KiRSTiNB Smith 
273 
For the present use theoretical values of and ct^^2 were determined, from which the 
values of v^, given in Table X are calculated. The n.^ and v^, of the table represent the 
weights given to the means of arrays respectively by the method of least squares and 
by our method of making ^ minimum. It will be seen that our method throws 
TABLE X. 
Age 
observed 
mp 
observed 
from X" 
a nunimum 
m„ 
from least 
squares 
3—4 
1 
5-3790 
115-25 
117-76 
117-95 
4—5 
7 
13-7170 
116-96 
118-44 
118-61 
5 g 
18 
28-5973 
117-47 
119- 13 
119-27 
6—7 
40 
56-0527 
119-10 
119-81 
119-94 
7—8 
7G 
95-3828 
120-.3O 
120-49 
120-60 
8—9 
125 
146-023 
121-63 
121-17 
121-26 
9—10 
177 
199-783 
121-72 
121-86 
121-92 
10—11 
235 
243-414 
122-82 
122-54 
122-59 
11—12 
261 
271-704 
123-14 
123-22 
123-25 
12—13 
309 
277-232 
123-89 
123-90 
123-91 
13—14 
263 
2.59-386 
124-86 
124-59 
124-58 
14—15 
198 
223-505 
12.5-71 
125-27 
125-24 
15—16 
214 
172-851 
126-16 
125-95 
125-90 
16—17 
162 
121-965 
126-53 
126-63 
126-57 
17—18 
95 
75-7303 
126-91 
127-32 
127-23 
18—19 
61 
43-0926 
127-02 
128-00 
127-89 
19—20 
13 
21-2448 
129-56 
128-68 
128-.55 
20—21 
7 
8-09110 
123-82 
129-36 
129-22 
21—22 
8 
6-42326 
126-50 
130-05 
129-88 
22—23 
2 
2-42653 
125-25 
1.30-73 
1.30-.54 
the weight more to the first half part of the groups of ages than the method of 
least squares. This is due to the heteroscedasticity of the material, the a'^^^^ 
varying from 27-2776 in the youngest group to 60-4676 in the eldest. The two 
last columns of Table X contain the wi^ calculated from our regression formula 
and from the usual formula; as might be expected our ?Hj,'s are closer to the 
means of the observations for the younger groups of ages and differ more for the 
higher ages than do the values obtained by the method of least squares. The 
calculated by (10) are for the two cases 18-45 and 18-67 and we have only raised 
the 'goodness of fit' P from '543 to "558 although the weighting in the two 
methods appeared sensibly different. 
The usual regression line is 
TOj, = 124-0467 + -662979 (^^ - 12-7007), 
124-0467 and 12-7007 being the general means, and regression hue from the xJ' 
formula may be written 
= 124-0411 + -682455 {x^ - 12-7007) 
from which is seen that it passes not far from the mean. 
In a similar way I have treated the regression of ages on height of head. Also 
I have here calculated the heteroscedasticity and have had to use a parabola to 
Biometrika xi 18 
