POSITION REGRESSION— PRIMARY BRANCHES. 



61 



Pearson (loc. cit. ) has shown that this expression is sufficiently ac- 

 curate for all ordinary purposes, and it is much easier to calculate than 

 the complete expression for the standard deviation of v. 



Table 33. — Correlation between leaf-number and position of primary -branch whorls. 



We see at once from table 33 that— 



(1) There is a very considerable degree of correlation between the 

 number of leaves per whorl and the position of the whorl. 



(2) The degree of correlation is very closely the same for all series. 

 We should expect, of course, that Series V and VI would give different 

 values for the coefficients, because in those cases we are dealing with 

 three and four different orders of branches together. 



(3) There can be no doubt that the regressions are not linear. The 

 differences between v and r are so considerable that I have not thought 

 it necessary to work out the probable errors for every case. The series 

 which gives the smallest difference between rand ^ is V (>?— r=0.0197), 

 but the apparent approach to linearity here is due to putting different 

 orders of branches together. Considering the primary branches alone, 

 the minimum difference between v and r is given by Series I (17 — r = 

 0.1142). We may take these two instances as a sample: 



It has been shown by Blakeman (loc. cit.) that if we let 



an approximate formula for the probable error of ^, i. e., E^^ is 



C 



Vn 



E^ 0.67449 



il/f 



\n+(i-v'y-(i-ry 



Working from this formula we have for Series I, 



and for Series V, 



C = 0.1364 ±0.0193, 

 ^ = 0.0191 ±0.0082. 



