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 conclusion
 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 relieved
 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 statistical
 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 outlying
 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

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