# Constructing the approximate confidence set for parameter vector beta in least square regression

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 $\beta$.

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 ?

• 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. – probabilityislogic Mar 1 '14 at 8:39
• Suppose the dimension of $\beta$ is 3 x 1, how would you approach this problem ? Thanks. Because I am completely clueless right now. – mynameisJEFF Mar 1 '14 at 15:43