Multiple regression analysis data

The following expressions can be used to estimate the temperature and enthalpy of steam. The expressions are based upon multiple regression analysis. The equation for temperature is accurate to within 1.5 % at 1,000 psia. The expression for latent heat is accurate to within + 3 % at 1,000 psia. Input data required to use these equations is the steam pressure in psia. The parameters in the equations are defined as t for temperature in F, for latent heat in Btu/lb, and P for pressure in psia. 

FIGURE 5.3 The Albumin in Acute Stroke (ALIAS) Phase II Trial. Data represent mean SEM. p-Value according to multiple regression analysis. Dead patients have been censored, (a) Mean change in NIH Stroke Scale score over time since treatment in rt-PA and non-rt-PA cohorts receiving the three lowest doses (Tiers I, 0.34 mg/kg II, 0.68 mg/kg III, 1.03 mg/kg) and three highest doses of albumin (Tiers IV, 1.37 mg/kg V, 1.71 mg/kg VI, 2.03 mg/kg). 

The translation of the statistical design into physical units is shown in Table 5. Again the formulations were prepared and the responses measured. The data were subjected to statistical analysis, followed by multiple regression analysis. This is an important step. One is not looking for the best of the 27 formulations, but the... 

Principal component analysis (PCA) of the soil physico-chemical or the antibiotic resistance data set was performed with the SPSS software. Before PCA, the row MPN values were log-ratio transformed (ter Braak and Smilauer 1998) each MPN was logio -transformed, then, divided by sum of the 16 log-transformed values. Simple linear regression analysis between scores on PCs based on the antibiotic resistance profiles and the soil physico-chemical characteristics was also performed using the SPSS software. To find the PCs that significantly explain variation of SFI or SEF value, multiple regression analysis between SFI or SEF values and PC scores was also performed using the SPSS software. The stepwise method at the default criteria (p=0.05 for inclusion and 0.10 for removal) was chosen. 

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... 

Comparison of the coefficients from the multiple regression analysis with available source emission data supports the validity of the models. 

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 ... 

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). 

The inverse relationship between limonin content and taste preference was confirmed in another study (41) using a stepwise multiple regression analysis of data from 60 samples of commercial frozen-concentrated orange juice (FCOJ) packed during two seasons. This and a latter report (42) concluded that limonin content was highly correlated with the flavor quality of the juice. 

Analysis of variance (ANOVA and MANOVA) has been used to investigate the influence of location on forms of metals in roadside soil (Nowak, 1995). Multiple regression analysis has proved valuable in processing sequential extraction data to obtain information on plant availability of trace metals in soils (Qian et al, 1996 ... 

Substituent Parameters. A significant advance was made, in the structure-activity studies with the Hill reaction, when Hansch and Deutsch (12) evaluated some of the published Hill inhibition data with a multiple regression analysis, an extra-thermodynamic approach, or the so-called sigma, pi (a, T ) regression analysis. The principle of the approach rests on the assumption that changes in biological activity can be correlated with measurable molecular or substituent parameters. This analysis involved equations of the following type ... 

Using the E values evaluated from pore size distribution curves (Equation 1) corresponding to different degrees of conversion and the conversion-time data, the values of effective diffusivities of CO2 in the core and shell sections (D and D a respectively) are determined from Equations 8 and 9by a multiple regression analysis as 0.08 cmz/s and 0.12 cmz/s respectively at 860 °C. 

The least squares fitting of approximate functional relationships to data with even multidimensional explanatory variable x typically goes under the (unfortunately obscure) name of multiple regression analysis, and is given an introductory treatment in most engineering statistics textbooks, including, for example, the ones by Devore,4 Vardeman and Jobe,5 and Vardeman6 listed in the references. A lucid and rather complete treatment of the subject can also be found in the book by Neter et al.7... 

Empirical polynomial descriptions of (approximately) how a response y depends upon proportions jcp jc2,. .., xp are popular mixture analysis tools. The process of fitting polynomials to mixture experiment data in principle uses the same least squares notion illustrated in the fitting of a parabola to the data of Table 5.2. However, the mechanics of using standard multiple regression analysis software in the mixture context is complicated somewhat by the basic constraint (5-15). For example, in view of (5-15) the basic (p + 1 parameter) linear relationship... 

The data for this series of drugs are shown in Table IV. Multiple regression analysis generated the following equations ... 

TABLE 11.14. Data on the Multiple Regression Analysis Between" Phytoavailable Metal, Soil Solution Metal Concentration (Ms), and Solid-Phase Metal Fractions ... 

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