114 MCEWEN AND MICHAEL. 



applied the method of multiple linear correlation and found that, 

 after eliminating the effect of precipitation, correlation between 

 temperature and yield was reduced from — 0.62 to — 0.48, and, 

 likewise, that, after eliminating the influence of temperature, correla- 

 tion between precipitation and yield was reduced from + 0.49 to 

 + 0.22. The functional relation he obtained between yield, tempera- 

 ture and precipitation is, in his notation, 



y = 11.2 - 0.48 ^ {f - 65.9°) + 0.22 ^ (p - 6.8) (49) 



where Oy — 3.0, ai = 3.0, and dp = 2.1 



In applying the method of successive approximation to these data 

 it is not our purpose to discuss, except incidentally, the results obtained, 

 but to give a simple, concrete illustration of the process actually fol- 

 lowed, first, in the case when variability within the group is neglected, 

 and second, in the case when this variability is taken into account. 

 In both instances the same notation is employed as in the analytic 

 demonstrations. It should be noted, however, that, in the case when 

 variability w^ithin the group is neglected, three independent variables, 

 X, y, and z, are used in the analytic demonstration, while, in this 

 illustrative problem, only two are involved. 



In the first instance, then, the initial step, as shown in table 5, is 

 to group the data with respect to temperature, arranging the twenty 

 seven entries according to its ascending order of magnitude, and simi- 

 larly, to group the data with respect to precipitation, arranging the 

 twenty-seven entries according to its increase. Secondly, each series 

 is divided into three groups of nine entries each (see p. 127), i. e. groups 

 1, 2, and 3 of the data arranged with respect to temperature, and 

 groups 4, 5, and 6 of the data arranged with respect to precipitation. 

 Thirdly, opposite each entry in groups 1, 2, and 3 is entered the num- 

 ber 4, 5, or 6 designating which precipitation group (^/-group) the 

 entry is in, and, similarly, opposite each entry in groups 4, 5, .and 6 

 is entered the number 1, 2, or 3 designating which temperature group 

 (a:-group) the entry is in. Lastly, the average wheat yield for each 

 group (A', B\ C^ D*, E*, and F*), the average temperature for each 

 of groups 1, 2, and 3 (Xi, Xo, and X3), the average precipitation for 

 each of groups 4, 5, and 6 (74, ys, and ye), and the number of entries 

 common to groups 1, 2, or 3, and 4, 5, or 6 {tin = tiM, ^15 = ^51, etc.) 

 are determined. Each of these steps is indicated in table 5. 



