Is it true that The confidence intervals for individual j's are wider than the confidence intervals for the vector ? Please explain why it is true or please explain why it is wrong.

Hi, I'm a bit confused about the concept of the multiple linear regression models. Since the confidence intervals for Vector B is an ellipsoid, I found it extremely difficult to determine whether it is wider than the one of individual Bj's.

\f- We can construct a (1 - o) x 100% confidence region for 8 to be all the points in the following ellipsoid (B - B)XX ( B - B) p 62 F(a; p, n - p)) = a