Regression analysis output

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... 

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 9.9 Regression analysis output fitting nickel data to a straight line.

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

Figure 9.11 Regression analysis output data using the printer terminal as a plotter.

Statistical analysis can range from relatively simple regression analysis to complex input/output and mathematical models. The advent of the computer and its accessibiUty in most companies has broadened the tools a researcher has to manipulate data. However, the results are only as good as the inputs. Most veteran market researchers accept the statistical tools available to them but use the results to implement their judgment rather than uncritically accepting the machine output. 

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,... 

The experiment depicted in Fig. 2 was designed to test the validity of the two fundamental assumptions introduced above, that is, linearity and reciprocity. Isolated mitochondria from rat liver were incubated in the presence of a constant input force A o.1 The output force Xp was varied within the physiologically relevant range through additions of glucose plus hexokinase. A linear regression analysis of the measured flows Jp and J0 as a function of Xp showed that linearity as well as reciprocity were fulfilled within experimental error. 

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

Figure 2.3. Linear regression analysis with Excel. Simple linear regression analysis is performed with Excel using Tools -> Data Analysis -> Regression. The output is reorganized to show regression statistics, ANOVA residual plot and line fit plot (standard error in coefficients and a listing of the residues are not shown here).

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. 

Regression Analysis. The GLM (General Linear Models) procedure of SAS was used to fit the experimental data to Equation 3. This procedure provides estimates of coefficients and intercept GLM also tests hypotheses and indicates the overall quality of the correlation. Output from the GLM procedure is shown in Tables IV, V, and VI numbers, which are listed to 6 decimal places in the original output, have been rounded off to If- places. 

THIS PROGRAM OUTPUTS THE RESULTS OF THE REGRESSION ANALYSIS WITH THE ESTIMATED VALUE OF THE DEPENDENT VARIABLE,... 

Table 2.2 SAS output from regression analysis of Table 2.1 using clearance as the dependent variable.

Before the process is placed in operation we have identified the values of its parameters from linear regression analysis of input-output experimental data. Thus we have postulated the following model ... 

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. 

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