Page 300 - Statistics for Environmental Engineers

L1592_frame_C34 Page 306 Tuesday, December 18, 2001 2:52 PM

TABLE 34.1
HPLC Calibration Data (in run order from left to right)
Dye Conc. 0.18 0.35 0.055 0.022 0.29 0.15 0.044 0.028
HPLC Peak Area 26.666 50.651 9.628 4.634 40.206 21.369 5.948 4.245

Dye Conc. 0.044 0.073 0.13 0.088 0.26 0.16 0.10
HPLC Peak Area 4.786 11.321 18.456 12.865 35.186 24.245 14.175
Source: Bailey, C. J., E. A. Cox, and J. A. Springer (1978). J. Assoc. Off. Anal. Chem., 61, 1404–1414.

TABLE 34.2
Results of the Linear Regression Analysis
Standard P
Variable Coefficient Error t (2-tail)
Constant 0.566 0.473 1.196 0.252
x 139.759 2.889 48.38 0.000

Analysis of Variance
Sum of Degrees of Mean
Source Squares Freedom Square F-Ratio P
Regression 2794.309 1 2794.309 2340 0.000000
Residual 15.523 13 1.194

Fitted model
50
y = 0.556 + 139.759x
HPLC Peak Area 30 mean response
95% confidence
40
interval for the
20

10 95% confidence
interval for
future values
0
0 0.1 0.2 0.3 0.4
Dye Concentration
FIGURE 34.2 Fitted calibration line with 95% confidence bounds for the mean and future values.

is shown with the data in Figure 34.2. Also shown are the 95% confidence bounds for the mean and
future values.
An estimate of the variance of the measured values is needed to make any statements about the
precision of the estimated parameters, or to compute confidence intervals for the line. Because there is
no true replication in this experiment, the mean residual sum of squares is used as an estimate of the
2
variance σ . The mean residual sum of squares is the residual sum of squares divided by the degrees of
2 15.523
freedom (s = ---------------- = 1.194), which is estimated with ν = 15 − 2 = 13 degrees of freedom. Using this
13
value, the estimated variances of the parameters are:
Var (b 0 ) = 0.2237 and Var (b 1 ) = 8.346

© 2002 By CRC Press LLC