3. Results and discussion
3.7. Stationary systems regression model development with restricted wind speed and
3.7.1. Variables and data description
The data used in this section was described in section 3.6.1. It was only the data collected from stationary systems. The candidate variables were “nozzle diameter”, “nozzle type”, “gun model”, “nozzle pressure”, “sprinkler spacing in percent of wetted diameter”, and “wetted diameter”.
3.7.2. Main effects selection
The main effect selections were conducted in PROC GLMSELECT using Forward, Backward, and Stepwise methods. The SLE and SLS values were set as their default levels. All the three methods selected the same variables which were “nozzle type”, “nozzle pressure”, “sprinkler spacing in percent of wetted diameter”, and “wetted diameter”. Those four variables passed the collinearity test with all the VIF values lower than ten.
3.7.3. Select interaction terms and quadratic terms
Stepwise, Forward, and Backward Selections were conducted under five different significance levels (SL), 0.1, 0.15, 0.2, 0.25, and 0.3, thus there were 15 resultant models (table 3-12). However, since most of the 15 models were the same, there were only two different models, one from Stepwise1 and another one from Backward1, to compare (table 3- 13). The interaction terms were limited to the second order. Comparing selection criteria values of the two models, the Backward1 model was better with higher a R2 and adjusted R2 and lower AIC, AICC, press residual, and SBC. However, this model had many more terms
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in the model (16 terms) than Stepwise1 (7 terms). Considering the slight difference of the adjusted R2 between the two models, the model from Stepwise1 was selected.
Table 3-12 Se lected variables fro m different selection methods
effects SL
stepwise1 Intercept nozt nozp Per_Over*nozt WD*nozt nozp*WD
Per_Over*Per_Over WD*WD SLE=SLS=0.1
stepwise2 Intercept nozt nozp Per_Over*nozt WD*nozt nozp*WD
Per_Over*Per_Over WD*WD SLE=SLS=0.15
stepwise3 Intercept nozt nozp Per_Over*nozt WD*nozt nozp*WD
Per_Over*Per_Over WD*WD SLE=SLS=0.2
stepwise4 Intercept nozt nozp Per_Over*nozt WD*nozt nozp*WD
Per_Over*Per_Over WD*WD SLE=SLS=0.25
stepwise5 Intercept nozt nozp Per_Over*nozt WD*nozt nozp*WD
Per_Over*Per_Over WD*WD SLE=SLS=0.3
forward1 Intercept nozt nozp Per_Over*nozt WD*nozt nozp*WD
Per_Over*Per_Over WD*WD SLE=0.1
forward2 Intercept nozt nozp Per_Over*nozt WD*nozt nozp*WD
Per_Over*Per_Over WD*WD SLE=0.15
forward3 Intercept nozt nozp Per_Over*nozt WD*nozt nozp*WD
Per_Over*Per_Over WD*WD SLE=0.2
forward4 Intercept nozt nozp Per_Over*nozt WD*nozt nozp*WD
Per_Over*Per_Over WD*WD SLE=0.25
forward5 Intercept nozt nozp Per_Over*nozt WD*nozt nozp*WD
Per_Over*Per_Over WD*WD SLE=0.3
backward1
Intercept nozt nozp nozp*nozt Per_Over Per_Over*nozt windsd windsd*nozt Per_Over*windsd WD WD*nozt
nozp*WD Per_Over*WD windsd*WD nozp*nozp Per_Over*Per_Over WD*WD
SLS=0.1
backward2
Intercept nozt nozp nozp*nozt Per_Over Per_Over*nozt windsd windsd*nozt Per_Over*windsd WD WD*nozt
nozp*WD Per_Over*WD windsd*WD nozp*nozp Per_Over*Per_Over WD*WD
SLS=0.15
backward3
Intercept nozt nozp nozp*nozt Per_Over Per_Over*nozt windsd windsd*nozt Per_Over*windsd WD WD*nozt
nozp*WD Per_Over*WD windsd*WD nozp*nozp Per_Over*Per_Over WD*WD
SLS=0.2
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effects SL
backward4
Intercept nozt nozp nozp*nozt Per_Over Per_Over*nozt windsd windsd*nozt Per_Over*windsd WD WD*nozt
nozp*WD Per_Over*WD windsd*WD nozp*nozp Per_Over*Per_Over WD*WD
SLS=0.25
backward5
Intercept nozt nozp nozp*nozt Per_Over Per_Over*nozt windsd windsd*nozt Per_Over*windsd WD WD*nozt
nozp*WD Per_Over*WD windsd*WD nozp*nozp Per_Over*Per_Over WD*WD
SLS=0.3
Table 3-13 Criteria of d ifferent models
stepwise 1 backward 1 Root MSE 3.29341 2.90546 Dependent Mean 81.73169 81.73169 R-Square 0.7872 0.8545 Adj R-Sq 0.7527 0.8075 AIC 219.31421 204.22479 AICC 3.61089 3.57182 PRESS 1121.4052 1067.4461 SBC 251.37102 258.47477
3.7.4. Final model determination
The model from Stepwise1 was analyzed in PROC GLM. The interaction of “nozzle pressure” and “wetted diameter” had a p-value (0.0575) slightly higher than 0.05. Dropping this interaction term resulted in R2 decreasing, but since the model was built for the purpose of predicting, this term was allowed to stay in the model. Therefore, the final model could be expressed as: 0 1 2 3 2 2 4 5 6 7 ( ) _ _
E CU nozt nozp Per Over nozt WD nozt nozp WD Per Over WD
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where, E(CU)=expected value of CU nozt=nozzle type
WD=wetted diameter nozp=nozzle pressure
Per_Over=sprinkler spacing in percent of wetted diameter 3.7.5. Model evaluation
The stationary model selected in this section did not perform as well as the stationary model in section 3.4 with lower R2 and adjusted R2 and wider CLM and CLI intervals, but it had fewer terms. The stationary model selected in this section fit the data better than the combined model in section 3.5 with a higher R2 and adjusted R2 and narrower CLM and CLI intervals, the average CLM and CLI intervals of the combined model in section 3.5 for the stationary system observations were 7 and 29, and of the stationary model in this section was 4 and 14).
3.7.6. Conclusions
1) Variables “nozzle type”, “nozzle pressure”, “sprinkler spacing in percent of wetted diameter”, and “wetted diameter” were selected as the candidate variables for further analysis in the main effect selection step. The final model was expressed in equation 3.6. It contains main effects, interaction terms and quadratic terms.
2) The final model, R2 was 0.7872, the adjusted R2 was 0.7527, the press residual was 1121, the root MSE was 3.2934, the maximum ranges of CLM and CLI were 7 and 15, the minimum ranges of CLM and CLI were 3 and 14, the average range of CLM is 5, and the average range of CLI is 14.
3) The residuals of the model were approximately normally distributed (Table A6-9, figure A6-1, fugureA6-2).
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3.8. References
Evans, R.O., Barker J.C., Smith J.T., Sheffield R.E. 1997a. AG-553-1, Field Calibration Procedures for Animal Wastewater Application Equipment - Stationary Sprinkler Irrigation System. NC Cooperative Extension Service & NC State University.
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