THE FUNCTIONAL RELATION OF ONE VARIABLE TO 



EACH OF A NUMBER OF CORRELATED VARIABLES 



DETERMINED BY A METHOD OF SUCCESSIVE 



APPROXIMATION TO GROUP AVERAGES: 



A CONTRIBUTION TO STATISTICAL 



METHODS. 1 



By George F. McEwen and Ellis L. Michael. 

 CONTENTS. 



Page 



1. Remarks on methods of acqmring knowledge 95 



2. General statement of problem and mode of attack 97 



3. Mathematical demonstration: 



A. The case when variability within the group is neglected . . 100 



B. The case when variabihty within the group is taken into 

 account 105 



4. Illustration of method by solution of a particular problem concern- 

 ing the relation between temperature, precipitation, and yield of 

 wheat in South Dakota 113 



5. Supplementary considerations 127 



6. Literature cited 133 



1. Remarks on Methods of Acquiring Knowledge. 



One method of acquiring knowledge, the deductive, is to formulate 

 fundamental concepts and principles that are simple but comprehen- 

 sive, and to attempt to deduce therefrom the sequences and other 

 relationships observed in nature. This implies that nature conforms 

 to a logical system and, consequently, discovery of the few basic 

 elements of the system, together with suitable logical treatment, 

 furnishes a description of the observed phenomena. Considered 

 quantitatively, this method of acquiring knowledge is the classical one 

 of applied mathematics. 



Another method is the "inductive" or, better, the empirical method. 

 One becomes directly aware of innumerable facts by means of sense 

 perceptions. ]Many are acquired without particular effort and seem 

 trivial, while special attention is directed toward acquisition of others 

 of more apparent significance. Closely associated with this process 

 of observation is that of description and classification, which makes 



1 Presented in abstract before the San Francisco Section of The American 

 Mathematical Society, April 7, 1917. 



