3. Fit a multiple linear regression model relating yield to CO2 temperature and
ID: 3359044 • Letter: 3
Question
3. Fit a multiple linear regression model relating yield to CO2 temperature and peanut particle size.
a) Clearly state the regression equation.
b) Test for significance of regression.
c) Use a t test to assess the contribution of CO2 temperature, given that peanut particle size is already in the model.
d) Use a partial F test to assess the contribution of peanut particle size, given that CO2 temperature is already in the model.
e) 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 and peanut particle size are factors.
3. Fit a multiple linear regression model relating yield to CO2 temperature and peanut particle size.
a) Clearly state the regression equation.
Ans: Yield=Bo+B1*Temp+B2*Particle size+error
b) Test for significance of regression.
Ans:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 80.19134 5.91972 13.546 4.82e-09 ***
Temp 0.26958 0.06103 4.417 0.000696 ***
Particle_Size -15.63831 1.50746 -10.374 1.17e-07 ***
Comment: The Temperature and Particle Siz have the significant effect on yield at 0.05 level of significance at 0.05 level of significance.
c) Use a t test to assess the contribution of CO2 temperature, given that peanut particle size is already in the model.
The estimated t-test value and p-value are 4.417 and 0.000696 respectively.
d) Use a partial F test to assess the contribution of peanut particle size, given that CO2 temperature is already in the model.
Ans:
Source DF SS MS F P
Regression 1 7990.5 7990.5 47.15 0.000
Residual Error 14 2372.5 169.5
Total 15 10363.0
Comment: The estimated p-value is 0.000. Hence, particle size has the significant effect on yield at 0.05 level of significance.
e) Find MSRes, R 2 and R 2 Adj for this model.
Ans: MSRes = 13.0180 R-Sq = 0.771, R-Sq(adj) = 0.755
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