0920 3707 2 309902 19584 8 3822 1419 cee

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Unformatted text preview: .59 195.84 376479.50 38.22 3764.13 Average 448.25 4.44 Sum 5762.35 n ∑ (V − V ) ( pH i b= i − pH i =1 n ∑ ( pH i =1 i − pH ) ) 2 = 3764.13 = 98.4867 38.22 a = V − b pH = 448.25 − 98.4867 × 4.44 = 11.0920 The linear relationship between output voltage and pH is: pH=11.0920+98.4867V 800 Output Voltage (mv) 700 600 Orignial Data 500 Linear (Orignial Data) 400 300 200 100 0 0 2 4 pH 6 8 13/19 CEE 202 – Engineering Risk & Uncertainty Spring 2011 (Bond) Homework 11 Diff. between Means; Least ­Squares b) What is a 99% confidence interval for those coefficients? From the table above, we can get n 2 2 SST = ( n − 1) SV = ∑ (Vi − V ) = 376479.50 , i =1 n 2 ( n − 1) S pH = ∑ ( pH i − pH ) 2 = 38.22 , i =1 n ∑ (V − V ) ( pH i ) − pH = 3764.13 , i i =1 n s= n 2 ( ∑ (Vi − V ) − b∑ (Vi − V ) pH i − pH i =1 i =1 ) n−2 376479.50 − ( 98.4867 ) × (3764.13 ) 8−2 = 30.9902 Or you can use SSE 5762.35 s= = = 30.9902 n−2 6 α = 1 − 0.99 = 0.01 , in each tail α 2 = 0.005; d.f.=n ­2=8 ­2=6 Using Table A4. or function tinv in Excel, we find that t0.005 = 3.707 for 6 degrees of freedom. Therefore, a 99% confidence interval for b is s 30.9902 β = b ± tα /2 = 98.4867 ± 3.707 × = n 2 38.22 ∑ pH i − pH = i =1 ( ) 98.4867 ± 18.5846or ( 79.9021,117.0714) From the table above, we can also get n ∑ pH 2 i = 195.84 , i =1 A 99% confidence interval for a is s α = a ± tα 2 n ∑ pH 2 i i =1 n ( n∑ pH i − pH i =1 = 11.0920 ± 3.707 × 2 ) 30.9902 195.84 = 8 × 38.22 14/19 CEE 202 – Engineering Risk & Uncertainty Spring 2011 (Bond) Homework 11 Diff. between Means; Least ­Squares 11.0920 ± 91.9515 or ( −80.8595,103.0435) c) Your labmate says, “This slope is very small. I don’t think your analyzer is working.” How do you answer? If the analyzer is working, it means that the ou...
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This document was uploaded on 03/06/2014 for the course CEE 202 at University of Illinois, Urbana Champaign.

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