Regression analysis output for

Table 14.4 shows a typical regression analysis output for the 2 factorial design in Table 14.3. Most of the output is self-explanatory. For the moment, however, note the regression analysis estimates for the parameters of the model given by Equation 14.5 and compare them to the estimates obtained in Equations 14.8-14.15 above. The mean is the same in both cases, but the other non-zero parameters (the factor effects and interactions) in the regression analysis are just half the values of the classical factor effects and interaction effects How can the same data set provide two different sets of values for these effects ...

Table 8 Regression Analysis Output for Blender Study ...

Table lOB Regression Analysis Output for Milling Study Percent... 

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

Figure 9.10 Regression analysis output for nickel with corrections for nickel and chromium.

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. 

Enter the output range where you want the regression analysis report to be copied (check New Worksheet Ply for reporting on a new worksheet). 

Table 14.4 Generic output for regression analysis of toxin concentration and rainfall...

From an inspection of the RSQUARE output, the five-variable equation with the highest correlation was selected for a more complete regression analysis. The five-variable equation (Equation 3) represents the best balance between high correlation and economy in the number of variable parameters. A serious disadvantage of having numerous independent variables in an empirical equation is the increased risk of a chance correlation (12). Consequently, the number of experimental observations required to establish statistical significance increases rapidly with the number of independent variables. In this study, l i experimental determinations were required to obtain statistical significance at the 95% confidence level. 

During the transient from the old to the new set point, we record the values of the manipulated variable and the controlled output. These values are shown in Table 31.2. Linear regression analysis using the input-output data of Table 31.2 produces the following values for the process parameters. 

Consequently, as the set point value changes we compute new values for xp and Kp using linear regression analysis on the input-output data. Then from eq. (16.1) we can compute the new value of the controller gain. This procedure can be repeated on-line every time we change the set point value. 

The system constants in Eqs. (1.6) and (1.7) are obtained by multiple linear regression analysis for a number of solute property determinations for solutes with known descriptors. The solutes used should be sufficient in number and variety to establish the statistical and chemical validity of the model [72-74]. In particular, there should be an absence of significant cross-correlation among the descriptors, clustering of either descriptor or dependent variable values should be avoided, and an exhaustive fit should be obtained. Table 1.4 illustrates part of a typical output. The overall correlation coefficient, standard error in the estimate, Fischer F-statistic, and the standard deviation in the individual system constants are used to judge whether the results are statistically sound. An exhaustive fit is obtained when small groups of solutes selected at random can be deleted from the model with minimal change in the system constants. 

An example of part of the output for fitting the solvation parameter model to a reversed-phase chromatographic system by multiple linear regression analysis... 

Multiple Regression Analysis for Optical Output Power ... 

For modelling mass flows and the link between concentrate input and neutral leach residue output, a regression analysis using non-parametric methods (in this case, neural networks) was applied. Intensive analysis and preparation of the available plant data (data reconciliation) had to be performed to produce the database used for modelling. 

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