# Statistics for Environmental Engineers

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0

0

3.72

3

4.33

3.62

0

0

1

0

0

3.62

4

4.62

3.98

0

0

1

0

0

3.98

5

4.55

4.03

0

0

1

0

0

4.03

6

4.78

4.50

0

0

1

0

0

4.50

7

5.20

4.49

0

0

1

0

0

4.49

8

5.60

5.19

0

0

1

0

0

5.19

Source: Lee, L. S. et al. (1992). Emir. Sci. Tech., 26, 2104-2110.

40.4 Threshold Concentration. The data below can be described by a hockey-stick pattern. Below some threshold value (t) the response is a constant plateau value (n = Yo). Above the threshold, the response is linear n = Y0 + P1(x — t). These can be combined into a continuous segmented model using a dummy variable z such that z = 1 when x > t and z = 0 when x < t. The dummy variable formulation is n = Y0 + P1(x — t)z, where z is a dummy variable. This gives n = Yfor x < t and n = Y0 + в(х — T) = Yo + вх — вт for x > t. Estimate the plateau value Y0, the post-threshold slope в1, and the unknown threshold dose T.

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