IX.—CORRELATION. 
EXERCISES. 
1. Find the correlation-coefficient and the equations of regression for the 
following values of X and ¥. 
[As 4 matter of practice it is never worth calculating a correlation-coeflicient 
for so few observations: the figures are given solely as a short example on 
which the student can test his knowledge of the work. ] 
2. The following figures show, for the districts of Example i., the ratios of 
the numbers of paupers in receipt of outdoor relief to the numbers in receipt 
of relief in the workhouse. Find the correlations between the out-relief ratio 
and (1) the estimated earnings of agricultural labourers; (2) the percentage 
of the population in receipt of relief. 
6°40 14 750 27 2:97 
4°04 15 4-44 28 538 
: 7:90 16 834 29 3-24 
3-31 17 0°69 30 7-61 
785 i 9-89 a 5-87 
045 i 4-00 &2 550 
10-00 Zu 602 ao 3:58 
4°43 2. 827 el 6-93 
478 22 158 Ly 6°02 
1 4-73 23 1604 36 4-92 
1 6°66 24 1-96 37 4°64 
1 1:22 25 9-28 38 10°56 
13 427 26 872 
3. Verify the following data for the under-mentioned tables of the preceding 
chapter. Calculate the means of rows and columns and draw diagrams showing 
the lines of regression, as figs. 36-39. for one or two cases at least. 
vo 1: VI 
Mean of X . - 00 mm, 4° years 6770ins. 5b 509-2 
aly r , 53.0, Barz? "Vege CL. 14,500 
tandar evia- 2 . . 
tion of X : g ? i » | 272, g 7:46 
Standard devia- 2 
tion of 7. : : - » Es.» 18,100 
ries eed © en © nl enn 
Coefficient of con- - - 
tingency (for the o 
grouping stated : = 
below) . 3 
189 
0°90 0°81 051 031 17