78 Economic Cycles: Their Law and Cause 



tate the discussion of the case.) By means of this law 

 of demand it is possible to predict the probable change 

 in the price that will follow upon a given change in 

 the quantity to be sold. In 1911, in the United States, 

 the quantity of corn produced was 2,531,488,000 

 bushels, and the mean farm price on December 1, 1911 

 was 61.8 cents. In 1912 the quantity of corn produced 

 was 3,124,746,000 bushels; what, then, was the probable 

 price of corn on December 1, 1912? The percentage 

 change in the quantity produced was 23.44. Sub- 

 stitute this value for x in the formula for the law of 

 demand y = — ,8896x+7.79, and solve for the value 

 of y. It is found that the probable change in price would 

 be a fall of 13.06 per cent., which, since the price in 

 1911 was 61.8 cents, would give 52.7 cents as the prob- 

 able price for December 1, 1912, whereas the actual 

 price was 48.7 cents. 



According to the theory of linear correlation, the 

 accuracy of the regression equation as a prediction 

 formula is measured by S = °" y V 1 — r 2 , where r is 

 the coefficient of correlation between the variables, 

 Vy is the standard deviation of the variable y about 

 its mean value, and S is the root-mean-square devia- 

 tion of the actual observations about the regression 

 line; or, in other words, S 2 is the mean value of the 

 mean-square deviations about the regression line, of 

 the observations in the several arrays of y's. From 

 the Table of the Probability Integral it is known 

 that in a symmetrical distribution of observations 

 about their mean value, 68 per cent, of all the observa- 



