Provide solutions using Matlab for help with calculations, but do not use any statistical software packages. Provide additional text to interpret and explain any printed computer output. A preliminary Matlab file providing data input is shown in the appendix.

Problem 3

a main-effects only model is written as yijk = + i + j + k ; i, j, k = 1, 2 where 1 = 2 = and similarly for the other factors.

Consider a factorial experiment with center points examining the effect of T, p and concentration on the yield of a chemical process. The data are shown in Fig. 3. Assume a main-effects only model (this is the fitlm default) and analyze the data.

1. Are all factors significant?

2. Are curvature effects associated with quadratic terms evident?

3. Suppose the coded values of the factors are slightly different from the targeted +/-}1 levels. The actual factor levels are shown in Fig. 4 for the factorial design. The zero values remain the same. Analyze the data and compare the results to the previous estimates. 4. What conclusions can you draw from this simple example?

Fig 3: (Process Variables Temp [120, 160, 120, 160, 120, 160, 120, 160, 140, 140, 140, 140]

Pressure [40, 40, 80, 80, 40, 40, 80, 80, 60, 60, 60, 60]

Conc [15, 15, 15, 15, 30, 30, 30, 30, 22.5, 22.5, 22.5, 22.5]

Coded variables X1 [-1, 1, -1, 1, -1, 1, -1, 1, 0, 0, 0, 0]; X2 [-1, -1, 1, 1, -1, -1, 1, 1, 0, 0, 0, 0]; X3 [-1, -1, -1, -1, 1, 1, 1, 1, 0, 0, 0, 0]; Yield [32, 46, 57, 65, 36, 48, 57, 68, 50, 44, 53, 56])

Fig 4: (X1: -0.75, 0.90, -0.95, 1, -1.10, 1.15, -0.90, 1.25; X2: -0.95, -1, 1.1, 1, -1.05, -1, 1, 1,15; X3: -1.133, -1, -1, -1, 1.14, 1, 1, 1)