<. 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 calcu- 
lated form of the contour lines for one case, RR and CC being 
the lines of regression. As each line of regression cuts every 
320