25 356 077 12127806 1266 123933 9776 502 220 212

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Unformatted text preview: D: n ∑(D − D)(H i i =1 ˆ ρ= i −H) −775 n −1 = = −0.9741 n 605.2 ×1046 2 Ⱥ Ⱥ 2 Ⱥ Ⱥ Ⱥ ∑ ( Di − D ) Ⱥ Ⱥ ∑ ( H i − H ) Ⱥ Ⱥ i =1 Ⱥ Ⱥ i =1 Ⱥ n −1 n −1 Ⱥ Ⱥ Ⱥ Ⱥ Ⱥ Ⱥ Ⱥ Ⱥ Ⱥ Ⱥ Ⱥ Ⱥ n ˆ Or ρ = r = − 0.9488 = −0.9741 11/19 CEE 202 – Engineering Risk & Uncertainty Spring 2011 (Bond) Homework 11 Diff. between Means; Least ­Squares 3) You’ve built a pH analyzer for testing the acidity of soils. Before using it for important research, you test the analyzer’s response against solutions with known pH and obtains the following results: Output Voltage (mV) pH 100 0.88 220 2.12 295 3.22 422 3.78 501 4.89 605 6.50 688 6.88 755 7.24 800 Output Voltage (mv) 700 600 500 400 300 200 100 0 0 2 4 6 8 pH The scattering plot between output voltage and pH shows that these two variables are linearly related. a) Determine a best estimate of the coefficients in a linear relationship between voltage and pH. Assume the linear relationship between Voltage (V) and pH is: V = a + bpH 1n V = ∑ Vi = 448.25 n i =1 12/19 CEE 202 – Engineering Risk & Uncertainty Spring 2011 (Bond) Vi Homework 11 Diff. between Means; Least ­Squares 1n pH = ∑ pH i = 4.44 n i =1 pH i Vi − V pHi − pH pH i2 2 (V − V ) ( pH i i − pH 2 ) (V − V ) ( pH − pH ) Vˆ = a + bpH (Vˆ − V ) i i i i i 2 i 100 0.88 -348.25 -3.56 0.77 121278.06 12.66 1239.33 97.76 5.02 220 2.12 -228.25 -2.32 4.49 52098.06 5.38 529.25 219.88 0.01 295 3.22 -153.25 -1.22 10.37 23485.56 1.49 186.77 328.22 1103.52 422 3.78 -26.25 -0.66 14.29 689.06 0.43 17.29 383.37 1492.13 501 4.89 52.75 0.45 23.91 2782.56 0.20 23.80 492.69 69.02 605 6.5 156.75 2.06 42.25 24570.56 4.25 323.10 651.26 2139.60 688 6.88 239.75 2.44 47.33 57480.06 5.96 585.29 688.68 0.46 755 7.24 306.75 2.80 52.42 94095.56 7.85 859.28 724.14 952...
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