical Methods in Research and Production, 4th ed., Oliver and Boyd, (1972), section 6.4 G.E.P. Box and G.C. Tiao, Bayesian Inference in Statistical Analysis, Addison-Wesley, (1973), section 5.1.2 Task: Model the yield of dyestuff from the preparation separately in Dyestuff and Dyestuff2 data.