Line without intercept

Many have the value 52.48. The intercepts are zero for the benzenes and for the acid amides, but the slopes differ slightly, being 52.4 51.8 respectively. The line having intercept zero and slope 50.3 fits all types of nitro compds without particular constants... 

The quantity ir/c is called the reduced osmotic pressure, and (7r/c)0 the limiting reduced osmotic pressure. Osmotic pressure results are most commonly encountered as plots of reduced osmotic pressure —with or without the R T— versus c. This form suggests that a plot of k/RTc versus c should be a straight line, the intercept and slope of which have the following significance ... 

We also observe that when the solvent follows Raoult s Law the partial pressure of the solute follows an arbitrary straight line which in the example illustrated is not the Raoult s Law line. This line will intercept the x2 - 1 axis not at P% but at some arbitrary point. We will reserve discussion of the behaviour of the solute in such dilute solutions until later. However, even without considering the properties of the solute, the very fact that the solvent follows Raoult s Law is of enormous value to us. It enables us to treat the so-called coiligative properties of solutions in a very straightforward manner,... 

If we go back and calculate the slope and intercept for the data set in Exercise 3-2 without the constraint that the line must pass through the origin, we get the solution vector 0.95, 0.09 for a line parallel to the line in Exercise 3-3 and 2.0 units distant from it, as expected. 

The release tests were performed using the USP dissolution method (apparatus I) and utilized 1000 ml of pH 1.2 simulated gastric fluid (USP XXI) or pH 6.8 simulated intestinal fluid (USP XXI) without enzymes, equilibrated to 37°C and stirred with the basket rotating at 50 or 150 rev/ min. Drug concentrations were assayed by UV spectrophotometry at 255 nm. The experiments were continued until 100% dissolution was achieved. The release data were analysed to zero order, calculating the slope and intercept of the line. Each data point is the average of six individual determinations. In all cases the standard deviation was less than 9%. 

Figure 8.5. Outliers in calibration (a) near the center of the data causing a shift in intercept and (b) at the extreme of the data (a point with high leverage), causing change in slope. The solid lines are fits to the data without outliers (solid points). The dashed lines are fits to the data with outliers (all points).

Recall that kexp and k0 are rate constants with and without surfactant, respectively, for the reaction in question, and that c and cCMC are surfactant concentrations in the reaction mixture and at the CMC, respectively. Therefore kexp> k0, c, and cCMC are experimentally accessible. Equation (28) predicts that a plot of (kexp — k0) -l versus (c — cCMC) -l is a straight line with a slope and intercept that have the following significance ... 

FIGURE 5.5 Graphical displays for the methanol model at 2274 nm without an intercept term (the model is constrained to go through the origin) using all 11 calibration samples. The RMSEC is 15.96% methanol, (a) Actual calibration model (-) and measured values ( ). (b) Calibration residual plot, (c) A plot of estimated values against the actual values for the calibration samples the drawn line is the line of equality. 

The Mandelkern-Flory viscosity data for cellulose tributyrate are plotted according to Eq. (58) in Fig. 18. It is seen that the line for the viscosities in the good solvent methyl ethyl ketone at 30° C passes without strain to the same intercept as the lines for the two high-temperature theta solvents. The intercept gives K = (9.7 1.5) 10-4 and a = 1.79 0.10, as listed in Table 9. Although, as discussed in the... 

The components Ks and K denote equilibrium constants for the E-S and E-I complexes, respectively. Equation 7.92, when plotted as l/Vp versus 1/[S] for various quantities of inhibitor I, produces a straight line for each I with a common y intercept, but a different slope. The slope would differ from that of a system without I by the factor... 

There are, of course, two ways in which a straight line can be fitted, one with and one without the intercept. Each generates different error sum of squares according to the model. The values of the coefficients and the errors are given in Table 2.4 for both datasets. Note that although the size of the term for the intercept for dataset B is larger dian dataset A, this does not in itself indicate significance, unless the replicate error is taken into account. 

The moisture uptake rates (MUR) can simply be obtained by weighing the sample after a given time (six days), but in such a case it is assumed that the moisture uptake is still in the linear phase. If, for instance, the weight gain is 5 mg per 10-g sample in six days, then the MUR is 5/(10 x 6) = 0.083 mg/g/day. If the MUR values are plotted versus relative humidity (RH) and the curve that intercepts the x axis at 20% RH is obtained from a straight line, the compound can be stored without moisture pickup in atmospheres of less than 20% RH. In addition, the hygroscopicity of materials is indicated as follows ... 

Equation (12.7) relates p to p, but both constants c and d contain parameters for the monomer and the product gas. Therefore, it is anticipated that Eq. (12.7) would hold between p and but that the intercept and the slope of a straight line would depend on the pumping characteristics of the monomer. Figure 12.3 depicts the p -pa relationship for the plasma polymerization of ethylene with and without a liquid N2 trap in the system. Although there exists a relationship given by Eq. (12.7), cannot be uniquely related to / o- In other words, the manipulation of by manipulation of the pumping rate does not control the value of p ... 

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