article reports on a study in which the accompanying data was obtained to relate y = specific surface area (cm²/g) to x₁ = % NaOH used as a pretreatment chemical and x₂ = treatment time (min) for a batch X1 3 3 3 9 9 9 15 15 15 x₂ 30 60 90 30 60 90 30 60 90 Predictor Constant NACH TIME accompanying Minitab output resulted from a request to fit the model Y=B₁ + B₂X₂ + B₂X₂ + 6. The regression equation is AREA = 6.05 + 0.142 NAOH - 0.0169 TIME s=0.4851 y 5.95 Error Total 5.60 5.44 6.22 5.85 5.61 8.36 7.30 6.43 Coef 6.0483 0.14167 -0.016944 R-sq = 80.74 Analysis of Variance SOURCE Regression. DE 2 Yes, because the P-value is less than 0.05. O Yes, because the P-value is more than 0.05. O No, because the P-value is less than 0.05. O No, because the P-value is more than 0.05. Stdev 0.5208 0.03301 0.006601 O Yes, because the P-value is less than 0.05. O Yes, because the P-value is more than 0.05. t-ratio 11.61 ss 5.8854 1.4118 7.2972 No, because the P-value is less than 0.05. O No, because the P-value is more than 0.05. 4.29 -2.57 R-sq (adj) 74.29 MS 2.9427 0.2353 P 0.000 0.005 0.043 (a) What proportion of observed variation in specific surface area can be explained by the model relationship? 0.807 F 12.51 (b) Does the chosen model appear to specify a useful relationship between the dependent variable and the predictors? (Use a = 0.05.) P-value=0.007 P 0.007 (c) Provided that % NaOH remains in the model, would you suggest that the predictor treatment time be eliminated? (Use a = 0.05.) P-value=0.043 (d) Calculate a 95% CI for the expected change in specific surface area associated with an increase of 1% in NaOH when treatment time is held fixed. (Round your answer to four decimal places.) 0.0609 ✔02224 ✔)cm²/g (e) Minitab reported that the estimated standard deviation of +₂ (15) +₂(30) is 0.323. Calculate a prediction interval for the value of specific surface area to be observed when % NaOH = 15 and treatment time = 30. (Use a = 0.05. Round your answers to two decimal places.) (5.22 x8.07 x)cm²/g
article reports on a study in which the accompanying data was obtained to relate y = specific surface area (cm²/g) to x₁ = % NaOH used as a pretreatment chemical and x₂ = treatment time (min) for a batch X1 3 3 3 9 9 9 15 15 15 x₂ 30 60 90 30 60 90 30 60 90 Predictor Constant NACH TIME accompanying Minitab output resulted from a request to fit the model Y=B₁ + B₂X₂ + B₂X₂ + 6. The regression equation is AREA = 6.05 + 0.142 NAOH - 0.0169 TIME s=0.4851 y 5.95 Error Total 5.60 5.44 6.22 5.85 5.61 8.36 7.30 6.43 Coef 6.0483 0.14167 -0.016944 R-sq = 80.74 Analysis of Variance SOURCE Regression. DE 2 Yes, because the P-value is less than 0.05. O Yes, because the P-value is more than 0.05. O No, because the P-value is less than 0.05. O No, because the P-value is more than 0.05. Stdev 0.5208 0.03301 0.006601 O Yes, because the P-value is less than 0.05. O Yes, because the P-value is more than 0.05. t-ratio 11.61 ss 5.8854 1.4118 7.2972 No, because the P-value is less than 0.05. O No, because the P-value is more than 0.05. 4.29 -2.57 R-sq (adj) 74.29 MS 2.9427 0.2353 P 0.000 0.005 0.043 (a) What proportion of observed variation in specific surface area can be explained by the model relationship? 0.807 F 12.51 (b) Does the chosen model appear to specify a useful relationship between the dependent variable and the predictors? (Use a = 0.05.) P-value=0.007 P 0.007 (c) Provided that % NaOH remains in the model, would you suggest that the predictor treatment time be eliminated? (Use a = 0.05.) P-value=0.043 (d) Calculate a 95% CI for the expected change in specific surface area associated with an increase of 1% in NaOH when treatment time is held fixed. (Round your answer to four decimal places.) 0.0609 ✔02224 ✔)cm²/g (e) Minitab reported that the estimated standard deviation of +₂ (15) +₂(30) is 0.323. Calculate a prediction interval for the value of specific surface area to be observed when % NaOH = 15 and treatment time = 30. (Use a = 0.05. Round your answers to two decimal places.) (5.22 x8.07 x)cm²/g
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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e
Transcribed Image Text:An article reports on a study in which the accompanying data was obtained to relate y = specific surface area (cm²/g) to x₁ = % NaOH used as a pretreatment chemical and x₂ = treatment time (min) for a batch of pulp.
X₁
3
3
3
9
9
9
15
15
15
X2
30
60
90
30
60
NAOH
TIME
90
30
60
90
Predictor
Constant
The accompanying Minitab output resulted from a request to fit the model Y = B₁ + B ₁ X ₁ + B ₂ X ₂ + ε.
The regression equation is
AREA = 6.05 +0.142 NAOH 0.0169 TIME
s = 0.4851
Error
Total
y
5.95
5.60
5.44
6.22
5.85
5.61
8.36
7.30
6.43
Coef
6.0483
0.14167
-0.016944
R-sq = 80.7%
Analysis of Variance.
SOURCE
Regression
DF
2
6
8
Stdev
0.5208
0.03301
0.006601
t-ratio
11.61
4.29
-2.57
R-sq (adj) = 74.2%
SS
5.8854
1.4118
7.2972
O Yes, because the P-value is less than 0.05.
O Yes, because the P-value is more than 0.05.
O No, because the P-value is less than 0.05.
O No, because the P-value is more than 0.05.
MS
2.9427
0.2353
p
0.000
0.005
0.043
F
12.51
P
0.007
(a) What proportion of observed variation in specific surface area can be explained by the model relationship?
0.807
✓
(b) Does the chosen model appear to specify a useful relationship between the dependent variable and the predictors? (Use a = 0.05.)
P-value = 0.007
Ⓒ Yes, because the P-value is less than 0.05.
O Yes, because the P-value is more than 0.05.
O No, because the P-value is less than 0.05.
O No, because the P-value is more than 0.05.
(c) Provided that % NaOH remains in the model, would you suggest that the predictor treatment time be eliminated? (Use a = 0.05.)
P-value = 0.043
(d) Calculate a 95% CI for the expected change in specific surface area associated with an increase of 1% in NaOH when treatment time is held fixed. (Round your answer to four decimal places.)
0.0609
0.2224
cm²/g
(e) Minitab reported that the estimated standard deviation of µ + ß₁(15) + ß₂(30) is 0.323. Calculate a prediction interval for the value of specific surface area to be observed when % NaOH = 15 and treatment time = 30. (Use a = 0.05. Round your answers to two decimal places.)
x cm²/g
5.22
X 8.07
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