Regression analysis results

Finally, it is worth mentioning a study in which chromatographic indices on IAMs were determined for 13 local anesthetics [22] (Table 5.2). Regression analysis result-... 

A scatterplot of the bacterial populations recovered, which is presented in Figure 3.2, appears to be linear. A linear regression analysis resulted in an value of 96.1%, which looks good (Table 3.3). Because the data were collected over time, the next step is to graph the e,s to the x,s (Figure 3.3). 

TABLE 11 Statgraphics Regression Analysis Results for P = 3 w = 19 Multiple Regression Analysis... 

The linear multiple regression analysis results for the first, second, third, and fourth trials are, respectively modeled as. 

To establish the prediction model, the software package XLSTAT was applied to perform the regression analysis using the experimental data. The regression analysis results and prediction model for aluminum are given in Table 32.10. The coefficient of determination (R ) is 0.815, which indicates that the prediction model has a satisfactory goodness of fit . 

Quantitative structure-activity relationships (QSAR), a concept introduced by Hansch and Fujita (1964) is a kind of formal system based on a kinetic model, which in turn is expressed in term of a first-order linear differential equation. Solution of the differential equation leads to a linear equation ( Hansch-Fujita equation ), the coefficients of which are determined by regression analysis resulting in a QSAR equation of a particular compound series. For a prediction, the dependent variable of the QSAR equation is calculated by algebraic operations. 

Table III. Equation 10 Regression Analysis Results For Unmoderated...

In Eq. (329), the unknowns and n, will be used as fitting parameters with as the independent variable. The regression analysis results of Eq. (329) are plotted in Fig. 25. 

Figure 19.27 shows the relationship between the calculated and the measured values in the pilot plant for and K. The agreement between the calculated and observed values was better for than for Ap p. However, more pronounced differences in values were observed for low gas temperatures. The reason for these differences is that the gas temperature of the field test was higher than that of the pilot plant and the value of the constant 6 of 7 was much larger than that of constant c of in Eqs (19.3) and (19.4). On the other hand, as shown in Table 19.6, the regression analysis results for the pilot plant data with the linear CR law assumption indicate that the effect of the variables on is similar to the field test results, but the constant b of Tg is the same as the constant c of 7. This means that the effect of gas temperature on in the pilot plant was smaller than that in the field test. Therefore, Eq. (19.4) was modified in order to fit the calculated value to the observed value as follows ... 

Unfilled samples were welded in accordance to a DOE matrix using the US-assisted hot plate welding process. The weld strengths achieved were very similar to the non-US-assisted weld samples and similar to the parent material strength. The regression analysis resulted in main effects plots that show tensile strength increased with heat time and amplitude, and decreased with US on-time. 

Standardizations using a single standard are common, but also are subject to greater uncertainty. Whenever possible, a multiple-point standardization is preferred. The results of a multiple-point standardization are graphed as a calibration curve. A linear regression analysis can provide an equation for the standardization. 

If a standard method is available, the performance of a new method can be evaluated by comparing results with those obtained with an approved standard method. The comparison should be done at a minimum of three concentrations to evaluate the applicability of the new method for different amounts of analyte. Alternatively, we can plot the results obtained by the new method against those obtained by the approved standard method. A linear regression analysis should give a slope of 1 and ay-intercept of 0 if the results of the two methods are equivalent. 

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. 

Multiple regression analysis can be executed by various programs. The one shown in the Appendix is from Mathcad 6 Plus, the regress method. Taking the log of the rates first and averaging later gives somewhat different result. 

Equations la and lb are for a simple two-phase system such as the air-bulk solid interface. Real materials aren t so simple. They have natural oxides and surface roughness, and consist of deposited or grown multilayered structures in many cases. In these cases each layer and interface can be represented by a 2 x 2 matrix (for isotropic materials), and the overall reflection properties can be calculated by matrix multiplication. The resulting algebraic equations are too complex to invert, and a major consequence is that regression analysis must be used to determine the system s physical parameters. ... 

The eomputer program PROGl determines the eonstants A and B from the regression analysis. Table 3-7 gives the results of the program with the slope -B equal to the reaetion rate eonstant kj. Eigure 3-19 shows a plot of In (D - D) against time t. 

Table 6-2 lists the results of the analysis. [To calculate we use the relationship Oa = see Eq. 6-7).) The regression analysis was also carried out without... 

We now consider a type of analysis in which the data (which may consist of solvent properties or of solvent effects on rates, equilibria, and spectra) again are expressed as a linear combination of products as in Eq. (8-81), but now the statistical treatment yields estimates of both a, and jc,. This method is called principal component analysis or factor analysis. A key difference between multiple linear regression analysis and principal component analysis (in the chemical setting) is that regression analysis adopts chemical models a priori, whereas in factor analysis the chemical significance of the factors emerges (if desired) as a result of the analysis. We will not explore the statistical procedure, but will cite some results. We have already encountered examples in Section 8.2 on the classification of solvents and in the present section in the form of the Swain et al. treatment leading to Eq. (8-74). 

Regression analysis of the results gave Eqs. 11 and 12 fora- and P-cyclodextrin systems respectively. 

Linear regression analysis was performed on the relation of G"(s) versus PICO abrasion index. Figure 16.10 plots the correlation coefficient as a function of strain employed in the measurement of loss modulus. The regression results show poor correlation at low strain with increasing correlations at higher strains. These correlations were performed on 189 data points. 

Purpose Perform a linear regression analysis over the selected data points display and print results, do interpolations, determine limits of detection. 

The final values of the rate constants along with their temperature dependencies were obtained with nonlinear regression analysis, which was applied to the differential equations. The model fits the experimental results well, having an explanation factor of 98%. Examples of the model fit are provided by Figures 8.3 and 8.4. An analogous treatment can be applied to other hemicelluloses. 

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