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In a regression what is the matrix $(X'X)^{-1}$? What do its interior elements represent?


marked as duplicate by amoeba, Nick Cox, gung regression Nov 1 '14 at 19:54

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  • $\begingroup$ I do believe that $(X'X)^{-1}$ is the covariance-variance matrix where each diagonal is the variance of $B_{i}$ and the other elements are co variances between different $\beta$'s. Unfortunately, I do not use Stata so I can't help you with your other question but maybe someone more informed can tel you :) Welcome to the site! $\endgroup$ – nicefella Mar 22 '14 at 17:34
  • $\begingroup$ Yes, that is the covariance matrix. The other one X * X' is called the Gram matrix and is useful when finding the dual solution. $\endgroup$ – Dave31415 Mar 22 '14 at 18:24
  • $\begingroup$ Try matrix list e(V) right after you have run the reg function. $\endgroup$ – Penguin_Knight Mar 22 '14 at 19:30
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    $\begingroup$ There is also a discussion of the role of $(X'X)^{-1}$ in regression here: blog.stata.com/2011/03/03/… $\endgroup$ – Maarten Buis Mar 23 '14 at 12:23
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    $\begingroup$ I stumbled across this question just after providing an answer to it at stats.stackexchange.com/questions/104704. To summarize, although this matrix is not the covariance matrix of the estimates of the regression coefficients, a scalar multiple of it is the covariance matrix. Because that multiple is usually not known, it typically is estimated (from the variance of the residuals). The square roots of the diagonal elements are routinely reported in regression output (as the "standard errors" of the coefficients). $\endgroup$ – whuber Jun 25 '14 at 22:08

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