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...
View
Full Document
 Spring '08
 Clark
 α, Pallavolo Modena, the00

Click to edit the document details