Write the following four restrictions in the form $\boldsymbol { R } \boldsymbol { \beta } = \boldsymbol { r } ,$ where the hypotheses are to be tested simultaneously.
$\begin{array} { l }
\beta _ { 3 } = 2 \beta _ { 5 } , \
\beta _ { 1 } + \beta _ { 2 } = 1 , \
\beta _ { 4 } = 0 , \
\beta _ { 2 } = - \beta _ { 6 } .
\end{array}$
Can you write the following restriction $\beta _ { 2 } = - \frac { \beta _ { 3 } } { \beta _ { 1 } }$ in the same format? Why not?

Question

Write the following four restrictions in the form $\boldsymbol { R } \boldsymbol { \beta } = \boldsymbol { r } ,$ where the hypotheses are to be tested simultaneously.
$\begin{array} { l } 
\beta _ { 3 } = 2 \beta _ { 5 } , \
\beta _ { 1 } + \beta _ { 2 } = 1 , \
\beta _ { 4 } = 0 , \
\beta _ { 2 } = - \beta _ { 6 } .
\end{array}$
Can you write the following restriction $\beta _ { 2 } = - \frac { \beta _ { 3 } } { \beta _ { 1 } }$ in the same format? Why not?

Quizplus · Accepted Answer

The Answer of Write the following four restrictions in the form $\boldsymbol { R } \boldsymbol { \beta } = \boldsymbol { r } ,$ where the hypotheses are to be tested simultaneously.
$\begin{array} { l } 
\beta _ { 3 } = 2 \beta _ { 5 } , \
\beta _ { 1 } + \beta _ { 2 } = 1 , \
\beta _ { 4 } = 0 , \
\beta _ { 2 } = - \beta _ { 6 } .
\end{array}$
Can you write the following restriction $\beta _ { 2 } = - \frac { \beta _ { 3 } } { \beta _ { 1 } }$ in the same format? Why not?

Write the Following Four Restrictions in the Form Rβ=r,\boldsymbol { R } \boldsymbol { \beta } = \boldsymbol { r } ,Rβ=r,

Write the Following Four Restrictions in the Form $\boldsymbol { R } \boldsymbol { \beta } = \boldsymbol { r } ,$