In a Lineair Single Regression example, I have a hypothesis:

H_0: ß = 0.

Normally T will than be:

T= (b - ß) / se(b)

but, since I test wherever ß = 0, i can use:

T= b / se(b)

Question 1) Is this correct? or is there another reason why i may use T = b / sec(b) ? (in stead of (b-ß)/se(b))

Now according to the book: (b-ß) / se(b) ~ t_(n-2)

So, if my N=20, I have to look in the Student's t-distribution table where "N" (or "df" as it is called in my table) is "18" (18=20-2)

Question 2) Why? Why do I have to look in the row where (df=18), why not t_(n-3) (df=17) or t_n (df=20)

Could anyone explain me why T = (b - ß) / se(b) commes with t_(n-2)? and not n-3, n-4, etc...?

Thank you!

Jeffrey