How can one prove that $ \frac{SSE}{\sigma ^ 2} $follows a $ \chi_{n-p} ^ 2 $ distribution using matrix notation? Where n is the number of observations and p is the number of parameters in the model.
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see https://stats.stackexchange.com/questions/20227/why-is-rss-distributed-chi-square-times-n-p?rq=1= or https://stats.stackexchange.com/questions/117406/proof-that-the-coefficients-in-an-ols-model-follow-a-t-distribution-with-n-k-d?noredirect=1&lq=1 – Christoph Hanck May 26 '21 at 10:01