Correlation coefficient adjusted

Several criteria can be used to select the best models, such as the F-test on regression, the adjusted correlation coefficient (R ad) and the PRESS [20] (Predictive error sum of squares). In general, even only adequate models show significant F values for regression, which means that the hypothesis that the independent variables have no influence on the dependent variables may not be accepted. The F value is less practical for further selection of the best model terms since it hardly makes any distinction between different predictive models. 

In practice, however, it is recommended to adjust the coefficient m, in order to obtain either the experimental vapor pressure curve or the normal boiling point. The function f T ) proposed by Soave can be improved if accurate experimental values for vapor pressure are available or if it is desired that the Soave equation produce values estimated by another correlation. 

Liquid chromatography was performed on symmetry 5 p.m (100 X 4.6 mm i.d) column at 40°C. The mobile phase consisted of acetronitrile 0.043 M H PO (36 63, v/v) adjusted to pH 6.7 with 5 M NaOH and pumped at a flow rate of 1.2 ml/min. Detection of clarithromycin and azithromycin as an internal standard (I.S) was monitored on an electrochemical detector operated at a potential of 0.85 Volt. Each analysis required no longer than 14 min. Quantitation over the range of 0.05 - 5.0 p.g/ml was made by correlating peak area ratio of the dmg to that of the I.S versus concentration. A linear relationship was verified as indicated by a correlation coefficient, r, better than 0.999. 

The study is based on four iinear hydrocarbons (in Ci, Ce to Ca) and the model uses Antoine and Clapeyron s equations. The flashpoints used by the author do not take into account all experimental values that are currently available the correlation coefficients obtained during multiple linear regression adjustments between experimental and estimated values are very bad (0.90 to 0.98 see the huge errors obtained from a correlation study concerning flashpoints for which the present writer still has a coefficient of 0.9966). The modei can be used if differences between pure cmpounds are still low regarding boiling and flashpoints. 

Note, however, there are two critical limitations to these "predicting" procedures. First, the mathematical models must adequately fit the data. Correlation coefficients (R ), adjusted for degrees of freedom, of 0.8 or better are considered necessary for reliable prediction when using factorial designs. Second, no predictions outside the design space can be made confidently, because no data are available to warn of unexpectedly abrupt changes in direction of the response surface. The areas covered by Figures 8 and 9 officially violate this latter limitation, but because more detailed... 

In order to obtain an in vitro-in vivo relationship two sets of data are needed. The first set is the in vivo data, usually entire blood/plasma concentration profiles or a pharmacokinetic metric derived from plasma concentration profile (e.g., cmax, tmax, AUC, % absorbed). The second data set is the in vitro data (e.g., drug release using an appropriate dissolution test). A mathematical model describing the relationship between these data sets is then developed. Fairly obvious, the in vivo data are fixed. However, the in vitro drug-release profile is often adjusted by changing the dissolution testing conditions to determine which match the computed in vivo-release profiles the best, i.e., results in the highest correlation coefficient. 

A number of performance criteria are not primarily dedicated to the users of a model but are applied in model generation and optimization. For instance, the mean squared error (MSE) or similar measures are considered for optimization of the number of components in PLS or PC A. For variable selection, the models to be compared have different numbers of variables in this case—and especially if a fit criterion is used—the performance measure must consider the number of variables appropriate measures are the adjusted squared correlation coefficient, adjR, or the Akaike S information criterion (AIC) see Section 4.2.3. 

As the model complexity increases, R2 becomes larger. In linear regression, R2 is the squared correlation coefficient between y and y, and d R2 is called the adjusted squared correlation coefficient. Thus adjR2 is a modification of the R2 that penalizes larger models. A model with a large value of adj 2 is preferable. Another, equivalent representation for adj 2 is... 

The calibration curves obtained with the output signals are shown in Figs. 9 and 10. Both curves were adjusted by a hyperbolic correlation with correlation coefficients of 0.9972 and 0.9909, respectively, for buffer... 

Table IV shows the overall analysis of variance (ANOVA) and lists some miscellaneous statistics. The ANOVA table breaks down the total sum of squares for the response variable into the portion attributable to the model, Equation 3, and the portion the model does not account for, which is attributed to error. The mean square for error is an estimate of the variance of the residuals — differences between observed values of suspensibility and those predicted by the empirical equation. The F-value provides a method for testing how well the model as a whole — after adjusting for the mean — accounts for the variation in suspensibility. A small value for the significance probability, labelled PR> F and 0.0006 in this case, indicates that the correlation is significant. The R2 (correlation coefficient) value of 0.90S5 indicates that Equation 3 accounts for 91% of the experimental variation in suspensibility. The coefficient of variation (C.V.) is a measure of the amount variation in suspensibility. It is equal to the standard deviation of the response variable (STD DEV) expressed as a percentage of the mean of the response response variable (SUSP MEAN). Since the coefficient of variation is unitless, it is often preferred for estimating the goodness of fit.

Ar)me et al. [26] presented rapid liquid chromatographic procedures for quality control of pharmaceuticals and human serum containing antihistamines, meclizine, and buclizine alone or in combination with pyri-doxine using acetonitrile water (80 20) as a mobile phase (pH adjusted to 2.6), methylparaben as internal standard deviation and UV detection was made at 230 nm. The results obtained showed a good agreement with the declared content. The method had good linearity in the range of 0.03-10 pg/ml for pyridoxine and (0.025-10 pg/ml) for meclizine and buclizine serum concentration with a correlation coefficient of 0.9999. 

The study was performed with a Class 1 member in the form of tablets. Changes in pH have no effects while changes in agitation intensity for USP apparatus II and IV have shown clear influences on the tablet erosion and subsequently on its release. Finally to simulate the fasted and fed state in vivo, fasted state stimulated intestinal fluid(Fassif) and fed state simulated intestinal fluid(Fessif) media were used. None of the USP traditional apparatus show a clear relationship with the in vivo results, especially in the fed conditions. In vitro data obtained by the ADS in the fasted state were consistent with those in vivo, as well as in the fed state after a slight time adjustment allowed in the FDA notes of guidance. A Level A of IVIVC was easily established with a good correlation coefficient in the fasted and fed states, respectively. The main results are presented in Fig. 13. 

Variable-temperature SSNMR was used by Tozuka et to investigate the observed polymorphism in clarithromycin. Polymorphic interconversions were identified using both powder X-ray diffraction (PXRD) and CPMAS NMR. The authors performed quantitation of two polymorphs (forms I and II) using carbonyl resonances that exhibited 1 ppm resolution. Relaxation and CP rate constants were not taken into account instead, relative peak areas were adjusted using a term derived from the preparation and analysis of a known set of standard mixtures. The correlation coefficient of measured peak intensity and weight content was found to be >0.99. 

In order to ascertain the linear relationship between the vapour pressure of a solute and the resulting peak area, a series of experiments were conducted on pure toluene as a function of p° between 4 and 77 kPa (eight data points) by adjustment of the equilibrium temperature. Statistic evaluation of the linear regression of the data obtained yielded a correlation coefficient of 0.9981, a relative standard deviation of 5.7%, and obeyed linearity according to MANDEL. 

HIV/AIDS human immunodeficiency virus/acquired immunodeficiency syndrome HUI Health Utilities Index HYEs healthy-year equivalents ICC intraclass correlation coefficient KDQOL Kidney Disease Quality of Life instrument MCS mental component summary scale of the SF-36 MOS-HTV Medical Outcomes Study HIV Health Survey MOT Medical Outcomes Trust MSQOL Migraine Specific Quality of Life NHP Nottingham Health Profile PCS physical component summary scale of the SF-36 QALY quahty-adjusted hfe year QOL quahty of life QOLIE Quality of Life in Epilepsy QWB Quality of WeU-Being scale SF-36 MOS 36-Item Short-Form Health Survey SIP Sickness Impact Profile VAS visual analog scale WY well year YHL years of healthy life... 

A correlation coefficient of 0.9957 obtained for a very diverse set of 110 polymers by using only two adjustable parameters and remaining completely within the formalism of connectivity indices essentially guarantees that Equation 3.9 will give reasonable predictions for the Vw of all polymers, including polymers containing structural units not found in the set of test cases. 

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