56 
On the Partial Correlation-Ratio 
Fig. C. Resrression of Heislit on Weisht. 
MeaLH Weight. 
cr^ Mean Height. 
64 
61 
58 
55 
52 
49 
46 
43 
40 
37 
34 
31 
26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 106 111 116 121 
Weight in lbs. 
5. The mean ages of the x, y arrays are given in Table XV. From this table 
^,jH^^ is calculated directly by the formula : 
ao \y^xv ^xy) } 
•7519, 
or 
Also 
and 
xv'^z 
yz' zx xy 
•7233, 
•8505. 
We see that the regression of age on height and weight is very far from planar. 
The difference 
,,H\ - ,,It^, = •0286. 
We have at present* no formula for the probable error of the multiple correlation 
ratio, but some idea of its magnitude may be obtained from Blakeman's formula f 
for the probable error of .^pq^y — r^^y : 
VW. 1 . V-rf^^ 
^2 — ^2 
x'l y ' xy 
Probable error of (^7j\ - r\y) QlUdVl + (l - -q^f - {1 - r'^f' 
* Since writing the above, tlie author has obtained a formula for the p.e. of ^i/H^. It is very 
similar to Pearson's well known formula for the p.e. of the simple 7j. 
t J. Blakeman. Biometrika, Vol. iv, p. 332. 
