88 



Agricultural Prices 



deviation, and bank clearings were over by .9 of the standard devi- 

 ation. The cycles of the hog prices, hog receipts and bank clear- 

 ings, as secured in this way by reducing for standard deviation, 

 are comparable. The results are charted in Charts III, IV, V. 



It may be seen from examining these charts that hog prices 

 seem to be related directly to bank clearings and inversely to hog 

 receipts. The problem is: Blend hog receipts and bank clear- 

 ings together in such a way as to secure hog prices. The mathe- 

 matical method of approach is by correlation coefficients and lines 

 of regression. 



First, a simple illustration of the method of securing correla- 

 tion coefficients : 



Take the two series, A and B, which deviate from their respec- 

 tive means by the amounts stated in Columns 2 and 3, In Column 

 1 is the year, which has nothing to do with the mathematics of the 

 case. Column 4 is A squared. Column 5 is B squared, and Column 

 6 is A multiplied by B. 



The standard deviation of A is the square root of the sum of 

 the A squares, or 18, divided by 4. The square root of 18 divided 

 by 4 is 2.1. Standard deviation of B, in like manner, is 3. The 

 sum of AB divided by 4, or +22 divided by 4, equals +5.5. The 

 correlation coefficient is +5.5 divided by the standard deviation 

 of A multiplied by the standard deviation of B, or 5.5 divided by 

 6.3, which gives +.87. A correlation coefficient of .87 is very 

 high, perfect correlation being 1. Correlation over .5 is consid- 

 ered fairly good, especially if there is a long list (fifty or more) 

 of figures in each series. 



The formula for determining A in terms of B is : 



A equals r B 



(T 



b 



