70 Economic Cycles: Their Law and Cause 



and variations in the amount of the commodity that is 

 demanded. 



The method may be illustrated by deriving the law of 

 demand for corn. In Table I of the Appendix to this 

 chapter are recorded, for the period of 1866-1911, in the 

 United States, the quantities of corn annually pro- 

 duced, the corresponding prices per bushel, the relative 

 changes in the quantity produced and the relative 

 changes in the price per bushel. If the correlation of 

 the relative change in the amount of corn that is pro- 

 duced and the relative change in the corresponding 

 price per bushel of corn is assumed to be linear, the 

 coefficient of correlation is r = — .789, and the equation 

 of regression is y = — .8896a*+7.79, the origin being at 

 (o,o). (See Figure 16.) 



In Tables 1 II, III, IV, of the Appendix to this 

 chapter, similar data are given for hay, oats, and 

 potatoes. The coefficients of correlation are, for 

 hay, r = —.715; for oats, r = —.722; and for potatoes, 

 r = —.856. The regression equations are, 



for hay, y = -. 7643a: +3.61; 

 for oats, y = — 1.0455a; +6.93; 

 for potatoes, y = — 1.2194s +15.75; 



the origin in all cases being at (o,o). 



The high coefficients of correlation that have just 



been given were obtained on the assumption that the 



correlation between relative change in amount de- 



1 The data of the Tables I, II, III, IV were taken from the Year- 

 book of the Department of Agriculture of the United States, for 

 1911. 



