EMPLOYMENT PSYCHOLOGY
regression of ¥ on X. The regression of X on V, by which X
is predicted from ¥Y, may be obtained by estimating the
means of the rows of figures.)
The regression line as thus determined may be represented
 by the regression equation:
(33) Y=a4+b-X
The multiplying constant b is the slope of the regression
line, the tangent of the angle formed by the regression line
with the horizontal. The additive constant a is necessary if
the point of origin of the regression line does not coincide
with the zero points of both abscissa and ordinate scales. Its
amount may be determined by inspection.
Reversing this process, the values of a and b may be obtained
 by the method of least squares (197, p. 9), and the
regression line may then be drawn from these determined
values. The formulas are
ZX .2YXV-zX.3Y
(34) gr nyo x Ew
>X:ZY-N-Z2XY
(35) ES
If the mean of the X’s is represented by a vertical line
through the scatter diagram and the mean of the ¥’s by a
horizontal line, the point of intersection of these twos lines
should also be the point of intersection of the two regression
lines. This point may be made the origin of the regression
lines by expressing all measures in terms of deviations from
the means of their distributions. Since the point of origin
then has zero value for both distributions, no additive constant
 is necessary. X and V, when they are given as deviations
 from their means, are represented by the symbols x and
y. The regression formula then becomes
(36) y=b-x
The multiplying constant b in the above case is equal to
7 2, Hence, if » and o,, 0. are known, the slope of the

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