Parameters slopes and intercepts

This chart corresponds to the original Shewhart-chart. For tmeness control, standard solutions, synthetic samples or RM/CRM samples may be analysed. Calibration parameters (slope and intercept) can also be used in a X-chart to check the constancy of the calibration. 

Based on linear regression parameters, slope and intercept. 

The correlation coefficient is of little interest the calculation of a confidence interval for both parameters (slope and intercept) and of the probabilities... 

These authors expand the basic relationship LOD=kiB/5 to include 1) the use of population statistics (vs. sample set statistics) 2) the use of the pooled standard deviation (vs. the blank standard deviation) 3) a consideration of situations where the intercept of the calibration curve is nonzero and 4) a consideration of the errors in cahbration parameters (slope and intercept). 

The ordinary linear least-squares regression is based on the assumption of an independent and normal error distribution with uniform variance (homoscedastic). In addition, linear regression based on ordinary least-squares presumes that errors in signal are much higher than those in concentration [error (Y) error (X)] it is also very sensitive to extreme data points, which may result in biased values of the regression parameters, slope, and intercept. 

Some comments on the theory of absolute reaction rates Before we turn to the connection between the temperature dependence of reaction rates, structure changes and the temperature of the environment, some comments are required on the relation of the Arrhenius parameters (slope and intercept of the plot) to those of the theory of transition states (or activated states). There is assumed to be a quasi equilibrium between such a state and the ground state of a reactant. The relative concentration of the transition state to that of the ground state is characterized by an equilibrium constant Eyring s theory led him to postulate the following relation between the rate constant of a reaction, k, and K ... 

In order to go further into the experimental check we constructed Arrhenius plots of the fluorescence quantum yield of BMPC in a few solvents (methanol, ethanol, propanol, hexanol and methylene chloride), all of which showed good linearity. The activation energies and A/kp ratios, calculated from the slopes and intercepts of those plots, are collected in Table 1. The smooth increase of both parameters in the alcohol series is mainly associated with the increase of solvent viscosity. On the other hand, decrease of the solvent dielectric constant from 32.7 (methanol) to 8.9 (dichloromethane) causes a small but significant increase of the activation energy also, this increase is probably somewhat compensated by the decrease of the viscous-flow... 

The model contains four parameters, the slope and intercept of the calibration line and two drift parameters a and p. All four parameters are estimated by applying the algorithm given in Table 41.10. Details of this procedure are given in Ref. [5]. 

The actual data, including replicates, mean, and range, in tabular form should follow, accompanied by a brief discussion of the data. It is important to explain any out-of-specification data. Statistical analyses for all parameters, which lend themselves to such analyses along with conclusions, should be incorporated into the document at this point. These statistical analyses should be accompanied by the results of experiments conducted to determine the poolability of batches, or commonality of slopes and intercepts of individual batches. Graphs of these data should be included as part of the documentation. 

Hydraulic fracturing fluids are solutions of high-molecular-weight polymers whose rheological behavior is non-Newtonian. To describe the flow behavior of these fluids, it is customary to characterize the fluid by the Power Law parameters of Consistency Index (K) and Behavior Index (n). These parameters are obtained experimentally by subjecting the fluid to a series of different shear rates (y) and measuring the resultant shear stresses (t). The slope and Intercept of a log shear rate vs log shear stress plot yield the Behavior Index (n) and Consistency Index (Kv), respectively. Consistency Indices are corrected for the coaxial cylinder viscometers by ... 

It makes sense to start with the well known task of finding the best straight line through a set of (x,y)-data pairs. We can refer back to Figure 4-3 which displays the sum of squares, ssq, as a function of the two parameters defining a straight line, the slope and the intercept. The task is to find the position of the minimum, the values for slope and intercept that result in the least sum of squares. 

From the replots presented in Figure 4.55, the values of K j of the substrates D-glucose-6-phosphate and NADP can be determined. In this case the slope is constant and equals A m G6p/l max- Furthermore, the tine obtained from the intercepts replot is defined by the following parameters slope = A m,NADp/ Vmax and intercept = 1/ Fmax- From these slopes and intercepts the values obtained for K j are A. oep = 0.156 mM and A m.NADP = 0.076 mM. 

Rapid Equilibrium Case. In the absence of significant amounts of product (i.e., initial rate conditions thus, [P] 0), the rate expression for the rapid equilibrium random Bi Uni mechanism is v = Uniax[A][B]/(i iai b + i b[A] + i a[B] + [A][B]) where is the dissociation constant for the EA complex, and T b are the dissociation constants for the EAB complex with regard to ligands A and B, respectively, and Umax = 9[Etotai] where kg is the forward unimolecular rate constant for the conversion of EAB to EP. Double-reciprocal plots (1/v v. 1/[A] at different constant concentrations of B and 1/v v. 1/[B] at different constant concentrations of A) will be intersecting lines. Slope and intercept replots will provide values for the kinetic parameters. 

The potential existence of these interrelationships has considerable significance both from a practical and theoretical standpoint. With them, it is possible to measure the O—H frequency shifts of any new hydroxyl compound with the three donors in Fig. 8 and locate these frequencies on the three straight constant base lines. The points can be connected to produce the constant-acid line whose slope and intercept can then be determined. The enthalpy of interaction of this acid with all the donors in the phenol correlation can then be predicted from the measured frequency shift for these donors and the constant acid line. By use of the E and C correlation, the internal consistency of the enthalpies predicted from the frequency shifts can be checked because the three enthalpies from the constant base line give three heats for the determination of the Ea and Ca parameters of the new add. 

The kinetic parameters of Eq. 9-44b are often obtained from experimental data through the use of reciprocal plots (Fig. 9-6). However, Eq. 9-44b is linear only if the concentration of one or the other of the substrates A and B is kept constant. For this reason a series of experiments is usually performed in which [A] is varied while [B] is held constant. Then [A] is held constant and [B] is varied. Each of these experiments leads to a family of lines (Fig. 9-6A) whose slopes and intercepts are measured. The slopes and intercepts of this family of curves are then plotted against the reciprocal of the second concentration, i.e.,... 

From the slope and intercept of these plots the saturation coverage and adsorption coefficient were obtained by application of the previously given equation. The results are listed in Table I, which also includes the area per dye molecule at saturation coverage and the standard free energy of adsorption, AG°. Although the latter parameter was calculated as before (23), its thermodynamic validity is questionable since reversibility of adsorption of these dyes was not demonstrated. The molecular... 

This method is probably the simplest of the software-based standardization approaches.73,74 It is applied to each X-variable separately, and requires the analysis of a calibration set of samples on both master and slave instruments. A multivariate calibration model is built using the spectra obtained from the master instrument, and then this model is applied to the spectra of the same samples obtained from the slave instrument. Then, a linear regression of the predicted Y-values obtained from the slave instrument spectra and the known Y-values is performed, and the parameters obtained from this linear regression fit are used to calculate slope and intercept correction factors. In this... 

The two parameters are determined experimentally by measuring the bed void volume at different linear velocities and a double-log plot of evsU.n and Ut are found as slope and intercept of a linear regression of experimental data in this plot. Additionally the parameters may be evaluated from literature correlations, which give a good estimate of the range of flow rates applicable for the fluidization of a certain matrix. Martin et al. [19] used two dimensionless... 

The parameters /3 and BkJp k-/) can be obtained from the slope and intercept, respectively, of plots of n q/C) versus various equilibrium solution concentrations. 

---