In fitting an adopted form to a relevant data set by least squares, always revert 

 to the original Yj^ values--but retain any X-transf orms in the fitted model. Assume, 

 for instance, that the use of X' = (X + 30) and Y' = (Y + 3) had been necessary to 

 orient the analyst's smoothed curve in figure 1 to the upper right quadrant as shown. 

 The Y-axis would then be labeled Y' and the X axis, X'. All procedures would be identi- 

 cal to those shown for the example except that the final model fitted would be: 



Y = Bq + Bi (X + 30)2.7 

 --and, Bq should approximate the constant added to Y in the adjustment process, or, 



fig T 3. 



APPENDIX B 



LEAST SQUARES FIT OF EXAMPLE MODEL 

 HAND CALCULATIONS 



Mean 



Observation 



Original 



data 



number 



X 



Y 



1 



200 



1 



2 



300 



1 



3 



370 



13 



4 



400 



24 



5 



500 



5 



6 



530 



30 



7 



600 



18 



8 



650 



30 



9 



660 



61 



10 



730 



60 



11 



750 



40 



£ 





283 



25.727 



Let X^-'' 



= X' 



0.163229 X 10^ 

 etc. 



X'Y 



0.1632229 X 10^ 0.2664170 x 10^^ 

 etc. etc. 



0.2915176 X 10^ 0.1094696 x 10^^ 0.1158486 x 10^^ 

 0.2650160 X 10^ 



Continuing the computations : 



I (x')2 = Z(x')2 - ((zx')2/n) = 0.3859179 x 10^^ 



I (x'y) = E(x'y) - (Z x'zY)/n = 0.3447002 x 10^° 



Bi = I(x'y) /I = 0.8931957 x lO"^ 



fig = Y - §1 x' = 25.72 - Bi (0.2650160 x 10^) 



= 2.06 



and 



Y 



= 2.06 -t- (0.8932 x lO'^) X^-^ 



37 



