58 
On the Partial Correlation-Ratio 
For the regression of age on height and weight, the values of ^^//^ — ^.yR^^ 
and of xyH%, given by the preceding equations, are tabulated below: 
TABLE XVI. 
Source 
(70) 
(71) 
(71) ' 
(72) 
(72) ' 
•0303 
•0392 
•0381 
•0273 
•026fi 
•7537 
•7625 
•7615 
•7507 
•7499 
Direct ] 
Calculation | 
•0286 
•7519 
We notice that (72) and (72)' give much better values than (71) and (71)'. 
This is to be expected for ^/3j^ is very small with a value of -0003, while ^jS^ is 
quite appreciable with a value of •3370, and since r^y, y-q.^., ^r]y are pretty nearly 
equal (cf. Table XIV), equations (72) and (72)' may be used to replace (70). 
Another point of interest is that there is very little to choose between the 
values given by the cumbersome formula (70) and those given by (72) and (72)'. 
If we now consider the regression of weight on height and age, we find that 
equation (70) is unsuitable for the calculation of zxH'^y ^ zx^v ■ 
For in this case ^.^^ = -0003, 
„i = -0057, 
xVz = -8448, 
,7j, = -8314, 
r„ = -8305, 
and we expect the right-hand side of (70) to be indeterminate (cf. Part I, p. 406). 
We find 
'fzxqzx' - qz'x = - -007104, 
Tzxqz^x - qzx^ = - -002767, 
and r,yq,2^ - r^^q,^ = - -000175. 
Thus the right-hand side of equation (70) depends on the ratio of quantities 
which practically vanish when their probable errors are taken into account. 
If, nevertheless, (70) is employed, it gives ^^fl^^ — zxR^v = -1580, and since 
zxR^v = -8427, we get zxH'^v = 1-0007 !, i.e. a value just greater than unity*. 
The values of ^^^H^y obtained from (71) and (72) are tabulated below: 
TABLE XVII. 
Source ^-,H'„ - ^^R^j .Ji^,, 
(71) •0054 •8481 
(72) ^0203 -8630 
(71) ' ^0048 ^8474 
(72) ' -0177 ■8604 
CaSratL} -0207 -8634 
* Of course by an amount < p.e. of ^^.R^ . 
