The article “Sensitivity Analysis of a 2.5 kW Proton Exchange Membrane Fuel Cell Stack by Statistical Method” (J. of Fuel Cell Sci. and Tech., 2009: 1–6) used regression analysis to investigate the relationship between fuel cell power (W) and the independent variables , , and .

a. Here is Minitab output from fitting the model with the aforementioned independent variables as predictors (also f

b. Fitting the model with predictors x3, x4, and the interaction x3x4 gave . Does this model appear to be useful? Can an F test be used to compare this model to the model of (a)? Explain.

c. Fitting the model with predictors as well as all second-order interactions gave (this model was also fit by the investigators). Does it appear that at least one of the interaction predictors provides useful information about power over and above what is provided by the first-order predictors? State and test the appropriate hypotheses using a significance level of .05.