2. Fit a multiple linear regression model relating yield to CO2 pressure, CO2 te

Question

2. Fit a multiple linear regression model relating yield to CO2 pressure, CO2 temperature and peanut particle size.

a) Clearly state the regression equation.

b) Test for significance of regression.

c) Calculate a confidence interval for the regression coefficient for peanut particle size.

d) Use a t test to assess the contribution of CO2 pressure, given that CO2 temperature and peanut particle size are already in the model.

e) Use a partial F test to do the proceeding part.

f) Find MSRes, R 2 and R 2 Adj for this model.

560 APPENDIX B TABLE B.7 Pressure (bars) Oil Extraction from Peanuts Data Particle Size Flow Rate (L/min) 40 40 40 40 40 40 40 40 Moisture 1% by weight) Temp 415 1.28 550 4.05 4.05 95 95 415 550 415 550 415 1.28 4.05 1.28 1.28 4.05 4.05 1.28 15 15 15 15 95 95 550 415 550 415 550 415 60 60 74 95 95 1.28 4.05 15 15 15 15 1.28 4.05 4.05 1.28 550 415 550 95 95 60 60 60 96 Source: "An Application of Fractional Experimental Designs," by M. R Kileo ulit pp. 19-23.

Explanation / Answer

The suitable model of the given data is ANOVA because CO2 pressure, CO2 temperature and peanut particle size are factors.

2. Fit a multiple linear regression model relating yield to CO2 pressure, CO2 temperature and peanut particle size.

a) Clearly state the regression equation.

Ans: The regression equation is

Yield=Bo+B1*pressure+B2*Temp+B3*Particle size+error

b) Test for significance of regression.

Ans:

Estimate Std. Error t value Pr(>|t|)   
(Intercept) 56.39320 15.46140 3.647 0.003343 **
Pressure 0.04906 0.02974 1.650 0.124922   
Temp 0.26961 0.05735 4.701 0.000513 ***
Particle_Size -15.59191 1.41687 -11.004 1.26e-07 ***

Conclusion: Temp and Particle_Size have significant effect on Yield at 0.05 level of significance.

c) Calculate a confidence interval for the regression coefficient for peanut particle size.

Ans:

2.5 % 97.5 %
(Intercept) 22.70569685 90.0807112
Pressure -0.01573603 0.1138539
Temp 0.14465194 0.3945753
Particle_Size -18.67899566 -12.5048189

d) Use a t test to assess the contribution of CO2 pressure, given that CO2 temperature and peanut particle size are already in the model.

Ans: t-value is 1.650 with corresponding p-value 0.124922. Hence, CO2 pressure does not have significant effect on yield at 0.05 level of significance.

e) Use a partial F test to do the proceeding part.

Analysis of Variance

Source DF SS MS F P
Regression 3 9589.6 3196.5 49.60 0.000
Residual Error 12 773.4 64.4
Total 15 10363.0

Comment: The some of the regressors have the significant effect on yields at 0.05 level of significance.

f) Find MSRes, R 2 and R 2 Adj for this model.

MSRes= 8.02785, R-Sq = 0.925, R-Sq(adj) = 0.907

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