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From Elements of Statistical Learning, on page 49 (in the context of least square regression), we are given the approximate confidence set (shown in image) for the parameter vector $\beta$.

enter image description here

I want to implement this in R. However, I have no idea how to make $\beta$ as the subject,i.e. I could not construct the confidence set in the following form

$$\beta \leq \hat{\sigma}^2 \chi^2_{p+1} \times something$$

I don't really know how to rearrange the terms (of the confidence set from the image).

Can someone kindly help me out here please ?

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  • $\begingroup$ What is the dimension of $\beta $ ? You won't get anything pretty unless it is 3 or less. Its essentially an "ellipse" but in more than two dimensions. $\endgroup$ – probabilityislogic Mar 1 '14 at 8:39
  • $\begingroup$ Suppose the dimension of $\beta$ is 3 x 1, how would you approach this problem ? Thanks. Because I am completely clueless right now. $\endgroup$ – mynameisJEFF Mar 1 '14 at 15:43

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