Regression analysis computer

The effect of added hydrochloric acid concentration was studied in order to determine whether or not the acid had any effect on pyrite and ash removal, sulfate-to-sulfur ratio, final heat content, and possible chlorination of the coal. Coal has many basic ash constituents, so increased ash removal was expected, as well as some suppression of the sulfate-to-sulfur ratio because the reaction that results in sulfate formation also yields eight moles of hydrogen ion per mole of sulfate (common ion effect). Added acid was studied in the range of 0.0 to 1.2M (0.0, 0.1, 0.3, and 1.2M) hydrochloric acid in 0.9M ferric chloride. Duplicate runs were made at each concentration with all four coals for a total of 32 runs. The results showed no definite trends (except one-uide infra) even when the data were smoothed via computer regression analysis. Apparently the concentration range was not broad enough to have any substantial effect on the production of sulfate or to cause the removal of additional ash over that which is removed at the pH of IM ferric chloride ( pH 2). 

This equation was solved by iterative computer regression analysis (9) using the data of the conductometric titration of 0,6% aqueous hexadecyltrimethylammonium bromide solutions with the different hexadecyltrimethylammonium bromide-cetyl alcohol molar ratios shown in Figure 2. Table I gives the results of this analysis. 

Although equations 5.13 and 5.14 appear formidable, it is only necessary to evaluate four summation terms. In addition, many calculators, spreadsheets, and other computer software packages are capable of performing a linear regression analysis based on this model. To save time and to avoid tedious calculations, learn how to use one of these tools. For illustrative purposes, the necessary calculations are shown in detail in the following example. 

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. 

A non-linear regression analysis is employed using die Solver in Microsoft Excel spreadsheet to determine die values of and in die following examples. Example 1-5 (Chapter 1) involves the enzymatic reaction in the conversion of urea to ammonia and carbon dioxide and Example 11-1 deals with the interconversion of D-glyceraldehyde 3-Phosphate and dihydroxyacetone phosphate. The Solver (EXAMPLEll-l.xls and EXAMPLEll-3.xls) uses the Michaehs-Menten (MM) formula to compute v i- The residual sums of squares between Vg(,j, and v j is then calculated. Using guessed values of and the Solver uses a search optimization technique to determine MM parameters. The values of and in Example 11-1 are ... 

Matsui75) has computed energies (Emin) which correspond to the minimal values of Evdw in Eq. 1 for cyclodextrin-alcohol systems (Table 2). Besides normal and branched alkanols, some diols, cellosolves, and haloalkanols were involved in the calculations. The Emi values obtained were adopted as a parameter representing the London dispersion force in place of Es. Regression analysis gave Eqs. 9 and 10 for a- and P-cyclodextrin systems respectively. 

The activation energy differences of My as well as of and M, and k /kp and kt/kp. were calculated from Arrhenius and Mayo plots, respectively, by linear regression analysis using a computer. Hie AEjjw values given in kcal/mole can be converted to kJ/mole by multiplying with 4.18. 

The partial differential equations describing the catalyst particle are discretized with central finite difference formulae with respect to the spatial coordinate [50]. Typically, around 10-20 discretization points are enough for the particle. The ordinary differential equations (ODEs) created are solved with respect to time together with the ODEs of the bulk phase. Since the system is stiff, the computer code of Hindmarsh [51] is used as the ODE solver. In general, the simulations progressed without numerical problems. The final values of the rate constants, along with their temperature dependencies, can be obtained with nonlinear regression analysis. The differential equations were solved in situ with the backward... 

S. de Jong and Th.J. R. de Jonge, Computer assisted fat blend recognition using regression analysis and mathematical programming. Fat Sci. Technol., 93 (1991) 532-536. 

Platt, J. Uy, O. Heller, D. Cotter, R. J. Fenselau, C. Computer-based linear regression analysis of desorption mass spectra of microorganisms. Anal. Chem. 1988,60, 1415-1419. 

For the regression analysis of a mixture design of this type, the NOCONSTANT regression command in MINITAB was used. Because of the constraint that the sum of all components must equal unity, the resultant models are in the form of Scheffe polynomials(13), in which the constant term is included in the other coefficients. However, the calculation of correlation coefficients and F values given by MINITAB are not correct for this situation. Therefore, these values had to be calculated in a separate program. Again, the computer made these repetitive and Involved calculations easily. The correct equations are shown below (13) ... 

The solution of problems in chemical reactor design and kinetics often requires the use of computer software. In chemical kinetics, a typical objective is to determine kinetics rate parameters from a set of experimental data. In such a case, software capable of parameter estimation by regression analysis is extremely usefiil. In chemical reactor design, or in the analysis of reactor performance, solution of sets of algebraic or differential equations may be required. In some cases, these equations can be solved an-... 

A major limitation of the linearized forms of the Michaelis-Menten equation is that none provides accurate estimates of both Km and Vmax. Furthermore, it is impossible to obtain meaningful error estimates for the parameters, since linear regression is not strictly appropriate. With the advent of more sophisticated computer tools, there is an increasing trend toward using the integrated rate equation and nonlinear regression analysis to estimate Km and While this type of analysis is more complex than the linear approaches, it has several benefits. First, accurate nonbiased estimates of Km and Vmax can be obtained. Second, nonlinear regression may allow the errors (or confidence intervals) of the parameter estimates to be determined. 

Simple and valence indices up to sixth order were computed for all the PAHs used in the present study database. The program MOLCONN2 [133, 152,154, 156] performed these calculations using the chemical structural formula as input. SAS [425] was used on a mainframe computer to perform statistical analyses. First, indices were selected which explained the greatest amount of variance in the data (i.e., R2 procedure). These indices were then used in a multiple linear regression analysis (REG procedure). 

All potency assays, from the simplest designs to the most complex Latin square design, necessitate potency estimation by computer. Low-precision assays employing plotting of zone sizes (response) against concentration of standards must be dealt with using computerized regression analysis, with the potency (standard equivalent) estimation calculated from the computed equation of the line. In this way, all opportunity for operator subjectivity is minimized. 

Another kind of data analysis, which has much broader application than analysis of variance is called regression. This method has the same mathematical basis as analysis of variance, but in most cases the calculations become very long and tedious. Without computers, regression methods would be very little used. Since the computers... 

The shelf life for a single batch is usually computed based on regression techniques. An appropriate approach to shelf life estimation when using regression analysis is by calculating the earliest time at which the 95% confidence limit for the mean intersects the proposed acceptance criterion [8]. A detailed description of shelf life calculations is provided in Sections 7.2.3 and 7.2.4. 

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