Show that when k = 2, the principal components of R XX correspond to the principal axes of the data ellipse for the standardized regressors Z 1 and Z 2 ; show that the halflength of each axis is equal...

Show that when k = 2, the principal components of R_XX
correspond to the principal axes of the data ellipse for the standardized regressors Z₁
and Z₂; show that the halflength of each axis is equal to the square root of the corresponding eigenvalue of R_XX
. Now extend this reasoning to the principal axes of the data ellipsoid for the standardized regressors when k > 2.