Why is my professor using for a regression problem where regression is out y(hat) + T(alpha/2), n-2* SE (of the model)*SQrt(1+1/n) to calculate…

Why is my professor using for a regression problem where regression is out y(hat) + T(alpha/2), n-2* SE (of the model)*SQrt(1+1/n) to calculate prediction interval. But to calculate confidene interverl he is using b + t(alpha/2, n-2)*SE(of the cofficent)

Why is he not dividing the second SE by Sqrt(n).

this is a simple or multiple regression problem

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