We are assuming that the i Nbeta0 beta1xi sigma 2 for a gi

We are assuming that the ?i ~ N(beta0 + beta1xi, sigma 2) for a given xi and independent of each other for i = 1 to n. Show that b0 - beta0 / has a t distribution with n - 2 degrees of freedom. You can assume that we have already established E b0= beta0 the variance of b0 is sigma 2 [1/n + xi 2/ Sxx] and SSE/sigma 2 ~ x2 n 2-2

Solution

E(b0) = Beta )

Hence E(b0) -Beta0/Se of b0 =

b0-Beta0/se follows a t distribution with n-2 df.