Hello, everybody!

Assume standart linear regressian model $\displaystyle Y=Xb+Z$, where X is N x p matrix and b is vector of parameters.

It is given, that one can calculate joint confidence band to parameter vector $\displaystyle b=(b_1,..,b_p)$ by
$\displaystyle Pr(\hat{b}_k-\sqrt{pf_\gamma \hat{s}^2}\leq b_k \leq \hat{b}_k+\sqrt{pf_\gamma \hat{s}^2}, k=1,..,p)=\gamma$,
where $\displaystyle f_\gamma$ is $\displaystyle \gamma$ - quantile of $\displaystyle F_{p,n-p}$ distribuion.

What I am concerned about is that term p under the square root. If I want to calculate confidence band for only one $\displaystyle b_k$,

then this p under square root is equal to 1?

That is:
$\displaystyle Pr(\hat{b}_k-\sqrt{f_\gamma \hat{s}^2}\leq b_k \leq \hat{b}_k+\sqrt{f_\gamma \hat{s}^2})=\gamma$ ?