Table 2. --Analysis of improvement of regression model attributable to adding variables. 



Dependent variable = LH 



Comparison 

 level 



Source 



d.f. 



Proportion of 

 remaining variance 

 explained.!/ 



Marginal 

 sum of squares!./ 



Mean 

 square 



HLB/B 



49469.808 

 2263.450 



2263.450 263.0 



2 [ H ^ D isp ] 



9 



0.065 



776 



592 



86 



288 



10 







isp 



9 



.060 



728 



725 



80 



.969 



9 



4 



3 1 . 



%sp 



9 



.0168 



260 



549 



28 



950 



3 



4 



[in {H) ] 



1 



. 151 



1491 



782 



1491 



782 



173 



3 



4 In {CR) 



10 



.048 



479 



677 



47 



967 



5 



6 



1 . 



isp 



9 



.0158 



219 



627 



23 



403 



, 2 



7 



[hD/D,{^/D) 2 ] 



2 



.108 



905 



914 



452 



957 



52 



6 



Error 



878 



7556.068 



8.606 



—^Increase in explanatory power for regression due to adding variables to the 

 model composed of those variables bracketed in the levels above. 



Finite Difference Model 



The dependent variable in this model is ln(ff 2 /#i)- When an expression for b 

 analogous to its form in the differential model is inserted in the finite difference 

 model (4), we obtain: 



ln{H 2 /H 1 ) = lr\{D 2 /D l ) [e^ + o 2i In {CR) + a 3 ln(Z? 2 /0i) + a h (ln(D 2 /0 1 )) 2 



+ a H ln{H) + o &i /ln(Z? 2 /E>i)] 



To compare the utility of the two alternative forms of the dependent variable, we 

 use the maximum likelihood index of fit (Furnival 1961) . The basis for the comparison 

 is the standard error of estimate of the untransformed dependent variable. Standard 

 errors of estimate for other transformations of the dependent variable are converted 

 for comparison by multiplying them by the inverse of the geometric mean of the deriva- 

 tive of the transformation. The derivative of In {H 2 /R\) with respect to AH is: 



3 ln{H 2 /Hi) 3 ln(l. + A#/#i) 



H 2 



Hi 



9A# 



1 



H 2 



in 



