Editorial 
and by (xxi) 
r~. = K, ^ : n (xxxi). 
l 1 
Since homoscedastic linear regression supposes (3 2 = /3 2 ' this result must be very 
close to 
V. = fr* - 1/(1 - i (A - 3 + A' - 3) j-^y (xxxii) 
for such distributions. 
For distributions in which the kurtosis is zero (/3» = 3) we reach 
r, „ = rxyHZ (xxxiii), 
* 
a result already reached for Gaussian distributions by Pearson and Filon in 1897 
It is now shown to be true for all homoscedastic, mesokurtic systems with linear 
regression. 
(5) Two further probable errors are of interest. If we write y x = ax + b for 
the regression line, what are the probable errors of 
a = r xy a y ja x and b =y - r X ya y x/a x ? 
It will be sufficient to give the values of cr„ and cr& when the frequencies are 
symmetrical and the regression linear. In this case 
r x<r x = v yu u = r x<r y = r y<r x = r xy = r xy> 
Writing r x = xj<r x , we have 
8a _ 8a y 8r xy _ 8a x 
a cr y r xy cr x 
and 8b — 8y — a8x — 8r X!/ a y t x — r XIJ r x 8a y + aT x 8a x . 
Whence proceeding in the usual manner we deduce 
<*a = Vl - r\yj (xxxiv)f, 
trj = a-y Vl — r 2 xy Vl + t x 2 /*J N = <r a six? + a x ~ (xxxv). 
These enable us to determine any significant difference between two regression 
lines. 
We can go a stage further and ask what is the probable error of the mean of an 
array, y x , as found from the regression line. We have 
8y x = + 8b. 
* Phil. Trans. Vol. 191, A, p. 242. 
t Cf. Phil. Tram. Vol. 191, A, p. 245. 
Biometrika ix 2 
