Y values

Table A2.4.3. y values of various electrolytes at different concentration.

If the r and y values are totally independent of each other the correlation coefficient is r = 0,... 

Consider the data shown in Figure 9.32. It is easy to see that there is a high degree ( correlation between the x and the y values. If we were to define a new variable, z = x +, then we could express most of the variation in the data as the values of this new variabl 2. The new variable is called a principal component. In general, a principal component is linear combination of the variables ... 

Vcaic,i is obtained by feeding the appropriate r,- value into the regression equation. Anothe common squared term is the residual sum of squares (RSS), which is the sum of square of the differences between the observed and calculated y values. TSS is equal to the sur of RSS and ESS. The is then given by ... 

Discriminant emalysis is a supervised learning technique which uses classified dependent data. Here, the dependent data (y values) are not on a continuous scale but are divided into distinct classes. There are often just two classes (e.g. active/inactive soluble/not soluble yes/no), but more than two is also possible (e.g. high/medium/low 1/2/3/4). The simplest situation involves two variables and two classes, and the aim is to find a straight line that best separates the data into its classes (Figure 12.37). With more than two variables, the line becomes a hyperplane in the multidimensional variable space. Discriminant analysis is characterised by a discriminant function, which in the particular case of hnear discriminant analysis (the most popular variant) is written as a linear combination of the independent variables ... 

Normally, one does not have hue values of the elements of the slope mah ix M for comparison. It is always possible, however, to obtain y, the vector of predicted y values at each of the known Xi from any of the slope vectors m obtained by the multivariate procedure... 

If the experimental values P and w are closely reproduced by the correlating equation for g, then these residues, evaluated at the experimental values of X, scatter about zero. This is the result obtained when the data are thermodynamically consistent. When they are not, these residuals do not scatter about zero, and the correlation for g does not properly reproduce the experimental values P and y . Such a correlation is, in fact, unnecessarily divergent. An alternative is to process just the P-X data this is possible because the P-x -y data set includes more information than necessary. Assuming that the correlating equation is appropriate to the data, one merely searches for values of the parameters Ot, b, and so on, that yield pressures by Eq. (4-295) that are as close as possible to the measured values. The usual procedure is to minimize the sum of squares of the residuals 6P. Known as Barkers method Austral. ]. Chem., 6, pp. 207-210 [1953]), it provides the best possible fit of the experimental pressures. When the experimental data do not satisfy the Gibbs/Duhem equation, it cannot precisely represent the experimental y values however, it provides a better fit than does the procedure that minimizes the sum of the squares of the 6g residuals. 

Values calculated in this way are plotted in Fig. 9-16 and also in Fig. 9-18. It will he noted that after about 10 units this latter curve becomes parallel to the cumulative-average-cost curve and that the Y values are (N + 1) times those obtained from the latter curve. 

X Y Value of expression Expansion factor Dimensionless Dimensionless... 

Set C)(x,y,0,t) = in Eq. (26-62) and determine the value of y at each centerhne point determined in step 2. Plot the y values to define the isopleth, using symmetry around the centerline. 

Table 4.11 lists the Y values for some alcohol-water mixtures and for some other solvents. The Y value reflects primarily the ionization power of the solvent. It is largest for polar... 

Once the <5 and y values of a given blend are determined, the values are positioned in the graphic chart given in Fig. 37 [77]. The blends that fall within the kidney-shaped area yield good solutions with all solvent grade polychloroprene types, except for Neoprene AH, and those which fall outside that area will not dissolve the polychloroprene. The solvent blends which fall within the shadow area, may or may not dissolve the polychloroprene depending on the amount of toluene. 

VALUE OF THE INDEPENDENT AND DEPENDENT VARIABLES X-VALUES Y-VALUE S ... 

There are several ways in which wecanproceed.Wecouldgoback to the set of y-values,... 

Therefore, the variance of Y is 100. The standard deviation of X is 1 and the standard deviation of Y is 10. Tlie larger value for tlie standard deviation in tlie case of Y reflects tlie greater dispersion of Y values about tlieir mean. 

Following the procedure presented earlier, the y values for sections I and IV were fixed, in such a way that constraints concerning these zones were fulfilled Yj = 3.8657 and 7 = 2.6901. Since the liquid flow rates in sections I and IV are constants in this study, the eluent flow rate is also constant and equal to Q) - Q y = 7.49 inL miirf... 

As the feed flowrate is known, all the TMB flowrates are calculated from Equation (13), for a given y value. Erom Equation (13), it follows that y must fall in this range ... 

There are no general rules allowing selection of the correct y value. The correct selection is a result of technico-economical optimization however, for a first guess y can be set to y = 1.02. 

Equation 13 is used to calculate the SMB flow rates. To ensure a throughput of 10 tons/year of the racemic mixture we need a feed flow rate of 1250 L h The y value must fulfill 1 < y < 1.22 with our recommended value of 1.02. 

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