Multiple correlations analysis

Table II. Multiple correlation analysis using Infestation...

Table III. Multiple correlation analysis using adult female dry weight as the dependent variable. (r2 = 0.35 ...

A randomized complete block experiment design could determine surfactant differences as well as or better than multiple correlation analysis. However, one of the objectives of this work was to try to obtain additional information from preexisting sets of data. For this, multiple correlation analysis is particularly well suited. 

Foaming properties can be quantitatively related to surfactant chemical structure, surfactant physical properties, and test conditions using the technique of multiple correlation analysis.(11) The current studies were restricted to linear correlation equations to permit the analyses to be performed on a small microcomputer. While non-linear equations having higher correlation coefficients than obtained herein can be developed, theoretical insights are often limited due to the complexity of the various terms of such equations. The quality of the correlations were assessed using the correlation coefficient (r ) criteria of Jaffe (12)... 

Surfactant critical micelle concentration (cmc) may be related to chemical structure using multiple correlation analysis. The cmc value plays an important role in surfactant adsorption, foaming, and interfacial tension properties. The 25 C cmc values of a series of high purity single component highly linear primary alcohol ethoxylates (Table 6) were analyzed using equation 4 ... 

Both the use of one atmosphere foaming experiments and the technique of multiple correlation analysis have a common purpose minimizing the effort required to develop new surfactants for mobility control and other EOR applications. Proper use of these techniques with due consideration of their limitations can substantially reduce the number of experiments required to develop new surfactants or to understand the effect of surfactant chemical structure on physical properties and performance parameters. ... 

The limitation of the use of one atmosphere foaming experiments to rank order the predicted surfactant performance in permeable media rather than in quantitatively or semi-quantitatively predicting the actual performance of the surfactants under realistic use conditions has already been mentioned. Multiple correlation analysis has its greatest value to predicting the rank order of surfactant performance or the relative value of a physical property parameter. Correlation coefficients less than 0.99 generally do not allow the quantitative prediction of the value of a performance parameter for a surfactant yet to be evaluated or even synthesized. Despite these limitations, multiple correlation analysis can be valuable, increasing the understanding of the effect of chemical structure variables on surfactant physical property and performance parameters. 

Foaming properties of alcohol ethoxylates and alcohol ethoxylate derivatives are related to chemical structure features such as hydrophobe size and linearity, ethylene oxide chain length, and the terminating group at the end of the ethylene oxide chain. Foaming properties may be mathematically related to chemical structure parameters using multiple correlation analysis. ... 

Other surfactant physical properties and performance parameters such as critical micelle concentration, cloud point, and interfacial tension may be related to surfactant chemical structure using multiple correlation analysis. 

Predictions of surfactant performance made based on multiple correlation analysis may not be valid if the surfactants involved have chemical structure parameters outside the range used to define the correlation equation. 

Table I. The dependent and Independent variables used in the multiple-correlation analysis ...

Subsequent to publication of the original work done by Udvardy (17), a multiple correlation analysis of all replicates of the data points was conducted at Mobay. A set of regression equations was generated for each binder studied. Each equation predicted one of the board properties in terms of a number of processing variables including panel density. Correlation coefficients were 0.8 for internal bonds for the Mondur E-lll panels with all others being 0.9 or greater. 

We wish to thank Dr. Darrell D. Nicholas, Mr. Roy D. Adams and Ms. Susan Mateer of the Institute of Wood Research at Michigan Technological University for their work in conducting the mixed hardwood flakeboard experimental program. We also wish to thank Dr. Michael 0. Hunt of Purdue University and Dr. William F. Lehmann of Weyerhaeuser Corporation for their help in the red oak flake-board work and Mr. Otto G. Udvardy of Borden Chemical for the aspen waferboard study. Finally, we would like to thank Dr. Ronald Taylor of Mobay Chemical Corporation for his considerable advice and help with the multiple correlation analysis. 

To gain insight into chemometric methods such as correlation analysis, Multiple Linear Regression Analysis, Principal Component Analysis, Principal Component Regression, and Partial Least Squares regression/Projection to Latent Structures... 

Miller first used Eq. (7-41) to correlate multiple variations, and this approach has more recently been subjected to considerable development. Many cross-interaction constants have been evaluated multiple regression analysis is one technique, but Miller and Dubois et ah discuss other methods. Lee et al. consider Pxy to be a measure of the distance between groups x and y in the transition state... 

Topliss JG, Costello RJ. Chance correlations in structure-activity studies using multiple regression analysis. J Med Chem 1972 15 1066-9. 

An important aspect of all methods to be discussed concerns the choice of the model complexity, i.e., choosing the right number of factors. This is especially relevant if the relations are developed for predictive purposes. Building validated predictive models for quantitative relations based on multiple predictors is known as multivariate calibration. The latter subject is of such importance in chemo-metrics that it will be treated separately in the next chapter (Chapter 36). The techniques considered in this chapter comprise Procrustes analysis (Section 35.2), canonical correlation analysis (Section 35.3), multivariate linear regression... 

Canonical Correlation Analysis (CCA) is perhaps the oldest truly multivariate method for studying the relation between two measurement tables X and Y [5]. It generalizes the concept of squared multiple correlation or coefficient of determination, R. In Chapter 10 on multiple linear regression we found that is a measure for the linear association between a univeiriate y and a multivariate X. This R tells how much of the variance of y is explained by X = y y/yV = IlylP/llylP. Now, we extend this notion to a set of response variables collected in the multivariate data set Y. 

This is already a considerable improvement. The natural question then is Which linear combination of K-variables yields the highest R when regressed on the X-variables in a multiple regression Canonical correlation analysis answers this question. 

A study of 398 male and 133 female civil servants in London, England, measured blood pressure, PbB, and serum creatinine concentration the study found no correlation between blood pressure and PbB after adjustment for significant covariates, including sex, age, cigarette smoking, alcohol intake, and body mass index in a stepwise multiple regression analysis (Staessen et al. 1990). 

A complication arises. We learn from considerations of multiple regression analysis that when two (or more) variables are correlated, the standard error of both variables is increased over what would be obtained if equivalent but uncorrelated variables are used. This is discussed by Daniel and Wood (see p. 55 in [9]), who show that the variance of the estimates of coefficients (their standard errors) is increased by a factor of... 

Cohen, J., Cohen, P. (1983). Applied multiple regression-correlation analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ Erlbaum. 

The results have been statistically processed by means of Spearman s non-parametrical correlation analysis and by multiple regression analysis to assess the complex effects induced by toxic and essential elements (Evstafyeva, Slusarenko, 2003 Evstafyeva et al., 2004). 

Fu et al. [16] analyzed a set of 57 compounds previously used by Lombardo and other workers also. Their molecular geometries were optimized using the semiempirical self-consistent field molecular orbital calculation AMI method. Polar molecular surface areas and molecular volumes were calculated by the Monte Carlo method. The stepwise multiple regression analysis was used to obtain the correlation equations between the log BB values of the training set compounds and their structural parameters. The following model was generated after removing one outlier (Eq. 50) ... 

Bruntz et al. applied multiple regression analysis and found that the method of least squares yielded a set of coefficients that produced a 0.84 correlation of ozone concentration with the data. Adding mixing height to the correlation yielded no statistically significant improvement in agreement with the assertions of Hanna. ... 

Correlation of Secondary Nucleation Rate. The nucleation rate equation (2) was correlated by using multiple regression analysis at 70 C. Only data corresponding to the accelerating phase of nucleation rate was used in the correlation. The rate equation obtained at 70 C is... 

Multiple regression analysis on this data (29), with the addition of a values, gave no improvement on these relationships. For a series of dinitrosopiperazines, however, for which no correlation was detected with log P values alone, a fair correlation could be generated when a was included ... 

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