Linear regression plots

Figure 1. Linear regression plot of tomato and radish seedling root growth inhibition with varying concentrations of phenyl aliphatic acids. Benzoic acid (V) phenylacetic acid (X) 3-phenyIpiropanoic acid (A) 4-phenylbutanoic acid ( ) trans-cinnamic acid (----) (1).

Figure 2. Linear regression plot of root growth inhibition of tomato and radish seedlings by o and -hydroxyphenyl) acids. o-Hydroxycinnamic acid, (o-hydroxyphenyl) acetic acid ( ) melilotic acid, 2-(o-hydroxyphenyl) butanoic acid ( ) o-hydroxy-benzoic acid, ( -hydroxypheny 1 )acetic acid (0) -hydroxycinnamic acid, =hydroxybenzoic acid, 3-( -hydroxyphenyl) propanoic acid (X) o-coumaryl glucoside, water control (----) (1 ). ...

The peak dynamic pressure in the shock front is called DP of an explosive. It has been established that a linear regression plot of experimental detonation pressures (DP) or Chapman-Jouguet Pressure (PCj) versus detonation velocities D for selected explosives fits the relationship in Equation 1.13 ... 

A four-point linear regression plot is constructed for calibration, where the x-axis represents added Hey concentration (pmol/l) and the -axis represents the ratio of areas of added Hcydnternal standard (IS). Concentrations of Hey in samples are calculated by dividing the ratio of the area of Hcy IS area by the slope of the calibration line. Thus, tHcy concentration = Hcy IS/slope (Fig. 2.2.3). 

Perhaps the most common situation involving graphing scientific data is to generate a linear regression plot with y error bars. In most situations, the error in the x data is regarded as being so much smaller than that of the y data that it can... 

Activation Energy Using Loss Modulus or Loss Factor Curve -Activation energy can be determined either from peak loss modulus or peak loss factor temperature. Table IV compares the data obtained by either methods along with the correlation coefficient of the linear regression plots for determining activation energy. It is evident that either method is equally satisfactory, as would be expected. 

Figure 4. An experimental subpicomole sequence on the HP G1005A sequencer A—Linear regression plot of total residue yields (corrected for the portion injected onto the PTH analyzer) The initial yield was 900 ftnoles and the repetitive yield was 92%. B—Chromatograms for selected cycles indicating the residue assignments in single letter code and the actual detected quantities in fmoles (not corrected for the portion injected).

Fig. 1.9. Dependence of retenlion factors, k, of homologous n-alkyl-.3.5-dinitroben/.oates on ihe concentration,

Figure 2. Plot of log total calcium vg pH. Dashed line, calculated solubility as a function of pH. Solid line, linear regression plot for experimental points below pH = 8.5.

Fig. 5. Classical linear regression plot. R is the regression line for a calibration curve o and b, the true 1% fiducial limits for future estimates of y. The bars show the probable standard deviations of measurements of y aX x = A, B, and C. e, d = the probable form of the actual 1% fiducial limits of a calibration curve in analytical chemistry when working near the limits of sensitivity.

One major difference with standard solutions is the requirement to construct what is known as a standard or calibration curve. Ihis is a series of standards of known, but different, concentrations that are used to calculate the concentration of the imknown sample solutions. Ihe caUhration curve is a linear regression plot of peak area versus concentration. Ihe closer the regression line is to a straight line (R = 1), the more accurate is the calculation of the imknown samples. 

Using parametric methods, it would be possible to make a linear regression plot of such data and test whether its slope differed significantly from zero (Chapter 5). Such an approach would assume that the errors were normally distributed, and that any trend that did occur was linear. The non-parametric approach is again simpler. The data are divided into two equal sets, the sequence being retained ... 

FigurO 4.4 Linear regression plot of actual surface tensions versus calculated values. Derived from an equation suggested by Beerbower which uses the three partial Hansen solubility parameters to calculate the surface tension of a liquid (e.g., surface tension = 0.0715 [8j +0.632 (5p +8 )].) The term Vm represents the solvent s...

Analysis o/ Kinetics of Inhibition. Under the above conditions, the rate of inactivation of the isomerase obeyed pseudo-first-order kinetics over several half-lives, for the range of inhibitor concentrations studied. The half-lives were determined- " from linear regression plots of the logarithm of enzyme activity as a function of time. 

Now what other information can be obtained from the data One obvious relationship to explore is the plot of E as function of log For ventricle the results are unambiguous. A least squares linear regression plot yields a slope between 56 and 57 mv, which is not significantly different than 58 mv. The correlation coefficient is 0.91. Atrium and sinus venosus presented a rather disquieting picture in that the slopes of the straight lines are about one half Nernstian. The correlation coefficient for atrium is lower, 0.72, but for sinus venosus the correlation coefficient is again 0.91. From these data it appears that the relation is a linear one but with only one half Nernstian slopes. 

The designed phantoms were used for performance assessment of two BMD systems including QCT and DEXA. Fig. 3 shows the linear regression plot between measured densities versus real densities of K2HPO4 solution which is performed by QCT technique as shown in the Fig. 2a. To calculate the measured density, the standard QCT procedure was used. Calculation algorithm is automatically run in the designed software. 

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