80 



Economic Cycles: Their Law and Cause 



curves y =a+bx+cx 2 -{-dx 3 , the graphs of which, in case 

 of the representative commodities corn, hay, oats, and 

 potatoes, are given in Figures 17, 18, 19, 20. What is 

 the gain in precision when the more complex curve is 

 substituted for the simple straight line? The scatter 

 of the observations about the straight line of regression 

 was measured, a while ago, by taking the root-mean- 

 square deviation of the observations about the line, 

 that is, by using S = o- y ^\— r 2 . In order to compare 

 with this result the distribution of the observations 

 about the more complex curve, y = a-\-bx-{-cx 2 -\-dx 3 , 

 the distribution about the latter curve will likewise be 

 measured by the root-mean-square deviation of the 

 observations. In the little table given below, the 

 measures of scatter of the observations for the two 

 types of demand curves are presented in a form that 

 will make comparison easy. 



Scatter of Observations About the Law of Demand 

 Root-Mean-Square Deviation of Observations 



It is clear that in all cases a gain in precision is ob- 

 tained by using the more complex curve. 



Before leaving this topic a remark should be made 



