IX.—CORRELATION. 179 
average weekly earnings of agricultural labourers in 38 English 
Poor-law unions of an agricultural type (the data of Example i., 
Chap. VIIL p. 137). (2) Y—the percentage of the population 
in receipt of Poor-law relief on the Ist January 1891 in each of the 
same unions (B return). The means of each of the variables are 
calculated in the ordinary way, and then the deviations z and y 
from the mean are written down (columns 4 and 5): care must 
be taken to give each deviation the correct sign. These deviations 
are then squared (columns 6 and 7) and the standard deviations 
found as before (Chap. VIII. p. 136). Tinally, every a is 
multiplied by the associated y and the product entered in column 
8 or column 9 according to its sign. These columns are then 
added up separately and the algebraic sum of the totals gives 
3(ry)= — 66604: therefore the mean product p=3(zy)/N= - 
17-53, and 
17-53 
T= 05x13 6 
There is therefore a well-marked relation exhibited by these data 
between the earnings of agricultural labourers in a district and 
the percentage of the population in receipt of Poor-law relief. 
A penny is rather a small unit in which to measure deviations in 
the average earnings, so for the regressions we may alter the unit 
of to a shilling, making o,= 171, and 
b=r2= 087, &,=rZ=_050. 
Ty Ox 
The regression equations are therefore, in terms of these units, 
z= -08T7y y= - 0-502. 
For practical purposes it is more convenient to express the 
equations in terms of the absolute values of the variables rather 
than the deviations: therefore, replacing « by (X - 1594) and y 
by (¥ - 367) and simplifying, we have 
X=1913-087Y . fa) 
Y=1164 - 050X ©) 
the units being 1s. for the earnings and 1 per cent. for the 
pauperism. The standard errors made in using these equations 
to estimate earnings from pauperism and pauperism from earnings 
respectively are 
a, M1 —12=154d. = 1-285. 
a, NT =r2= 0:97 per cent.