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

question 9

Essay

Consider the following symmetric and idempotent Matrix A: A = I - 1n\frac { 1 } { n } ??' and ? = [11…1]\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?

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