Hello, everybody!

Assume standart linear regressian model 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 b=(b_1,..,b_p) by
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 f_\gamma is \gamma - quantile of 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 b_k,

then this p under square root is equal to 1?

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