Multiple regression analyses product

If the odds ratio for pattern 1 (joint effect of genotype and drug) is significantly greater than the product of odds ratios for patterns 2 (independent effect of genotype) and pattern 3 (independent effect of drug), then there is evidence for statistical (multiplicative) interaction. This analysis can be carried out in the context of multiple regression analysis by the inclusion of an interaction term. 

Multiple regression analysis is a useful statistical tool for the prediction of the effect of pH, suspension percentage, and composition of soluble and insoluble fractions of oilseed vegetable protein products on foam properties. Similar studies were completed with emulsion properties of cottonseed and peanut seed protein products (23, 24, 29, 30, 31). As observed with the emulsion statistical studies, these regression equations are not optimal, and predicted values outside the range of the experimental data should be used only with caution. Extension of these studies to include nonlinear (curvilinear) multiple regression equations have proven useful in studies on the functionality of peanut seed products (33). 

Optimization techniques may be classified as parametric statistical methods and nonparametric search methods. Parametric statistical methods, usually employed for optimization, are full factorial designs, half factorial designs, simplex designs, and Lagrangian multiple regression analysis [21]. Parametric methods are best suited for formula optimization in the early stages of product development. Constraint analysis, described previously, is used to simplify the testing protocol and the analysis of experimental results. 

The alkaline hydrolysis of phthalate diesters has been fit to the Taft-Pavelich equation (Eq. 9). Dimethyl phthalate (DMP) hydrolyzes to phthalic acid (PA) in two steps DMP + H20->MMP + CH30H and MMP + H20- PA + CH30H. The first step is about 12 times faster than the second, and nearly all the diester is converted to the monoester before product PA is formed. Other diesters are assumed to behave similarly. An LFER was obtained from rate measurements on five phthalate esters (Wolfe et al., 1980b). The reaction constants, p and S, were determined by multiple regression analysis of the measured rate constants and reported values of cr and Es for the alkyl substituents. The fitted intercept compares favorably with the measured rate constant (log kOH = — 1.16 0.02) for the dimethyl ester (for which a and s = 0 by definition). Calculated half-lives under pseudo-first-order conditions (pH 8.0, 30°C) range from about 4 months for DMP to over 100 years for di-2-ethylhexyl phthalate. 

More recently a method for the mathematical processing of pyrograms of an ethylene-propylene copolymer using factorial analysis and multiple regression analysis was described [232]. This method permits the rapid determination of a peak or a group of peaks for calculating the content of the degradation products of interest. 

We know that the product degraded more than 10% (450 mg/mL) over the 12-week period. In addition, in the tenth week of accelerated stability testing, the product degraded at an increasing rate. The chemists want to know the rate of degradation, but this model is not linear. Table 4.2 shows the multiple regression analysis of y on Xi and X2 for Example 4.1 (Table 4.1)... 

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). 

As an example, the data from Ketchum (37) for the rate of phosphate absorption as a function of both phosphate and nitrate concentration can be satisfactorily fit with a product of two Michaelis-Menton expressions. The resulting fit, obtained by a multiple nonlinear regression analysis, is shown in Figure 5. The Michaelis constants that result are 28.4 p.g NOa-N/liter and 30.3 pg P04-P/liter, with a saturated absorption rate of 15.1 X 10 8 pg P04-P/cell-hr. This approximation to the growth rate behavior as a function of more than one nutrient must be regarded as only a first approximation, however, since the complex interaction reported between the nutrients is neglected. 

Tso, T.C., J.F. Chaphn, J.D. Adams, and D. Hoffmaim Simple correlation and multiple regression among leaf and smoke characteristics of hurley tobaccos 7th Intemat. Tob. Sci. Cong., Manila, The Philippines, CORESTA Inf. Bull., Spec. Edition 1980 Paper APST 05, 137 Beitr. Tabakforsch. Int. 11 (1982) 141-150. Tso, T.C., J.E. Chaplin, K.E. LeLacheur, and T.J. Sheets Pesticide-treated V5. pesticide-free tobacco 1. Tobacco production and leaf analysis Beitr. Tabakforsch. Int. 10 (1980) 114-119. 

Identification of different polymers, their properties, and their morphological differences normally requires extensive testing and complicated time-consuming analysis. Many statistical analysis methods have been combined with NIR to identify dissimilar textile products, including PCA, linear or multiple regression, PLS, derivative math, Mahalanobis distance (i.e.. Discriminate Analysis), nearest neighbors techniques, and neural networks. Most textile fibers, yarns, and fabrics have chemical sfrucfures fhaf yield complex NIR specfra, and as such these species normally require three or... 

While the enors of individual component quantification are high, multiple linear regression analysis reports the scores as 83% A and 17% B, very close to the actual mixture composition given the high difference in boiling points between these two products. Regression results 87% A/13% B B = 0.9479 (column normalized). 

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