Statistics for Environmental Engineers

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1 + (x0-x)2 n E(xi — x)2


The prediction interval for the future single observation (y f = b0 + bxxf) to be recorded at a setting xf is:


1+n +



(b0 + bixf )± tu.a/2S



(x/-x)2 S(xt — x)


Note that this prediction interval is larger than the confidence interval for the mean response (n0) because the prediction error includes the error in estimating the mean response plus measurement error in y. This introduces the additional “1” under the square root sign.

Case Study: A Linear Model


Data from calibration of an HPLC instrument and the fitted model are shown in Table 34.1 and in Figure 34.2. The results of fitting the model y = в0 + в1x + e are shown in Table 34.2. The fitted equation:


y = b0 + b1 x = 0.566 + 139.759x


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.

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