PREDICTION OF VOCATIONAL SUCCESS 199 
regression line may be determined exactly and not by esti- 
mation, and the regression equation takes the form: 
(37) y=roPx 
This formula gives the most probable value of y corre- 
sponding to a given value of x, both in terms of deviations 
from their means. 
This formula may also be expressed in terms of the orig- 
inal measures: 
(38) Y =r (X~—m,) +m, 
in which 7, is the mean of the ¥’s and 7. the mean of the 
X's. 
The criterion (¥) may be predicted from test score (X) 
by either the regression line or the regression equation. 
If X is to be predicted from ¥, the letters should be trans- 
posed wherever they occur in the above discussion. 
For good discussions of the regression line and regression 
equation, see Thurstone (196) and Rugg (157). 
The regression equation gives for each value of the known 
variable only the most probable value of the predicted vari- 
able. The error of this predicted value cannot be deter- 
mined from the regression equation alone. The standard 
error of estimate of a second variable, predicted from the 
first, may be found by the formula given by Kelley (86, p. 
173): 
(39) o21=0\V 1—1? 
This formula applies if the measures are either in their orig- 
inal form, or expressed as deviations from their respective 
means. If the measures are expressed as deviations from 
their respective means with the standard deviation as the 
unit of measurement (that is, as x/¢,), then the formula for 
the standard error of estimate is 
e=V1—7r? 
40)