Analytical Chem istry - DePauw University

184 Analytical Chemistry 2.0( 6 6 1451 0 3644 44 9499b 1= × . ) − ( . × . )= 122.9852( 6× 0. 0499) −( 0. 3644)44. 9499− ( 122. 985×0. 3644)b 0== 0.02246The calibration equation isS std = 122.98 × C std + 0.02Figure 5.14 shows the calibration curve for the weighted regression and thecalibration curve for the unweighted regression in Example 5.9. Althoughthe two calibration curves are very similar, there are slight differences in theslope and in the y-intercept. Most notably, the y-intercept for the weightedlinear regression is closer to the expected value of zero. Because the standarddeviation for the signal, S std , is smaller for smaller concentrations ofanalyte, C std , a weighted linear regression gives more emphasis to thesestandards, allowing for a better estimate of the y-intercept.Equations for calculating confidence intervals for the slope, the y-intercept,and the concentration of analyte when using a weighted linearregression are not as easy to define as for an unweighted linear regression. 8The confidence interval for the analyte’s concentration, however, is at its8 Bonate, P. J. Anal. Chem. 1993, 65, 1367–1372.6050weighted linear regressionunweighted linear regression40S std 30201000.0 0.1 0.2 0.3 0.4 0.5C stdFigure 5.14 A comparison of unweighted and weighted normal calibration curves.See Example 5.9 for details of the unweighted linear regression and Example 5.12for details of the weighted linear regression.