HI, what you have found there is the math-version of a regular table. You have defined three columns, but are only using the first. You could as well use
l
to make it left-aligned, and r for right-aligned.
If you want to align all equations at the euqal sign, you can use the more commonly used align-environment. Please click on
open in writelatex to see the output and compare the appearance of the sum.
Code: Select all
\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{equation}
\begin{array}{l}
(m_{i}^{*},b_{i}^{*}) =
\frac{\arg\min}{m,b}\sum_{t=i}^{i+w}\|x_{t}-m\cdot(t-i)-b\|^{2} \\
\displaystyle(m_{i}^{*},b_{i}^{*}) = \frac{\arg\min}{m,b}\sum_{t=i}^{i+w}\|x_{t}-m\cdot(t-i)-b\|^{2} \\
y_{i}=x_{i}-m_{i}^{*}\cdot i - b_{i}^{*} \\
i=1,\ldots,z
\end{array}
\end{equation}
\begin{align}
(m_{i}^{*},b_{i}^{*}) &=
\frac{\arg\min}{m,b}\sum_{t=i}^{i+w}\|x_{t}-m\cdot(t-i)-b\|^{2} \\
y_{i}&=x_{i}-m_{i}^{*}\cdot i - b_{i}^{*} \\
i&=1,\ldots,z\notag
\end{align}
\end{document}
Please also note that i changed the argmin part. You can read much more about math mode in Herberts ebook, it might even be on your machine right now. You can also look it up on CTAN -> voss-mathmode. Reading all isn't necessary, but skimming the pdf might be a good idea.
The smart way: Calm down and take a deep breath, read posts and provided links attentively, try to understand and ask if necessary.