RELATION OF VARIABLFS. 



121 



TABLE 7. 

 Definition of Function.\l Relations. 



In computing a value of w for given values of x and y, say x = 73.4 

 and y = 3.6, correction is first made for the group which, from equa- 

 tion (82) and table 7, is 



w = 12.73 - 3.08 - 1.30 = 8.35 



(83) 



However, this value fo.* w corresponds not to .r = 73.4 and y = 3.6, 

 but, since variability within the group was neglected, to a; = 69.27 

 and y = 4.32. Correction for this neglected variability may be made 

 by running a linear regression in each group and introducing the 

 regression coefficients into equation (83); by plotting the averages 

 and ascertaining the type of equation as stated above, and then com- 

 puting the constants from the averages, and replacing equation (83) 

 by the equation so obtained; or by a simple process of interpolation 

 like the following. Since — 3.08 is the change in iv due to a change in 

 X from X2 = 65.27 to X3 = 69.27, the change in w due to a change in x 

 from X3 = 69.27 to x = 73.4 should be approximately proportional. 

 That is the change in ^v due to the variability of x in group 3 is approxi- 



mately given by 



73.4 



69.27 



X (- 3.08) = - 3.09, and, in the 



69.27 - 65.27 

 same way, the change in w due to the variability of y in group 4 is 



Of* /i QO 



approximately given by — '-^ X (— 1.30) = — 0.36. Intro- 



ducing these approximate corrections into equation (83) gives 



w = 8.35 - 3.09 - 0.36 = 4.7 



(84) 



