3. A 2 factorial experiment was run to study a filtering system for coal. Three

Question

3. A 2 factorial experiment was run to study a filtering system for coal. Three factors were varied in the experimental process: Factor A: percent solids circulated initially in the overflow Factor B: flow rate of the polymer Factor C: pH of the tank The amount of solids in the underflow of the cleaning system determines how clean the coal has become. The data can be found in the file "HW 9 mining engr.jmp." All assumptions have been satisfied. Test the appropriate hypotheses. State the hypothesis or hypotheses of interest, the associated test statistic and p value, the decision and conclusion.

Explanation / Answer

Factorial Regression: responce versus A, B, C

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Model 7 490.235 70.034 254.43 0.000
Linear 3 400.413 133.471 484.90 0.000
A 1 356.360 356.360 1294.65 0.000
B 1 11.989 11.989 43.56 0.000
C 1 32.064 32.064 116.49 0.000
2-Way Interactions 3 10.211 3.404 12.37 0.002
A*B 1 5.748 5.748 20.88 0.002
A*C 1 4.463 4.463 16.21 0.004
B*C 1 0.001 0.001 0.00 0.967
3-Way Interactions 1 79.611 79.611 289.23 0.000
A*B*C 1 79.611 79.611 289.23 0.000
Error 8 2.202 0.275
Total 15 492.437

Model Summary

S R-sq R-sq(adj) R-sq(pred)
0.524649 99.55% 99.16% 98.21%

Coded Coefficients

Term Effect Coef SE Coef T-Value P-Value VIF
Constant 12.752 0.131 97.22 0.000
A 9.439 4.719 0.131 35.98 0.000 1.00
B 1.731 0.866 0.131 6.60 0.000 1.00
C -2.831 -1.416 0.131 -10.79 0.000 1.00
A*B -1.199 -0.599 0.131 -4.57 0.002 1.00
A*C -1.056 -0.528 0.131 -4.03 0.004 1.00
B*C 0.011 0.006 0.131 0.04 0.967 1.00
A*B*C 4.461 2.231 0.131 17.01 0.000 1.00

Regression Equation in Uncoded Units

responce = 12.752 + 4.719 A + 0.866 B - 1.416 C - 0.599 A*B - 0.528 A*C + 0.006 B*C
+ 2.231 A*B*C

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