The article “Sensitivity Analy

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 methodology to investigate the relationship between fuel cell power (W) and the independent variables ₁  H₂ pressure (psi), ₂  H₂ flow (stoc), ₃  air pressure (psi), and ₃  airflow (stoc). Here is the Minitab output from fitting the model with the aforementioned independent variables as predictors (also fit by the authors of the cited article):

a. Does there appear to be a useful relationship between power and at least one of the predictors? Carry out a formal test of hypotheses.

b. Fitting the model with predictors ₃, ₄, and the interaction ₃₄ gave R²  .834. Does this model appear to be useful? Can an F test be used to compare this model to the model of part (a)? Explain.

c. Fitting the model with all 4 predictors as well as all second-order interactions gave R²  .960 (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.