where beta is a column vector of the coefficient estimators: The values of those

Question

where beta is a column vector of the coefficient estimators: The values of those estimators are obtained by finding the value of beta? that minimizes the sum of the squared residuals given by: u'u = (y-Xbeta)'(y - Xbeta) = y'y - 2 betax'y + (xbeta)'xbeta What is the dimension of the sum of the squared residuals, u'u? Using the properties of the transpose operator, show that u'u = y'y - 2betaX'y + beta'X'Xbeta After differentiating u'u with respect to beta, the "least squares" coefficient estimates are obtained by solving the following first-order condition for beta. X'Xbeta = X'y Use the above condition to derive an expression for the vector of coefficient estimates, beta. Suppose |X'X| = 0, i.e. the determinant of X'X equals zero. In that case, would it be possible to obtain beta? Briefly explain.

Explanation / Answer

Ans;

The estimate of the variance = MSE = SSE/(n-k) = 54/(30-3) = 54/27 = 2.0

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