I first tired to type up some maths without using any $$. And there was a ! Missing $ inserted warning message. So I've added the $$ at the beginning and at the end of each line like this
$$H_0:\beta_2=0 $$ \\
$$H_1:\beta_2 \neq 0 $$ \\
$$ F=\frac{(SS_{null}-SS_{full})\triangle p}{MS_{res}} \sim F_{\triangle p,n-p}=F_{1,13} $$ \\
Then I got an Missing $ inserted. <inserted text> error message for the last line. Where am I supposed to put the $$ sign?
Is it necessary to use them whenever I type up maths-related stuff? Can I just use it at the beginning and at the end of the document? Many thanks!

$$in LaTeX: see http://tex.stackexchange.com/questions/503/why-is-preferable-to). (I'm assuming LaTeX, but the example could of course be a plain TeX one.) – Joseph Wright Sep 20 '14 at 09:56$errors then you have tex (and most likely latex) post the complete log file you get from running your document – David Carlisle Sep 20 '14 at 10:44