36 WICKSELL, THE CORRELATION FUNCTION OF TYPE A, AND THE REGRESSION OF 1TS CHARACTER1STICS. 



Table I. 









1 



2 



3 



4 



5 



C 



7 



8 





K.l 





V Å*) 









3 



22 



38 



76 



65 



20 



12 



4 



246 



3,82 



1,90 



+ 0,42 



1 



5 



43 



159 



380 



531 



358 



153 



54 



4 



1087 



3,50 



1,77 



+ 0,12! 



2 



20 



183 



746 



1458 



1590 



926 



323 



49 



7 



5302 



3,15 



1,61 



+ 0.17 



3 



42 



360 



1451 



2297 



2059 



934 



222 



34 



4 



7403 



2,83 



1,47 



+ 0,23 



4 



54 



542 



1588 



2048 



1497 



505 



101 



14 



1 



0350 



2,51 



1,40 



+ 0,26 



5 



45 



387 



906 



926 



506 



139 



25 



3 





2928 



2,18 



1,30 



+ 0,31 



6 



34 



160 



312 



255 



96 



21 



2 







886 



1,82 



1,21 



+ 0,25 



7 



10 



47 



69 



34 



16 



2 









178 



1,53 



1,18 



+ 0,50 



8 



5 



2 



9 



4 













20 



1,10 



1.14 



- (1,47 





215 



1724 



5262 



7440 



6371 



2950 



852 



160 



20 



25000 









yx 



3,80 



3,50 



3,17 



2,83 



2,50 



2,17 



1,86 



1,46 



1,20 











In the marginal columns the characteristics of the arrays are given. The mo- 

 ments corrected for errors of grouping are 



m, =3,24 94 

 l> 2 o = 1,6613 

 r s0 = 0,3909 J',, = — 0.1324 



l' i0 =^ 8,0995 ^31 = 2,7103 



The characteristics are 



p' 3 o = —0,0 3 04 



,■>*, 



0,0027 



O', = 1,2 8 89 

 [t, i = + 0,03 07 

 p' 3l = + 0,004 1 



/',, = — 0,5528 

 V 22 = 3,4814 



V = — 0,3305 



f>22 = + 0,0067 



?n 2 = 3,2505 



>' 03 = 1,6831 

 )' l2 == — 0,1 361 

 r ]3 = 3,7925 



(i 2 = 1,2974 

 J i2 = + 0,03 1 1 

 p',3 = + 0,00 1 2 



l' us = 0,4054 

 r 04 = 8,3664. 



Po3 



— 0,0319 



— 0,00 1 9. 



The coefficients of correlation of higher order are 



r. M = + 0,ooo6 



J 'o3 = — 0,0002 



The formulae of regression will be 



?- 40 = + 0,0004 



r 04 = — 0,0012. 



y x — m 2 = + O.ooos — 0,3275 (x — raj — 0,0005 {x — ra,) 2 + 0,ooo2 (x — m,) 3 , 

 x v — m l = —0,ooo3 — 0,3224 (?/ — w 2 ) — 0,0002 {y — m 2 y — 0,ooo7 (y — ra 2 ) :! . 



The curve of scedasticity of x on y is given by 



o y {x) = 1,4624 — 0,1060 (y — m 2 ) + 0,0105 (y — ra : ) 2 . 



The goodness of fit of our curves will be seen from plate 1. 



Example 2. Case of non-linear regression. Correlation between weight of new- 

 born child and weight of placenta. Boys. Material supplied by the Maternity 

 Hospital of Lund. 1 



1 E. Widmark and S. Wicksell; Om viktsförhållandet mellan barn och etterbörd. Allm. Svenska Läkar- 

 tidningen Nr. 32 1917. 



