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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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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: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:
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.
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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