Consider the following inverse model matrix. (a) How many

Chapter 12, Problem 119SE

(choose chapter or problem)

Consider the following inverse model matrix.

\(\left(X^{\prime} X\right)^{-1}=\left[\begin{array}{cccc} 0.125 & 0 & 0 & 0 \\ & 0.125 & 0 & 0 \\

0 & 0 & 0.125 & 0 \\ 0 & 0 & 0 & 0.125 \end{array}\right]\)

(a) How many regressors are in this model?

(b) What was the sample size?

(c) Notice the special diagonal structure of the matrix. What does that tell you about the columns in the original X matrix?

Equation Transcription:

$(X'X{)}^{-1}=$ [ ${\ }_{{\ }_{0\ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\ \ \ \ \ \ \ \ \ \ 0\ \ \ \ \ \ \ 0.125}^{0\ \ \ \ \ \ \ \ \ \ \ \ \ \ 0\ \ \ \ \ \ 0.125\ \ \ \ \ \ \ \ 0}\ }^{{\ }_{0\ \ \ \ \ \ \ \ \ \ 0.125\ \ \ \ \ \ 0\ \ \ \ \ \ \ \ \ \ \ \ 0}^{0.125\ \ \ \ \ \ \ 0\ \ \ \ \ \ \ \ \ 0\ \ \ \ \ \ \ \ \ \ \ \ 0}\ \ \ }$ $]$

Text Transcription:

(X^ X)^-1=[ 0.125 & 0 & 0 & 0 \\ & 0.125 & 0 & 0 \\

0 & 0 & 0.125 & 0 \\ 0 & 0 & 0 & 0.125 ]

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Consider the following inverse model matrix. (a) How many

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