Linear regression curve

Figure 4.21. Residuals for linear (left) and quadratic (right) regressions the ordinates are scaled +20 mAU. Note the increase in variance toward higher concentrations (heteroscedacity). The gray line was plotted as the difference between the quadratic and the linear regression curves. Concentration scale 0-25 /ag/ml, final dilution.

The linearity of a method is defined as its ability to provide measurement results that are directly proportional to the concentration of the analyte, or are directly proportional after some type of mathematical transformation. Linearity is usually documented as the ordinary least squares (OLS) curve, or simply as the linear regression curve, of the measured instrumental responses (either peak area or height) as a function of increasing analyte concentration [22, 23], The use of peak areas is preferred as compared to the use of peak heights for making the calibration curve [24],... 

Fig. 5. Comparison of linear regression curve fitting for the data of Figs. 4a and 4b showing (a) mean and (b) the nonuniformity.

Figure 8-15. Electrostatic binding energy (evaluated according to the equation inserted in the top part of plot) as a function of inhibitory activity.111,112 V denotes molecular electrostatic potential generated by inhibitors molecules in the position of any PAL atom given as a subscript R is the correlation coefficient corresponding to the linear regression curve. Points enumeration corresponds to the inhibitors designation introduced in Figure 8-12...

Figure 48 shows the usefulness of solid electrolyte cyclic voltammetry (SECV) for extracting transfer coefficients. The peak potentials are plotted against the logarithm of the sweep rates. The value can be obtained from the slope of the linear regression curve. It is calculated to be 0.63, which is close to the value, 0.59, obtained from the steady-state potentiostatic study. Similarly, based on the equation for anodic peaks. 

From the slope of the linear regression curve in Figure 49, the anodic transfer coefficient... 

Figure 2. Calcidated alkalinity (CTA) shown as a function of measured titration alkalinity (TA). Linear regression curve (slope = 1.009) also is...

The linearity of a method is its ability to provide measurement results that are directly proportional to the concentration of the analyte or are directly proportional after mathematical transformation. The linearity is usually documented as the linear regression curve of the measured responses as a function of increasing analyte... 

The linear regression curve was obtained by 1/AF vs l/[HSA]n and n for different values. The best linear n value was used in the equation, and K can be obtained from the intercept divided by the slope. When n=l, the linear regression equation was better than n=2, and this showed that MB-P-CD/HP-P-CD-HSA was a complex of 1 1 1. The binding constant could be obtained by substituting n values into the formula (3). The results are shown in Table 2. Experimental results showed that the existence of P-CD/HP-P-CD did not change the interaction trend of MB with HSA, and the addition of P-CD made the interaction of MB and HSA more facile. Similarly HP-P-CD further promoted their reaction. Both CDs can increase the binding constant of MB and HSA. 

Figure 13,20. (b) Transition energies vs. reciprocal chain-length. Symbols experimental data from (a) and HMO calculated values. Lines linear regression curves [137] (c) UV-Vis transition energies vs. reciprocal chain-length for absorption and fluorescence measurements of anT molecules in solution [38],... 

Figure 18.2 Plot of thyroid activity and filled linear regression curve as a function of time for a euthyroid subject.

FIGURE 13.2 Biochemical plots for the enz5me kinetic characterizations of biotransformation, (a) Direct concentration-rate or Michaelis-Menten plot (b), Eadie-Hofstee plot (c), double-reciprocal or Lineweaver-Burk plot. The Michaelis-Menten plot (a), typically exhibiting hyperbolic saturation, is fundamental to the demonstration of the effects of substrate concentration on the rates of metabolism, or metabolite formation. Here, the rates at 1 mM were excluded for the parameter estimation because of the potential for substrate inhibition. Eadie-Hofstee (b) and Lineweaver-Burk (c) plots are frequently used to analyze kinetic data. Eadie-Hofstee plots are preferred for determining the apparent values of and Umax- The data points in Lineweaver-Burk plots tend to be unevenly distributed and thus potentially lead to unreliable reciprocals of lower metabolic rates (1 /V) these lower rates, however, dictate the linear regression curves. In contrast, the data points in Eadie-Hofstee plot are usually homogeneously distributed, and thus tend to be more accurate. 

FIGURE 8.14 Compressibility factor FEj/RF versus P/T at T= 493 K for SAN and EVOH copolymers the solid curve was calculated with the S-S equation of state for SAN copolymers. It follows the linear regression curve through aU data points. 

FIGURE 8.15 Fraction of sites occupied versus 1/V atT= 493 K for SAN and EVOH copolymers. The solid curve is the linear regression curve through the data points in the range of low reduced pressure. The linear range of y as a function of 1/V corresponds to the pressure range from normal pressure up to around 100 MPa. 

Here we test Eq. (8.30) for random copolymers by plotting surface tension versus pIk) I (Figure 8.17). The linear regression curve (correlation 0.9999) results for EVOH copolymers. It has the slope... 

FIGURE 1 The intrinsic viscosity of polymer blend solutions versus composition of blend in mass fraction W, solvent-chloroform, polymer blend of poly(hydroxy butyrate) (PHB), and poly(ethylene oxide), the solid curve represents the linear regression curve. 

Fig. 7A,B. Positive correlation between d and A280/A260. A Paired values for each fraction shown in Fig. 6 were replotted. Results were obtained with oligomers of varying chain length. B The experimental values shown in Fig. 5 were replotted with the paired A280/A260. Results were obtained at various temperatures. 7 = correlation coefficient y = ax + b, expresses the least square linear regression curve...

Fig. 6.26 Diagram of log 10 shear strain rate versus loglO shear stress/shear modulus curves obtained for temperatures of 1573, 1673 and 1773 K. Symbols represent experimental data, solid lines are best fit linear regression curves and dashed lines are data from Yoo [98] plotted using the value of the stress exponent n = 4.5 obtained in this study. The maximum error on the differential stress is ...

Figure 20.21. Behavior of the apparent density of silica sonogels during sintering. Lines are second-order linear regression curves included as a visual guide only.

Figure 23.10. Total effective thermal conductivity of an evacuated opacified silica aerogel (p = 153 kg m , opacifier 2.8% carbon black) as function of T (gas pressure Pg < 0.01 Pa). A linear increase in this representation can be observed with increasing temperatures due to the diffusive radiative heat transfer according to (23.12). Solid line linear regression curve, dashed lines corresponding 95% coincidence interval.

Figure 8 Linear regression curves for the median diameter and the perc en-tage smaller than 100 mesh (148 pm). Actual data are shown overlaid on the regression (correlation) curve. Equations developed from the actual data are presented in the upper left corner. The equation follows the mathematics for...

The largely linear regression curve in the double logarithmic scale is determined by the logarithmic values of specified load and corresponding lifetime. Results with less than ten hours lifetime should not be included in the evaluation [1014]. 

Figure 2 A calibration curve B correlation vivo-vitro. - This patient was not included to compute the linear regression curve.

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