INTRODUCTION 



The analyst often initiates a two-dimensional regression analysis by hand-fitting 

 the expected curve for an XY relation through a set of plotted data points called the 

 "graphed curve" in this paper. 



Assume he wants next to find a mathematical form of the independent variable, X, 

 which when scaled to the graph emulates the graphed curve with acceptable accuracy. If 

 the curve is linear, X itself is, of course, the appropriate form. But if the curve is 

 nonlinear, a matching nonlinear form of X should be the object of his search. Once hav- 

 ing found a suitable form, the analyst can rescale it to the actual data points of any 

 relevant data set^^by least squares, and the development of the estimating equation is 

 complete. 



In this paper we have attempted to reduce the effort required to find acceptable 

 transforms of the X class. The analyst simply compares a scaled version of his graphed 

 curve to graphed Standards (page 9) and selects the two adjacent ones most nearly like 

 his own in shape, a process hereinafter referred to as "Matchacurve . " 



Interpolation between the transforms given for these Standards results in identifi- 

 cation of the best alternative offered by the system. It is this transform of X that 

 is finally fitted to a relevant data set by least squares. 



Three unique sets of standard curves are presented. Each set is based on a selected 

 array of n in X , with limits as shown: 



Set n-array limits 



1 1.00 £ n <. 20.00 



2 0. 10 <. n <. 1.00 



3 -2.00 <. n <. -0.01 



Each set of Standards is transformed as required (see Appendix C) to appear in each 

 of the four basic positions in which the analyst's curve can occur in the upper right 

 quadrant so that there are 12 sets of Standards in all--3 sets in each of 4 positions. 



-Either the data set from which the graphed curve is derived or some other set to 

 which this curve is judged applicable. 



