342 
On Linearity of Regression 
Substituting these values in formula (xxii) we may exhibit the result so as 
show the numerical contribution of each term in the form 
^ „ 1 
' N 
I7-1970 
= ^!7-1970 
•2928 + -9870 - 1-1980 
•0129 + -2704 - -5673 
+ •5492) 
•5038 - ^3099 + •54921 
= {7-1970 - •2544} = ^ {6^9426} (xxxii). 
This gives 
Peai'son gives 
Hence 
From the formula 
2^ =1011, 
= -0682. 
=-0242. 
2, = •0359. 
N ' 
2," = -0013. 
Hence from formulae (xxvi) and (xxviii) we get 
2f=^0108, 2^ =-0217. 
Hence, finally E^ = ^0682, E^ = -0073, E^ = ^0147, 
while, from the simple formulae (xxiii), (xxvii), (xxix) we get 
E'^ = 0694, E'i = 0071, E'^ = •OlSO. 
These give 
= 2-6728, 
2-8236. 
J,, -^= 2-7389, ^ 
E ^ E ^ E y 
Illustration B. On the Correlation between Age and Head Height in Girls. 
Age is taken as the .r-character and height of head as the ?/-character. 
We have in this case 
Xp 
3— k 
1 
115^2500 
0^0000 
k— 5 
7 
116^9643 
5^7706 
5— 6 
18 
117^4722 
5-8552 
6— 7 
40 
119^1000 
5-9282 
7— 8 
76 
120-3026 
5-9764 
8— 9 
125 
121-6340 
5-2732 
9—10 
177 
121-7246 
6-7754 
10—11 
2.35 
122-8160 
5-9306 
11—12 
261 
123-1427 
6-4178 
12—13 
309 
123-8908 
6^4122 
13— H 
263 
124-8622 
6-7178 
14—15 
198 
125-7146 
7-1730 
15—16 
214 
126-1565 
6-9326 
16—17 
162 
126-5340 
7-7392 
17—18 
95 
126-91.32 
6-3358 
18—19 
61 
127-0205 
6-2470 
19—20 
13 
129-5577 
9-6812 
20—21 
7 
123-8214 
5-0622 
21—22 
8 
126-5000 
8-2828 
22—23 
2 
125^2500 
1-9148 
