IX.—CORRELATION. 175 
any definite trend, to right or to left, upward or downward. 
Two variables for which = is zero are, however, conveniently 
spoken of as uncorrelated. Table VI. and fig. 39 will serve as an 
illustration of a case in which the variables are almost uncor- 
related but by no means independent, » being very small (- 0'014), 
but the coefficient of contingency C (for grouping of qu. 3) 0-47. 
Figs. 36, 37, 38 are drawn from the data of Tables II., III., and 
IV., for which » has the values +091, + 0-51, and + 0-21 respec- 
tively, the correlation being positive in each case. The student 
Num?™ -» Ff Mothers Children. 
) 
he 
RR 
F16. 38.—Correlation between number of a Mother's Children and number of 
her Daughter’s Children (Table 1V.): means of rows shown by circles 
and means of columns by crosses : #= + 0°21. 
should study such tables and diagrams closely, and endeavour to 
accustom himself to estimating the value of » from the general 
appearance of the table. 
13. The two quantities 
0, a, 
b, = i b, = tr 
are termed the coefficients of regression, or simply the regressions, 
b, being the regression of z on y, or deviation in z corresponding 
on the average to a unit change in the type of y, and b, being 
pm. 
aL