Regression analysis, linear

The following entries from Table I were used for the initial linear regression analyses of T(experimental) versus AE(x) ... 

Inclusion of entries 1 and 2 into the initial T versus AE(r) linear regression analyses for reactions 1 and 4 did not appreciably affect the slopes, intercepts or correlation coefficients of the plots. 

The slopes, Y-intercepts and squares of correlation coefficients for the linear regression analyses of the T versus AE(ir) plots (equation 7) for reactions 1-4 for one-hour and ten-hour half life rates of decomposition to form free radical products are given in Table II. 

Table IV. Slopes and Intercepts of Linear Regression Analyses for Reactions 1-4...

If the T values of Table I are first fitted against EA values, without first fitting with EE(v) values, poor linea correlations result. For example, for tKe one-hour half-life temperatures of reactions 1 and 4, the squares of the correlation coefficients for these linear regression analyses are only 0.51 and 0.55, respectively. 

A series of experiments investigated the effect of laser pulse intensity on the distribution of damage. For each pulse intensity, DNA samples were exposed to three different doses. The quantum yield for the formation of lesions, expressed with respect to total DNA bases, was then calculated by linear regression analyses. At all intensities, the formation of lesions was found to be linear with respect to the applied dose. Oxidized nucleosides, including... 

Correlations between PbB levels and urinary ALA similar to those observed in occupationally exposed adults have also been reported in non-occupationally exposed adults (Roels and Lauwerys 1987) and children (unpublished data of J.J. Chisolm, Jr., reported by NAS 1972). Linear regression analyses conducted on data obtained from 39 men and 36 women revealed that increases in urinary ALA may occur at PbB levels of >35 pg/dL in women and >45 pg/dL in men (Roels and Lauwerys 1987). A significant linear correlation between PbB level and log ALA was obtained for data in children 1-5 years old with PbB levels of 25-75 pg/dL. The correlation was seen primarily at PbB levels >40 pg/dL, but some correlation may persist at <40 pg/dL (NAS 1972). 

Fig. 2 Plot of P-Cl distances (in A) vs average P-N distances (in A) for P-chloro-NHPs (diamonds) and for all compounds (R2N)2PC1 (except P-chloro-NHPs) listed in the CSD data base (open squares). The solid and dashed lines represent the result of linear regression analyses. R2 is the square of the correlation coefficient in the regression analysis. (Reproduction with permission from [55])...

Similar investigations were carried out using 2-propanol as the organic modifier instead of 1-propanol. The parameters of linear regression analyses are compiled in Table 3.5. It has been concluded from the results that the retention on both stationary phases is of mixed character hydrophilic, electrostatic and steric molecular parameters are equally involved in the retention [83],... 

Much lower infiltration factors were found for coarse particles than for PM2.5 in four European cities (Table 1). Infiltration factors were estimated from linear regression analyses of simultaneously measured indoor and outdoor coarse particle concentrations. The lower infiltration of coarse particle is consistent with lower penetration and higher decay rates of coarse particles due to gravitational settling and impaction, see Sect. 3. Studies conducted in the USA have reported substantially lower infiltration rates for coarse particles as well [17, 18]. 

The above studies clearly show that a number of different equations often describe rate data for soil constituents satisfactorily based on linear regression analyses. However, no single equation best describes every study, and conformity of data to a particular equation does not necessarily indicate that it is the best one to use. Moreover, one must be very careful not to attach mechanistic significance to linear plots based on the use of a given model. 

Petrographic analysis of the separated macerals, density determinations, and elemental analyses were performed at Argonne National Laboratories. The ash content of these samples is less than 1%. The oxygen levels reported here are obtained by difference. Computer correlations of the resulting parameters were done using the Statistical Analysis System on the VS/CMS system at the ER E-Linden site. Linear-regression analyses are also performed with that system. In the correlation plots which follow, samples will be identified by coal rank and maceral group. 

The standard curves obtained from the CP-80,794 assay are shown in Figure 6.32. Background subtraction routines are applied to obtain the best linear regression analyses and smallest y-intercept. The accuracy and precision of this assay are highlighted in Table 6.17, and representative HPLC chromatograms are shown in Figure 6.33. 

Least squares linear regression analyses of the data over the range of 20%-50% ACN gave the following equations ... 

As discussed above, CFPP and LTFT of biodiesel and its blends in petro-diesel demonstrate nearly linear correlation with respect to CP. Results from linear regression analyses yielded the following equations ... 

Manganese concentrations were measured by atomic absorption spectrophotometry and anticonvulsant concentrations by EMIT (Syva, Palo Alto. CA). Linear regression analyses indicate no significant correlation between manganese concentration and any anticonvulsant concentration. 

Non-linear regression analyses involve relatively complex calculations and thus are well suited to computer assistance. However, the program must have a well developed sequence of steps or algorithm to follow. Some methods are better than others. The program is asked to find the minimum point on a weighted sum of squares (objective or minimized function) surface. For two parameters, this can be represented as a three-dimensional surface (Fig. 4). 

Table 10 Linear regression analyses of calibrator curve data...

To derive the parameters r, the atmospheric transmittance, and L, the path radiance, linear regression analyses were performed on radiances from the satellite measurements, L, and radiances derived from shipboard measurements of temperature, L, versus elapsed distance, X, along selected parts of the track. These track segments were selected nearest in time to the satellite overpass and where temperature gradients were large enough to minimize the relative errors due to satellite-measured thermal noise and the lower AVHRR temperature resolution of 0.5 °C in the 8-bit data from Redwood City. 

Linear regression analyses indicated that the psychomotor index scores declined with increasing prenatal PCB exposure at both 6 and 12 months. At 6 months, the PDI was estimated to decrease 0.96 points for every increase of 1 ppm in PCBs. This would mean a drop of 2.6 points if a child moved from the 5th to the 95th percentile of PCB exposure. At 12 months, the drop was estimated at 1.34 points/ppm. Neither the 6-month nor the 12-month mental index scores were related to transplacental PCB exposure (Gladen et al. 1988). Similar analyses were run to examine postnatal exposure in breast-fed children. Postnatal exposure to PCBs was not associated with the PDI or MDI scores at either time period. 

Linear regression analyses using the NOS as the dependent variable and either maternal PCB-cord sum, maternal PCB-serum sum, or the child s PCB level at 42 months as the exposure found no associations between this outcome and any of these exposure variables. (Each exposure variable was modeled separately). Potential confounders in each model included the study center, the type of feeding during early life, the duration of breast feeding, and several items from the obstetrical optimality score (i.e.,... 

As with the one-compartment holus IV model, these equations yield essentially the same values of V and CL as those estimated from the linear regression analyses of the previous sections for a one-compartment model. Comparison to Equations (10.111) and (10.112) shows that these equations are essentially identical to those for the bolus TV case, providing an initial glimpse of the universal nature of these AUC relationships. 

Figure 2. Metal ligand neutral bond energies vs. 4s 3d promotion energy for first row transition metals. Data are shown for MH (open circles) and MCH3 (closed circles). Lines are linear regression analyses of the two systems.

There are two stepwise multiple linear regression analyses that have derived a mathematical formula for determining a lithium dose based on a number of dependent variables. 

Simple and multiple linear regression analyses were applied to the data collected above to predict the best estimator of exposure to PERC. PERC in blood was the best predictor followed by PERC in exhaled air. TCA per gram of creatinine in urine was the least reliable predictor. 

Zane, P.A., Brindle, S.D., Cause, D.O., O Buck, A.J., Raghavan, P.R., and Tripp, S.L. (1990) Physicochemical factors associated with binding and retention of compounds in ocular melanin of rats correlations using data from whole-body autoradiography and molecular modeling for multiple linear regression analyses. Pharm. Res., 7, 935-941. 

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