Adequacy of the Model Fit

Regression models are then recalculated for each group. In the next step, an F test is conducted for (1) y intercept equivalence, (2) parallel slopes, and (3) coincidence, as previously discussed. If the two regression functions are not different—that is, they are coincidental—the model is considered appropriate for evaluating the individual x, variables. If they differ, one must determine where and in what way, and correct the data model, applying the methods discussed in previous chapters. If the split group regressions are equivalent, the evaluation of the actual X predictor variables can proceed. In previous chapters, we used a partial F test to do this. We use the same process 

Example 10.1 A researcher was interested in determining the logio microbial cotmts obtained from a contaminated 2.3 cm coupon at different temperatures and media concentrations. The researcher thought that temperature variation from 20°C to 45°C and media concentration would affect the microbial colony counts. 

After developing this model, the researcher discovered that the interaction term, Xi-X2 = X3, was omitted. Fifteen readings were collected, and the regression equation, y = ho + hi i + b2X2 + hjXa, was used. Table 10.1 provides the raw data (x y, and e,). Table 10.2 provides the regression analysis. 

Section B of Table 10.2 is the analysis of variance of the regression model 

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FIGURE 47.9 Diagnostic plots used in the model evaluation of the linear regression model that related log(AUC) to log(dose) incorporating subject type (1 for diseased subjects (patient), and 0 for healthy subject) as covariate. Top row The left and right panels are residuals showing that the adequacy of the model fit. Bottom row The left panel plot reinforces the fact that the model adequately describes the data. The right-hand plot shows the adequacy of the error model. 

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