Use the result of part (b) of Exercise 20 to show that
![](https://test.transtutors.com/qimg/2aa5f59f-1bc6-420b-b0de-87073ae95abe.png)
is a value of a random variable having the standard normal distribution. Also, use the first part of Theorem 3 and the fact that
are independent to show that
is a value of a random variable having the t distribution with n - 2 degrees of freedom.
Exercise 20
Under the assumptions of normal regression analysis, show that
(a) the least squares estimate of α in Theorem 2 can be written in the form
![](https://test.transtutors.com/qimg/f862717b-f239-449a-a481-3605575d1898.png)
(b)
has a normal distribution with
![](https://test.transtutors.com/qimg/38b27f58-e03b-4ae6-acf2-2e945085e529.png)
Theorem 2
![](https://test.transtutors.com/qimg/57c1fd31-efbf-495a-99f8-c1e8d2639a61.png)