The F-Statistic with Q = 2 Restrictions When Testing for the Restrictions

question 17

Essay

The F-statistic with q = 2 restrictions when testing for the restrictions ?₁ = 0 and ?₂ = 0 is given by the following formula: $$F = \frac { 1 } { 2 } \left( \frac { t _ { 1 } ^ { 2 } + t _ { 2 } ^ { 2 } - 2 \hat { \rho } _ { t _ { 1 } , t _ { 2 } } t _ { 1 } t } { 1 - \hat { \rho } _ { t _ { 1 } , t _ { 2 } } ^ { 2 } } \right)$$ Discuss how this formula can be understood intuitively.