346 
On Linearity of Regression 
Hence from formula (xxii) we have 
2 = = 4 {■6128 - -2428 + l-Ol 34 - '9598 
-•1705 + -9708 --6241 
+ •0173} 
= -i {-6128 - -1893 + ^1762 + -0173} 
= ~ {-0128 + -0042} = ^ { 0170} (xxxv). 
This gives 
Pearson gives 
Hence 
From the formula 
= 0206, 
•0139. 
•0054. 
2, = •OOSO. 
= ^0002. 
Hence from formulae (xxvi) and (xxviii) we get 
2f=^0229, 2^=^0153. 
Hence, finally 
^^ = •0139, £'^=•0154, ^^=^0103, 
while, from the simple formulae (xxiii), (xxvii) and (xxix) we get 
^^ = •0139, E'i = -0U2, E\ = -0102. 
These give 
= 13^2341, -X - 14^6291, ^ = 13^9785. 
-or ( % 
In order to appreciate the significance of the results in these four cases they 
are collected and tabulated as follows : 
j^Note: ■ar = log<,^=logio^xlog<,10^ 
TO 
r 
3 
■57 
3 
^\ 
E 
E^ 
A 
•1856 
•0194 
•0423 
2-6728 
2-7389 
2-8236 
E' 
E 
E'~E 
-0694 
-0682 
-0012 
•0071 
■0073 
•0002 
•0150 
■0147 
■0003 
B 
•0298 
•0053 
•0089 
2-5752 
2-5879 
2-5973 
E' 
E 
E'~E 
-0116 
■0114 
-0002 
•0021 
•0020 
•0001 
■0034 
■0034 
■0000 
C 
•3669 
■1701 
•1757 
13-4052 
15-8934 
15-3972 
E' 
E 
E'~E 
■0238 
■0274 
■0036 
•0107 
•0084 
•0023 
■0114 
■0093 
■0021 
D 
•1836 
•2226 
•1438 
13-2341 
14-6291 
13-9785 
E' 
E 
E'~E 
-0139 
-0139 
■0000 
•0152 
•0154 
•0002 
■0102 
•0103 
•0001 
