Regression analysis output response

The regression analysis output from MINITAB is listed in Tables 12A and 12B for the two responses, dissolution and solvent, respectively. The regression coefficients are listed for coded and uncoded levels of the factors. The magnitudes of the coded coefficients are more comparable than the uncoded coefficients as the scales of the three factors were standardized to a common scale to make the scales of the coded coefficients equal in magnitude. 

Table 12B Regression Analysis Output for Coating Study Solvent Response Response Surface Regression—Solvent vs. AirPress, SprayRate, AirTemp...

Figure 3 shows the output of the Yates analysis of Property B response, and Figure 4 shows the regression analysis. The adjusted R is high (95%), so this model explains the data very well. Also,... 

Section 1.4, 92 factors are studied but we find only 11 of these to be important. This is in line with the principle of effect sparsity, see Chapters 1 and 8. The simplest definition of importance occurs when an experiment has a single response (output from computer code) and the factors have only additive effects that is, the input-output relation is modelled by a first-order polynomial in regression terminology or a main effects only model in analysis of variance terminology (also see Chapter 8). The most important factor is then the one that has the largest absolute value for its first-order effect or main effect the least important factor is the one whose effect is closest to zero. 

We view the real or the simulated system as a black box that transforms inputs into outputs. Experiments with such a system are often analyzed through an approximating regression or analysis of variance model. Other types of approximating models include those for Kriging, neural nets, radial basis functions, and various types of splines. We call such approximating models metamodels other names include auxiliary models, emulators, and response surfaces. The simulation itself is a model of some real-world system. The goal is to build a parsimonious metamodel that describes the input-output relationship in simple terms. 

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