證明題總是卡住...
3. Let Bo and ₁ denote the least squares estimators of Bo and 3₁. Define SSE = Σ(Yi-Bo-
i=1
B₁X₁)². Show that
(a) E (SSE) = 0²,
(b) cov(Y, ₁X) = 0.
4. In Section 10.4, we defined a test statistic
where s² =
T =
VSEZ
SSE. In addition, it is known that T~:
n-2'
(a) Show that (1) can be re-written as
1
tn-2.
T =
r√n-2
(1)
(2)
(b) Use Part (a) to test Ho: p = 0 vs H₁ p 0. [Hint: (2) can be regarded as a test
statistic under Ho.]
