Analytical Chem istry - DePauw University

Chapter 5 Standardizing Analytical Methods175Substituting these values into equation 5.17 and equation 5.18, we findthat the slope and the y-intercept are( 6 66 701 1 500 182 31b 1= × . )−( . × . )= 120. 706 ≈120.712( 6×0. 550)−( 1.500)( ) = ≈182. 31− 120. 706×1.500b 0=60. 209 021 .The relationship between the signal and the analyte, therefore, isS std = 120.71 × C std + 0.21For now we keep two decimal places to match the number of decimal placesin the signal. The resulting calibration curve is shown in Figure 5.11.Un c e r t a i n t y in t h e Re g r e s s i o n An a l y s i sAs shown in Figure 5.11, because of indeterminate error affecting our signal,the regression line may not pass through the exact center of each data point.The cumulative deviation of our data from the regression line—that is, thetotal residual error—is proportional to the uncertainty in the regression.We call this uncertainty the standard deviation about the regression,s r , which is equal tosr =∑( y − y ˆ i i)2in − 25.19Did you notice the similarity between thestandard deviation about the regression(equation 5.19) and the standard deviationfor a sample (equation 4.1)?605040S std 30201000.0 0.1 0.2 0.3 0.4 0.5C stdFigure 5.11 Calibration curve for the data in Table 5.1 and Example 5.9.