POSITION REGRESSION— PRIMARY BRANCHES. 



Mean leaf number 



67 



seemed hardly worth while to plot 

 the lower-order curves, because 

 if the higher ones fail to represent 

 the data, it is reasonably certain 

 that the lower will, and further, 

 six superimposed curves on the 

 same data tend to make a rather 

 confused diagram. As will be 

 seen from equations iv and V 

 above , the fourth and fifth order 

 curves are sensibly identical, and 

 hence it is unnecessary to plot 

 both of them. 



Examining these curves, we 

 see that they signally fail to give 

 as good a result as we want and 

 have reason to expect. The third 

 and fifth order curves do not give 

 at all the form of the curve at the 

 lower end of the range. This is 

 clearly the most important part of 

 the curve and a failure to give a 

 good graduation here is fatal and 

 at once throws out of court the 

 lower-order curves. The sixth- 

 order curve does somewhat better, 

 especially at the start of the range, 

 but it is evident that the fit is a 

 purely artificial one and does not 

 help us any towards the law of 

 growth we are seeking. In the 

 first place, this curve has alto- 

 gether too many points of inflexion 

 to correspond to the biological 

 facts. It is, in a word, fitting 

 itself to the "errors" rather than 

 to the general sweep of the obser- 

 vations. The artificial character 

 of the graduation is well brought 

 out at the upper end of the range, 

 where the curve takes a very 

 sharp and sudden turn downward, 

 corresponding to nothing in the 

 observations. We may be quite 

 sure that the correct expression 



Fig. 11 6i.s.— Regression line and fitted parabolas, 

 showing change of mean leaf-number with po- 

 sition. Primary branches, Series I, II, and III 

 combined. Observations, » ; third 



order parabola, — — — — — — ; fifth-order parabola, 



^..>...».^.«^ ; sixth-order parabola,— •^.^•—•. 



