Consider the following symmetric and idempotent Matrix A: A = I - $\frac { 1 } { n }$ ??' and ? = $\left[ \begin{array} { c }
1 \
1 \
\ldots \
1
\end{array} \right]$ a. Show that by postmultiplying this matrix by the vector Y (the LHS variable of the OLS regression), you convert all observations of Y in deviations from the mean.
b. Derive the expression Y'AY. What is the order of this expression? Under what other name have you encountered this expression before?

Question

Consider the following symmetric and idempotent Matrix A: A = I - $\frac { 1 } { n }$ ??' and ? = $\left[ \begin{array} { c } 
1 \
1 \
\ldots \
1
\end{array} \right]$ a. Show that by postmultiplying this matrix by the vector Y (the LHS variable of the OLS regression), you convert all observations of Y in deviations from the mean.
b. Derive the expression Y'AY. What is the order of this expression? Under what other name have you encountered this expression before?

Quizplus · Accepted Answer

The Answer of Consider the following symmetric and idempotent Matrix A: A = I - $\frac { 1 } { n }$ ??' and ? = $\left[ \begin{array} { c } 
1 \
1 \
\ldots \
1
\end{array} \right]$ a. Show that by postmultiplying this matrix by the vector Y (the LHS variable of the OLS regression), you convert all observations of Y in deviations from the mean.
b. Derive the expression Y'AY. What is the order of this expression? Under what other name have you encountered this expression before?

Consider the Following Symmetric and Idempotent Matrix A: a = 1n\frac { 1 } { n }n1​

Consider the Following Symmetric and Idempotent Matrix A: a = $\frac { 1 } { n }$