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The yield of a chemical process is being studied. The two most important variabl

ID: 3183545 • Letter: T

Question

The yield of a chemical process is being studied. The two most important variables are thought to be the pressure and the temperature. Three levels of each factor are selected, and a factorial experiment with two replicates is performed. The yield data follow:

Temperature

Pressure

200

215

230

150

90.1

90.5

89.9

90.3

90.6

90.1

160

90.5

90.8

90.4

90.7

90.9

90.1

170

90.4

90.7

90.2

90.2

90.6

90.4

a. Analyze the data and draw conclusions. Use = 0.05.

b. Prepare appropriate residual plots and comment on the model’s adequacy.

c. Under what conditions would you operate this process?

please use minitab and show graphs if possible..Thanks!

Temperature

Pressure

200

215

230

150

90.1

90.5

89.9

90.3

90.6

90.1

160

90.5

90.8

90.4

90.7

90.9

90.1

170

90.4

90.7

90.2

90.2

90.6

90.4

Explanation / Answer


—————   01/04/2017 9:52:42 PM   ————————————————————

Ho(null hypothesis):- No differ significance.

vs H1:- differ significance.

MTB > Name C4 "FITS1" C5 "RESI1" C6 "SRES1".

MTB > GLM;
SUBC>   Response 'response';
SUBC>   Nodefault;
SUBC>   Categorical 'temparature' - 'pressure';
SUBC>   Terms temparature pressure;
SUBC>   TMethod;
SUBC>   TAnova;
SUBC>   TSummary;
SUBC>   TCoefficients;
SUBC>   TEquation;
SUBC>   TFactor;
SUBC>   TDiagnostics 0;
SUBC> GFOURPACK;
SUBC>   Fits 'FITS1';
SUBC>   Residuals 'RESI1';
SUBC> SResiduals 'SRES1'.

General Linear Model: response versus temparature, pressure

Method

Factor coding (-1, 0, +1)


Factor Information

Factor       Type   Levels Values
temparature Fixed       3 150, 160, 170
pressure     Fixed       3 200, 215, 230


Analysis of Variance

Source         DF   Adj SS   Adj MS F-Value P-Value
temparature   2 0.30111 0.15056     8.55    0.004
pressure      2 0.76778 0.38389    21.80    0.000
Error          13 0.22889 0.01761
Lack-of-Fit   4 0.06889 0.01722     0.97    0.470
Pure Error    9 0.16000 0.01778
Total          17 1.29778

Comment :- The p value less than 0.05 so that reject null hypothesis.
Model Summary

       S    R-sq R-sq(adj) R-sq(pred)
0.132691 82.36%     76.94%      66.19%


Coefficients

Term            Coef SE Coef T-Value P-Value   VIF
Constant     90.4111   0.0313 2890.80    0.000
temparature
150        -0.1611   0.0442    -3.64    0.003 1.33
160         0.1556   0.0442     3.52    0.004 1.33
pressure
200        -0.0444   0.0442    -1.00    0.333 1.33
215         0.2722   0.0442     6.15    0.000 1.33


Regression Equation    # this is the model

response = 90.4111 - 0.1611 temparature_150 + 0.1556 temparature_160 + 0.0056 temparature_170
           - 0.0444 pressure_200 + 0.2722 pressure_215 - 0.2278 pressure_230


Fits and Diagnostics for Unusual Observations

Obs response      Fit    Resid Std Resid
12   90.1000 90.3389 -0.2389      -2.12 R

R Large residual


Residual Plots for response

from the we can say that ,data follow normally distribution and variance is constant in the versus fit.