Rainfall and the Crops 39 



yield per acre and time is r = .382 ± .090, and the regres- 

 sion equation is, y = .204x +26.93, where y = yield per 

 acre, .x = time, and the origin is at 1870. The secular 

 trend is eliminated by means of the facts summarized 

 in the regression equation: Beginning with the year 

 1870, as many times .204 are subtracted from the 

 yield per acre for the several years, as the respective 

 years differ from 1870. For example, the yield for the 

 year 1872 was 39.8 bushels per acre; consequently the 

 reduced yield for that year was 39.8-2(.204) =39.8- 

 .408 =39.39. Figure 10 traces the yield per acre of corn 

 freed from the secular trend. 



Of the four leading crops of Illinois that form the 

 basis of our investigation, only two, corn and potatoes, 

 show a significant x tendency to secular change. The 

 correlation between the yield per acre and time is, 

 for hay, r = .013 ±.105 and, for oats, r = .043 ±.105; 

 consequently the figures for the yield per acre of these 

 two crops have not been reduced. In the case of 

 potatoes, r = .122 ±.104, and the regression equation 

 is y = .233x+ 70.51, where the origin is at 1870. The 

 figures for the actual yield per acre and the reduced 

 yield per acre for corn and potatoes, as well as the 

 figures for the yield of hay and of oats, are given '-' in 

 Table I of the Appendix to this chapter. 



1 The indicated secular trend in potatoes is not significant in 

 the mathematical sense, because the probable error of the coefficient 

 of correlation is nearly as large as the coefficient itself. I have 

 nevertheless eliminated the indicated secular trend before using the 

 data. 



2 The raw data were taken from Bulletins 56, 58, 62, 63 of the 



