<. THEORY OF STATISTICS.
and equal to oy, (2) that the regression of 2) on z, is strictly
linear. Similarly, of course, if we assign to x; any value %,, we
will find (1) that the standard-deviations of all arrays of z, are
the same: (2) that the regression of xz, on z; is strictly linear.
n Axes of Measurement Xx
3 M = Mean of whole surface
— and is also the summit of
the surface
RR.CC.-Lines of means
ow»
Contour lines and Axes of
normal correlation surface
Yi
Fic. 50.— Principal Axes and Contour Lines of the normal
Correlation Surface.
5. The contour lines are, as in the case of independence, a
series of concentric and similar ellipses; the major and minor
axes are, however, no longer parallel to the axes of 2; and z,, but
make a certain angle with them. Fig. 50 illustrates the calculated
 form of the contour lines for one case, RR and CC being
the lines of regression. As each line of regression cuts every

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