Statistics regression

The fitting procedure should provide three pieces of information  

The statistical measure of the quality of the regression is used to determine whether the model provides a meaningful representation of the data. The parameter estimates are reliable only if the model provides a statistically adequate representation of the data. The evaluation of the quality of the regression requires an independent assessment of the stochastic errors in the data, information that may not be available. In such cases, visual inspection of the fitting results may be useful. Issues associated with assessment of regression quality are discussed further in Section 19.7.2 and Chapter 20. 

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Step 8. Set the logical value Stats=true if you wish the program to return additional regression statistics. 

Three tests of this characteristic were discussed in the previous chapters the FDA/ICH recommendation of linear regression with a report of various regression statistics, visual inspection of a plot of test results versus the actual concentrations, and use of the Durbin-Watson Statistic. Since we previously analyzed these tests we will not further discuss them here, but will summarize them in Table 65-1, along with other tests for nonlinearity that we explain and discuss in this chapter. 

Beside mid-IR, near-IR spectroscopy has been used to quantitate polymorphs at the bulk and dosage product level. For SC-25469 [34], two polymorphic forms were discovered (a and /3), and the /3-form was selected for use in the solid dosage form. Since the /3-form can be transformed to the a-form under pressure by enantiotropy, quantitation of the /3-form in the solid dosage formulation was necessary. Standard mixtures of both forms in the formulation matrix were prepared, and spectra were measured in the near-IR via diffuse reflectance. Utilizing a standard, near-IR multiple linear regression, statistical approach, the a- and /3-forms could be predicted to within 1% of theoretical. This extension of the diffuse reflectance IR technique shows that quantitation of polymorphic forms at the bulk and/or dosage product level can be performed. 

Other statistical parameters that can be used include examination of residuals and the output from the ANOVA table of regression statistics. This may indicate that a non-linear response function should be checked [9]. 

Where regression statistics are involved the relationship should not be extrapolated beyond the observed data range for the independent variable. 

Regression statistics showed that 97.8% of the variation iixlfog polar solutes in isopropyl alcohol was accounted for by Equation 3.40. The quality of Equation 3.40 was also evaluated by a cross-validation method (Myers, 1990 Tripos, 1992). In this study, the dataset was divided into... 

Regression statistics showed that Equation 3.46 was robust for different classes of compounds with a wide range of polarity. The predictive performance of Equation 3.46 was further evaluated by the prediction of the aqueous solubility of 48 new compounds including substituted benzenes, pyridines, polycyclic aromatics, and steroids. These compounds were not included in the development of Equation 3.46. Results are listed in Table 3.4. The relationship between the experimental... 

Table II. Regression statistics for each partitioning alcohol in Figure 2 showing the correlation constants of Equation 2. Underneath the correlation constants are the upper and lower bounds of the 95% confidence interval.

Coefficient of determination-regression statistical significance-lack of fit of regression... 

In a previous section we mentioned that outliers and highly deviating values in a series of measurements are known to have a severe elfect on most tests. In regression models also, the parameters are most sensitive to the response values near the borders of the calibration range. In order to moderate the influence of possible outliers one should try robust techniques. These so-called nonparametric regression statistics start from the common model ... 

Figure 2.3. Linear regression analysis with Excel. Simple linear regression analysis is performed with Excel using Tools -> Data Analysis -> Regression. The output is reorganized to show regression statistics, ANOVA residual plot and line fit plot (standard error in coefficients and a listing of the residues are not shown here).

LogP has been introduced as an additional descriptor in the new release of VolSurf A training set of 7871 diverse chemical structures was used to build a linear equation to calculate the logP values by fitting the structures with the other VolSurf descriptors. Using a five-component PLS regression, statistics give an r = 0.82, a = 0.82, and a SDEC [13] value = 0.74. The structures and data stem from Hansch et al. [18]. 

Berges, J. A. 1997. "Ratios, regression statistics, and spurious correlations." Limnology and Oceanography 42 1006-1007. 

The customary practice is to plot In A against z and by regression analysis determine the slope, from which S is calculated. From this result ages can be assigned to events recorded in a core, and uncertainties can be estimated from the regression statistics. 

Figure 11-4. Table of regression statistics returned by LINEST for slope and intercept of a straight line.

Figure 11-6. Slope of a straight line through the origin, with regression statistics.

In contrast to the results returned by FINEST, the output is clearly labeled, and additional statistical data is provided. Regression data for the example shown in Figure 11-1 is shown in the three tables of Figure 11-14. Three tables are produced regression statistics, analysis of variance, and regression coefficients. (The coefficients table has been broken into two parts to fit the page.)... 

Figure 11-14. Data obtained by using Regression from the Analysis ToolPak (from top) Regression Statistics, Analysis of Variance, Regression Coefficients and Statistics.

Figure 12-8. Method for obtaining regression statistics of coefficients obtained by the Solver (part 1).

Figure 12-10. Comparison of regression statistics returned by LI NEST.

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