UNITED STATES DEPARTMENT OF AGRICULTURE 
BULLETIN No. 504 
OFFICE OF THE SECRETARY 
Contribution from the Office of Farm Management 
W. J. SPILLMAN, Chief 
Washington, D. C. PROFESSIONAL PAPER May 23, 1917 
THE THEORY OF CORRELATION AS APPLIED TO FARM- 
SURVEY DATA ON FATTENING BABY BEEF. 
By H. R. Tolley, Scientific Assistant. 
CONTENTS. 
Page. 
Introduction 1 
Theory of correlation 1 
Computation of the coefficients, 6 
Page. 
Interpretation of the coefficients 8 
Summary 13 
INTRODUCTION. 
This paper sets forth the results of an experiment in applying the 
theory of correlation, hitherto used chiefly in the analysis of biologi- 
cal, sociological, psychological, and meteorological statistics, 1 to the 
study of some of the data of the Office of Farm Management. 
The material for the investigation was obtained from 67 records 
taken during the years 1914 and 1915 from farmers of the corn belt 
who were fattening baby beef for market. 2 The factors considered 
were: The profit or loss per head, the weight, value per hundred- 
weight, value of feed consumed per head, cost at weaning time, and 
date of sale (see Table L). Coefficients of correlation were computed 
for every pair of these factors and used as a measure of the relation- 
ship existing between them. 
THEORY OF CORRELATION. 
The writer will not attempt a detailed explanation of the theory 
of correlation but will discuss briefly the meaning of coefficients of 
correlation and the method by which they are obtained. 
1 Yule, G. U. : " Introduction to the Theory of Statistics," 1912. Yule, G. U. : " On the 
Theory of Correlation," Jour. Roy. Stat. Soc, 1897, p. 812. Davenport, C. B. : " Statisti- 
cal Methods, With Special Reference to Biological Variation," 1914. Hooker, R. H. : 
" The Correlation of the Weather and the Crops," Jour. Roy. Stat. Soc, 1907, p. 1. 
Smith, J. W. ; " Effect of Weather on Yield of Corn," Monthly Weather Review, vol. 42, 
p. 72 ; and " Effect of Weather on Yield of Potatoes," ibid., vol. 43, p. 232. Brown, Wm. : 
" Essentials of Mental Measurement," 1911. 
2 For detailed account of the methods by which these data were obtained and the costs 
computed, see Report 111, Office of the Stcretary, 1916. 
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