7.54 In an effort to obtain maximum yield in a chemical reaction, the values of the following variables were chosen by the experimenter: x₁ = temperature (°C) x₂ = concentration of a reagent (%) x3 = time of reaction (hours) Two different response variables were observed: y₁ = percent of unchanged starting material y2 = percent converted to the desired product
7.54 In an effort to obtain maximum yield in a chemical reaction, the values of the following variables were chosen by the experimenter: x₁ = temperature (°C) x₂ = concentration of a reagent (%) x3 = time of reaction (hours) Two different response variables were observed: y₁ = percent of unchanged starting material y2 = percent converted to the desired product
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question

Transcribed Image Text:7.54 In an effort to obtain maximum yield in a chemical reaction, the values of the
following variables were chosen by the experimenter:
y
29
24
26
22
27
21
33
TABLE 7.3 Gas Vapor Data
34
32
34
20
36
34
23
24
32
concentration of a reagent (%)
time of reaction (hours)
Two different response variables were observed:
X1
33
31
33
37
36
35
59
60
59
60
34
60
60
60
62
62
53
36
51
51
54
35
56
60
x₁ = temperature (°C)
X₂
x3
60
60
35
59
62
36
38
61
y₁ percent of unchanged starting material
y2 = percent converted to the desired product
X3
3.32
3.10
3.18
3.39
3.20
3.03
4.78
4.72
4.60
4.53
2.90
4.40
4.31
4.27
4.41
4.39
X4
3.42
3.26
3.18
3.08
3.41
3.03
4.57
4.72
4.41
4.53
2.95
4.36
4.42
3.94
3.49
4.39
y
(a) Find ß and s².
(b) Find an estimate of cov(B).
40
745828
46
55
29
22
31
45
37
37
33
27
34
19
16
22
X1
90
90
92
91
61
59
88
91
63
60
60
59
59
37
35
37
X2
64
60
92
92
62
42
65
89
62
61
62
62
62
35
35
37
PROBLEMS
X3
7.32
7.32
7.45
7.27
3.91
3.75
6.48
6.70
4.30
4.02
4.02
3.98
4.39
2.75
2.59
2.73
183
Xa
6.70
7.20
7.45
7.26
4.08
3.45
5.80
6.60
4.30
4.10
3.89
4.02
4.53
2.64
2.59
2.59
The data are listed in Table 7.4 (Box and Youle 1955, Andrews and Herzberg
1985, p. 188). Carry out the following for y₁:

Transcribed Image Text:y
18.38
20.00
11.50
25.00
52.50
82.50
25.00
30.67
12.00
TABLE 7.4 Chemical Reaction Data
61.25
60.00
Y₁
57.50
31.00
60.00
72.50
60.33
49.75
41.5
33.8
27.7
21.7
19.9
15.0
12.2
4.3
19.3
6.4
37.6
18.0
26.3
9.9
25.0
14.1
15.2
15.9
19.6
TABLE 7.5 Land Rent Data
X1
15.50
22.29
12.36
31.84
83.90
72.25
27.14
40.41
12.42
Y2
45.9
53.3
57.5
58.8
60.6
58.0
58.6
52.4
184 MULTIPLE REGRESSION: ESTIMATION
69.42
48.46
69.00
26.09
62.83
56.9
55.4
46.9
57.3
55.0
58.9
77.06
58.83
59.48
50.3
61.1
62.9
60.0
60.6
X2
17.25
18.51
11.13
5.54
5.44
20.37
31.20
4.29
8.69
6.63
27.40
31.23
28.50
29.98
13.59
45.46
35.90
X3
.24
.20
.12
.12
.04
.05
.27
.10
.41
.04
.12
.08
X1
.21
.17
.05
.16
.32
162
162
162
162
172
172
172
172
167
177
157
167
167
167
167
177
177
160
160
y
8.50
36.50
60,00
16.25
50.00
11.50
35.00
75.00
31.56
48.50
77.50
21.67
19.75
56.00
25.00
40.00
56.67
X2
23
23
30
30
25
25
30
30
27.5
27.5
27.5
32.5
22.5
27.5
27.5
20
20
34
34
X1
9.00
20.64
81.40
18.92
50.32
21.33
46.85
65.94
38.68
51.19
59.42
24.64
26.94
46.20
26.86
20.00
62.52
X3
3
8
5
8
5
8
5
8
6.5
6.5
6.5
6.5
6.5
9.5
3.5
6.5
6.5
7.5
7.5
X2
8.89
23.81
4.54
29.62
21.36
1.53
5.42
22.10
14.55
7.59
49.86
11.46
2.48
31.62
53.73
40.18
15.89
X3
.08
.24
.05
.72
.19
.10
.08
.09
.17
.13
.13
.21
.10
.26
.43
.56
.05
(c) Find R² and R².
(d) In order to find the maximum yield for y₁, a second-order model is of
interest. Find and s² for the model y₁ = Bo+B₁x1 + B₂X₂ + B3X3+
B₁x + B5x+B6x + B7x1x2 + B8X1x3 + B9x2x3 + 8.
(e) Find R² and R for the second-order model.
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