Significant figures least-squares line

How many significant figures should we keep for the least-squares line The standard deviations give us the answer. The slope has a standard deviation of 1.0, and so we write the slope as 53.8 l.o at best. The intercept standard deviation is 0.42, so for the slope we write 0.6 0.4. See also Example 3.22. 

Figure 5 Least-square regression lines fit for the linear relationship between mean and standard deviation of PVT reaction times (msec). Data are from n = 13 subjects undergoing 88 hr (3.67 days) of total sleep deprivation. This figure illustrates that while all subjects experienced a decline in neurobehavioral performance on the PVT, as illustrated by increased reaction times when responding to the visual stimuli, there is a significant degree of interindividual variability in the magnitude of neurobehavioral impairment, evident by the differing lengths of the lines fit to the data. (From Ref. 44.)...

A least square error technique was used to determine values for the parameters AN and K from the experimental data. Examination of these parameters and base fuel properties yielded one significant correlation between AN and Nf. Figure 5 illustrates this straight line relationship. 

The data are plotted (for illustration) as the probit vs. log Pr-vt. The value of Pt-s, is computed from P solid line corresponds to a least-squares fit of the PB data. The TB data (M) fall significantly to the left of the line. The numbers in parentheses indicate the sample size (see Figure 8). 

To evaluate the validity of Eq. 4.42, the experimental data of Vj2 for 46 polymer blends are plotted in Figure 4.6 as a function of the computed values of the bracketed sum [Brandrup and Immergut, 1989]. The straight line represents the least squares fit. It is noteworthy that the exponent n = 0.402 is close to 1/2, predicted by Helfand et al., lower than 3/4, predicted by Roe et al., and significantly lower than the value of 3/2 derived by Joanny and Leibler. 

Figure 7-3. Relation between [Na ] and [H ] in the secretion of five Heidenhain pouch dogs stimulated with histamine injections before ( ) and after (x) irrigation of the pouches with eugenol. The thick line is the regression calculated by least squares, and the two finer lines define the limits of one standard deviation about the mean. The dotted line is regression calculated by the method of Bartlett Biometrics 5 207, 1949. (From Davenport HW, Warner HA, Code CF. Functional significance of gastric mucosal barrier to sodium. Gastroenterology 47 A42- 52, 1964.)...

The lattice constants of the chalcopyrite material were determined from the x-ray diffraction patterns. Lattice constants were calculated to at least three significant figures. They were used to construct actual iso-lattice constant maps like those shown in Fig. 10 where it is evident that these lines depart from the strictly linear behavior predicted by Vegard s law. The experimentally deduced curves are then subjected to a least squares fit to calculate values for the a coefficients of Eq. (14). 

A significantly different simation is faced in the case of the bismuth absorption line at 306.772 nm, which directly overlaps with a molecular absorption band of OH, as shown in Figure 8.2 (a). In this case least-squares BC not only corrects for the noise in the vicinity of the atomic line, as shown in Figure 8.2 (b), but also improves significantly the SNR of the measurement, and hence the LOD that can be obtained at that absorption line. 

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