Mathematical Study of Supply and Demand 



89 



In this formula, r is the correlation coefficient and o-a is the 

 standard deviation of A, and ^b is the standard deviation of B. Sub- 

 stituting for the specific problem, we get : 



2.1 



A equals .87 



3.0 

 A equals .609 B 



B or 



When B is — 5 we would expect A to be 3.05 ; when B is +1 we 

 would expect A to be +.609; when B is + 3, we would expect A to 

 be 1.827. 



Suppose now, in addition, that there are three series: A, B and 

 C, and that the object is to determine A in terms of B and C. The 

 three series stand: 



We already know that the standard deviation of A is 2.1, and 

 of B is 3.0, and that the correlation coefficient between A and B 

 is +.87. Using the customary method, wc find that the standard 

 deviation of C is 2.55 and tliat the correlation coefficient of A and 

 C is —.89, and of B and C —.59. To find A in terms of B and 

 C, we use the following formula : 



lib — ac rbo ^a 

 A equals • — !> 



^ ~ '■'be <^1) 



+ 



ah 'be 



In this formula ''ab means correlation coefficient between A 

 and B, etc. ; aa. means standard deviation of A. 

 Substituting, we get : 



+ .87 — .53 2.1 —.89 + .51 2.1 



A equals B C 



.65 3.0 .65 2.55 



or, A equals .37 B — .49 C 



Applying this formula, we find that when C is +2 and B is — 5, 

 as in the year 1901, we would expect A to be — 2.83, and when C 



