An ammonia bath is the one most widely used for depositing Pd-Ni alloy coatings. The article “Modelling of Palladium and Nickel in an Ammonia Bath in a Rotary Device” (Plating and Surface Finishing, 1997: 102–104)

reported on an investigation into how bath composition characteristics affect coating properties. Consider the following data on x1
Pd concentration (g/dm3

), x2
Ni concentration (g/dm3

), x3
pH, x4
temperature (°C), x5
cathode current density (A/dm2

), and y
palladium content (%)

of the coating.

Obs pdconc niconc pH temp currdens pallcont 1 16 24 9.0 35 5 61.5 2 8 24 9.0 35 3 51.0 3 16 16 9.0 35 3 81.0 4 8 16 9.0 35 5 50.9 5 16 24 8.0 35 3 66.7 6 8 24 8.0 35 5 48.8 7 16 16 8.0 35 5 71.3 8 8 16 8.0 35 3 62.8 9 16 24 9.0 25 3 64.0 10 8 24 9.0 25 5 37.7 11 16 16 9.0 25 5 68.7 12 8 16 9.0 25 3 54.1 13 16 24 8.0 25 5 61.6 14 8 24 8.0 25 3 48.0 15 16 16 8.0 25 3 73.2 16 8 16 8.0 25 5 43.3 17 4 20 8.5 30 4 35.0 18 20 20 8.5 30 4 69.6 19 12 12 8.5 30 4 70.0 20 12 28 8.5 30 4 48.2 21 12 20 7.5 30 4 56.0 22 12 20 9.5 30 4 77.6 23 12 20 8.5 20 4 55.0 24 12 20 8.5 40 4 60.6 25 12 20 8.5 30 2 54.9 26 12 20 8.5 30 6 49.8 27 12 20 8.5 30 4 54.1 28 12 20 8.5 30 4 61.2 29 12 20 8.5 30 4 52.5 30 12 20 8.5 30 4 57.1 31 12 20 8.5 30 4 52.5 32 12 20 8.5 30 4 56.6

a. Fit the first-order model with five predictors and assess its utility. Do all the predictors appear to be important?

b. Fit the complete second-order model and assess its utility.

c. Does the group of second-order predictors (interaction and quadratic) appear to provide more useful information about y than is contributed by the first-order predictors?

Carry out an appropriate test of hypotheses.

d. The authors of the cited article recommended the use of all five first-order predictors plus the additional predictor x6
(pH)2

. Fit this model. Do all six predictors appear to be important?