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 (oC) x5 = cathode current density (A/dm2), and y = palladium content (%) of the coating.

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?

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