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

question 2

Essay

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?

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Definitions:

Milgram Experiment

A psychological experiment conducted by Stanley Milgram in the 1960s to study obedience to authority, where participants were instructed to administer electric shocks to another person.

Stanford University Prison Experiment

A psychological study conducted by Philip Zimbardo in 1971 at Stanford University, where students were assigned roles of prisoners and guards to explore the effects of perceived power.

Generalization

Drawing a conclusion about a certain characteristic of a population based on a sample from it.

Logical Support

The provision of reasons or evidence to justify a claim or argument.