THEORY OF STATISTICS. 
The equation (8) tells us therefore that a rise of 2s. in earnings 
in passing from one district to another means on the average a 
fall of 1 in the percentage in receipt of relief. A natural con- 
clusion would be that this means a direct effect of the higher 
earnings in diminishing the necessity for relief, but such a 
conclusion cannot be accepted offhand. Equation (@) indicates, 
for instance, that every rise of a unit in the percentage re- 
lieved corresponds to a fall of 0-87 shillings, or 101d. in earnings: 
this might mean that the giving of relief tends to depress wages. 
Which is the correct interpretation of the facts? The above 
3 
3 12 75 Rr! 5 ig 77 18 r 79 . 20 12! 
3 A 
3 
fx 2 
S 
$1 
N [7 J 
12 Pe . ar 21 
Average weekly earnings of Agriculiural Labourers. 
F16. 40.—Correlation between Pauperism and Average Earnings of Agricultural 
Labourers for certain districts of England (data of Table VII.) : RR, 
CC, lines of regression : r= — 0°66. 
regression equations alone cannot tell us this, and it is in the 
discussion of such questions that most of the difficulties of statisti- 
cal arguments arise. 
As a check on the whole of the arithmetical work, and to test 
whether the correlation coefficient is unduly affected by a few out- 
lying observations, or, perhaps, by the regression not being linear, 
it is always as well to draw a diagram representing the results 
obtained. Take scales along two axes at right angles (fig. 40) 
representing the variables, and insert a dot (better, for clearness, 
a small circle or a cross) at the point determined by each observed 
pairof X and ¥. Complete the diagram by inserting the two lines 
180