偏相関
ρ X Y ⋅ Z = ρ X Y ⋅ Z ∖ { Z 0 } − ρ X Z 0 ⋅ Z ∖ { Z 0 } ρ Z 0 Y ⋅ Z ∖ { Z 0 } 1 − ρ X Z 0 ⋅ Z ∖ { Z 0 } 2 1 − ρ Z 0 Y ⋅ Z ∖ { Z 0 } 2 . {\displaystyle \rho _{XY\cdot \mathbf {Z} }={\frac {\rho _{XY\cdot \mathbf {Z} \setminus \{Z_{0}\}}-\rho _{XZ_{0}\cdot \mathbf {Z} \setminus \{Z_{0}\}}\rho _{Z_{0}Y\cdot \mathbf {Z} \setminus \{Z_{0}\}}}{{\sqrt {1-\rho _{XZ_{0}\cdot \mathbf {Z} \setminus \{Z_{0}\}}^{2}}}{\sqrt {1-\rho _{Z_{0}Y\cdot \mathbf {Z} \setminus \{Z_{0}\}}^{2}}}}}.}
ρ X Y ⋅ Z = ρ X Y − ρ X Z ρ Z Y 1 − ρ X Z 2 1 − ρ Z Y 2 {\displaystyle \rho _{XY\cdot Z}={\frac {\rho _{XY}-\rho _{XZ}\rho _{ZY}}{{\sqrt {1-\rho _{XZ}^{2}}}{\sqrt {1-\rho _{ZY}^{2}}}}}}