EMPLOYMENT PSYCHOLOGY 
much weight to give scores in each test when combining 
scores in the several tests in the series. When making prac- 
tical applications the proper weighting of tests is found by 
solving the multiple regression equation. The multiplying 
constant for each test is the partial regression coefficient of 
the criterion on that test, when each of the remaining tests 
is held constant. The equation for three variables when raw 
scores are used is as follows: 
(47) Xi=l0: X04 050 Xs +C 
In this formula the &’s and the C are constants so chosen 
that when the scores in tests 2 and 3 are multiplied by the 
&’s and added to C, a final measure, X,, is obtained which 
will give the highest possible correlation with the criterion 
(84, p. 14). X, is not to be confused with the criterion as 
actually measured. The formula for the multiplying con- 
stants for three variables are (233, p. 237): 
I Ll bio —0b13 + bs 
(48) bros I —bss + ba 
bis = ryt , 13 =p yehe, 
g2 a3 
b... may be obtained by substitution in the above formula. 
For » variables the formula for X, is 
(49) Xi =br.au..nX2 +0134. n Xt» +b1n2s...0yXn+C 
The formula for the multiplying constants for # variables 
is (233, p- 237): 
Wi b19.34...cn—1y — D1m.sa...cn—1y 2 Ona.380 + (n—1) 
(50) EE I —ban.3s...n-1) * bugsa...n—1) 
These may be computed from &’s of lower orders by the 
above formulas. 
The formula for the additive constant, C, for three vari- 
ables is 
(51) C=M;—b123M>—b132M3 
M, is the mean of the measurements of the criterion, and 
M, and MM. the means of tests 2 and 3. The formula for the 
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