126 MCEWEN AND MICHAEL. 



B = 12.47 + - (2(^ + 3/) - ^ { - 0.236(0.597rf + 0.246/) 



+ 0.5(0.179rf - 0.246/) + 1.4(- 0.179(Z - 0.664/) | (119) 



C = 8.93 + - (5d-\-lf) --{- 2.389(0.597(Z + 0.246/) - 



1.3(0.179(i - 0.246/) - 1.0(-0.179f/ - 0.664/)} (120) 



D = 9.69 + - (2a + 5c) - -{ - 0.629(0.590a + 0.092c) - 

 y y 



0.724(0.273a-0.092c)+5.633(-0.273a-0.408c)} (121) 



E = 11.68 + - (2a + 3c) - ^ {l.971(0.590a + 0.092c, - 

 9 9 



0.949(0.273a-0.092c)-3.920(-0.273a-0.408c;} (122) 



F = 12.41 + - (5a + Ic) - - ( - 1.422(0.590a + 0.092c) + 

 y y 



1.813(0.273a-0.092c)-1.773(-0.273a-0.408c)} (123) 



These equations reduce to 



A = 12.38 + 0.0218f/ + 0.4750/ (124) 



B = 12.47 + 0.2560f/ + 0.4567/ (125) 



C = 8.93 + 0.720c/ + 0.0671/ (126) 



D - 9.69 + 0.4562a + 0.8100c (127) 



E = 11.68 + 0.0029a + 0.1258c (128) 



F = 12.41 + 0.5402a + 0.0637c (129) 



which are of the same form as equations (50) to (55). The solution 

 gives A = 12.13, B = 12.13, C = 8.60, D = 12.55, E = 12.13, and 

 F = 12.64; and, from equations (41) to (48), Si = 0.32, 82=- 

 0.32, S3 = - 1.44, S4 = - 0.376, S5 = 0.05, and Se = 0.413. 



Using these relations to compute the value of ^v corresponding to 

 X = 73.4 and y = 3.6 gives 



w = 12.13 - 3.53 + 0.42 - 5.95 + 0.27 = 3.34 (130) 



a fair approximation to the value 3.95 given when regressions in each 

 group were used. 



