HP 



For each model then, we are able to specify the basic A Fortran IV computer program for table output from the 



APR-effect as: ^ s model follows: 



YPAPR 1.35 



^,1.35 { * (APR) 

 V (24) ) ' ' 



where: 



YPAPR = INTERCEPT + SCALAR FOR THE SIGMOIDS* 

 SIGMOIDS OVER COVER. 



YPAPRL is used in the model for lime soils. 



YPAPRN is used in the model for nonlime soils. 

 INTERCEPTS: 



NON-LIME: FLORNL = 1581 + 12.0968 * N03 

 LIME: FLORL = 1458 + 12.0968 * N03 



SCALARS FOR SIGMOIDS: 



NON-LIME: YPCNL= 4003 + 1 6.9355 ♦ N03 - FLORNL 

 LIME: YPCL = 1983 + 16.9355 *N03 - FLORL 



SIGMOIDS OVER COVER: 



INFLECTION POINTS (INFL): 

 NON-LIME: INL = 0.1 + 0.0006869 * (30-NO3)'-9 

 LIME: IL = 0.1 + 0.0001054 * (30-NO3)2-6 



SIGMOIDAL POWER (N): 



NON-LIME: NNL = 7.4 - 0.003067 * (SO-NOS)^-^ 

 LIME: NL = 1 1 .0 - 0.001 372 * (30-NO3)2-6 



LIMITS: 



< cover<50, IF cover >50, HP = HP @ cover = 50 

 <APR < 25 



< N03 < 30, IF N03 >30, HP = HP @ N03 = 30 



After derivation from both prior knowledge and the data 

 at hand, the model was mathematically readjusted to the 

 data with a relatively simple coefficient that forces the fitted 

 model through zero, 



b = z:xY/zx^ 



where X = the model herbage production value forspecified 

 levels of APR, cover, and N03; and Y = the related observed 

 value of herbage production. A weighting factor of 1/y" was 

 evaluated and discarded since it was poorly related to the 

 variance about the least-squares fitted model (R^ = 0.03). 

 The b-value for the 19 observations was 0.9618 or, in other 

 words, the initially derived model was about 4 percent high 

 with respect to the least-squares fit. For the final model R^ 

 is 0.84 and Sy.x is about 287 lb/acre (321 kg/ha). Values 

 for the relation are given in table 1. 



Note that Sy x is likely to be underestimated here since 

 unknown degrees of freedom are sacrificed in exploiting 

 the data as explained. Models developed in this way are 

 probably best used as advanced hypotheses, to be tested 

 and scaled (b = SXY/SX^) to new data sets. In the absence 

 of better information such models can, of course, be used 

 as interim predictors with suitable caution. 



6 



