Question

13.17. Process yield. The yield (Y) of a chemical process depends on the temperature (X1) and pressure (X2). The following nonlinear regression model is expected to be applicable: Prior to beginning full-scale production, 18 tests were undertaken to study the process yield for various temperature and pressure combinations. The results follow. 18 100 100 398 16 17 2 100 100 43 100 128 32 103 a. To obtain starting values for yo, Vi, and V2, note that when we ignore the random error term, a logarithmic transformation yields Y- Po + AiX + B Xi2, where Y-log10 Yi, Po logo为, β,-M , Xİı = logo Xil, A = ½, and Xa = logo Xi2. Fit a first-order multiple regression model to the transformed data, and use as starting values go - antilogio bo, 8b, and 82 -b2 b. Using the starting values obtained in part (a), find the least squares estimates of the param eters ro, n, and ½

Full data set:
   12.0    1.0    1.0
   32.0   10.0    1.0
  103.0  100.0    1.0
   20.0    1.0   10.0
   61.0   10.0   10.0
  198.0  100.0   10.0
   38.0    1.0  100.0
  133.0   10.0  100.0
  406.0  100.0  100.0
    8.0    1.0    1.0
   38.0   10.0    1.0
   98.0  100.0    1.0
   14.0    1.0   10.0
   56.0   10.0   10.0
  205.0  100.0   10.0
   43.0    1.0  100.0
  128.0   10.0  100.0
  398.0  100.0  100.0

Answer 1

Hope this clarifies your query.