\documentclass{article}
\usepackage{amsmath,calc}
\begin{document}
\begin{align*}
R(-1) &= \sum_{i=1}^m A(i)R(i-1) \\
R(-2) &= \sum_{i=1}^m A(i)R(i-2) \\
&\mathrel{\makebox[\widthof{=}]{\vdots}} \\
R(-k) &= \sum_{i=1}^m A(i)R(i-k)
\end{align*}
\end{document}
The "proper" way to do this would, I suppose, be to turn on the numbering of the equations you want to number. You can do this by right clicking the equation and selecting Number this formula. There is also a keyboard shortcut, Alt + M N (hold down Alt, press M, release both, press N), which will work if the cursor is inside in equation.
Of course this is tedious work if you have a lot of equations, so it is better to number as you go. Either by adding a normal displayed equation and numbering as mentioned above, or inserting a numbered equation directly, with Insert --> Math --> Numbered formula.
This is also quite tedious, Ctrl+Shift+M is much easier. What one can do is to modify this shortcut to insert a numbered formula instead, or add a new shortcut for this purpose. Changing keyboard shortcuts are done in Tools --> Preferences --> Editing --> Shortcuts, see e.g. Shortcuts for Lemma, Claim, Theorem etc for details. A function you can use for such a shortcut is
command-sequence math-mode on; math-mutate equation;math-number-toggle
Again though, this doesn't help if one already has written the entire document with unnumbered equations. Then the trick mentioned in the LyX wiki, that you seem to have found, is more convenient: go to Document --> Settings --> LyX preamble and add the following two lines:
\renewcommand\[{\begin{equation}}
\renewcommand\]{\end{equation}}
This won't add numbering of the equations within LyX, but in the PDF they will be numbered.
Best Answer
Insert → Math → Ams Align Environment
and then in the left part
y_tand the right= A'X_t, then hitctrl-enterto get a new line.