# Statistics for Environmental Engineers

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The value of k at the given values of the variables is:

00 = k =

(Sp-S)Q

SXV

(200-20)(1)

20(2000)(1)

0.0045

The other coefficients of the linearized model are:

0

0

0

S

0

0

S

X

Q

 дк ))))Q))))))) dS0 SXV dk Q dS SXV dk Co I о CO dX = SX2V dk Co 0 I Co 1 d))))Q))) SXV

1

20(2000)(1

2.5 x 10-5

1= 20(2000)(1) =

200 — 20

20(2000)2 ( 1 )

200 — 20 = 20(2000)(1) =

-2.5 x 10-5 = -2.25 x 10-6 0.0045

The variance of k, assuming all covariances are zero, is:

3.11 x 10-7

ot = 0s„Oso + 02sG2s + 0WX + 02qoQ

which is computed from the separate contributions of the variables using the values and variances given earlier, and as shown in Table 49.1.

The estimated total variance is ok = 3.11 x 10 7 and the standard deviation is ok = 0.00056. These numbers are small, but the expected value of k = 0.0045 is also small. A better perspective is obtained by finding an approximate 95% confidence interval for the estimated value of k, based on the linear approximation of the true model:

k = 0.0045 ± 2(0.00056) = 0.0045 ± 0.0011

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