96 Economic Cycles: Their Law and Cause 



precision with which prices may be predicted from the 

 demand curves. Or, to put the idea in another form, 

 the productivity of the soil is as closely related to the 

 prices of crops as the supply of the commodity is related 

 to the same prices. In the chapter on the "Law of 

 Demand," we found that, when the relative change in 

 the supply is given, the mean shift in the corresponding 

 change of price may be obtained from the regression 

 equation, and that, furthermore, the root-mean-square 

 deviation of the observations may be computed by 

 the formula S= cr y^ / l-r 2 . This same formula may 

 be used for a similar purpose in case of the yield-price 

 curves. 



We come now to the second stage in the derivation of 

 the relation between price and the yield per acre of 

 crops. We assume that the relation between the yield 

 per acre and the price of a crop is skew, and that the 

 relation between the two may be expressed by an 

 equation of the form y =a-\-bx-\-cx~+dx 3 . 



In Figure 21, the skew yield-price curves of our four 

 representative commodities are drawn to a percentage 

 scale. The equations to the curves, which were com- 

 puted by the Method of Least Squares, are given upon 

 the Figure. The root -mean-square deviation of the 

 observations from their respective yield-price curves 

 are given in the following Table which, for purposes 

 of comparison, reproduces the coefficients that were 

 found, in the preceding chapter, to measure the devia- 

 tion of the observations about the skew laws of de- 

 mand. 



