Lining up nonconsecutive multi-line equations

Question

I have the following code:

\documentclass[fleqn, 12pt]{article} 
\usepackage{amsmath,amsfonts,amssymb}
\usepackage{graphicx}
\graphicspath{ {./images/} }
\setlength{\parskip}{\baselineskip}%
\setlength{\parindent}{0pt}%
\begin{document}
\raggedright

From the model, 
\begin{align}
&E( Y_i - \bar{ Y } ) = E[ ( \beta_0 + \beta_1 X_i ) - ( \beta_0 - \beta_1 \bar{ X } ) ] \nonumber \\
&( \text{Since the first normal equation gives} \ \ Y_i  = \beta_0 + \beta_1 X_i \ \ \text{and} \ \ \bar{Y} = \beta_0 + \beta_1 \bar{X}) \nonumber \\
& \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \beta_1( X_i - \bar{X} ) \nonumber
\end{align}

\end{document}

Notice that the lines

&E( Y_i - \bar{ Y } ) = E[ ( \beta_0 + \beta_1 X_i ) - ( \beta_0 - \beta_1 \bar{ X } ) ] \nonumber \\ 

and

& \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \beta_1( X_i - \bar{X} ) \nonumber

are separated by the line

&( \text{Since the first normal equation gives} \ \ Y_i  = \beta_0 + \beta_1 X_i \ \ \text{and} \ \ \bar{Y} = \beta_0 + \beta_1 \bar{X}) \nonumber \\

Despite this, I want the line

& \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \beta_1( X_i - \bar{X} ) \nonumber

to line up at the = sign with the first line

&E( Y_i - \bar{ Y } ) = E[ ( \beta_0 + \beta_1 X_i ) - ( \beta_0 - \beta_1 \bar{ X } ) ] \nonumber \\ 

This is why I put the \ \ \ \ \ \ \ \ \ \ \ \ \ \

Is it possible to somehow do this using &, whilst maintaining the line in the middle as it is? Or, perhaps, some other way to automatically have them align?

EDIT: The reason I had to use & to put the middle line as its own line is because, if I put it on the same line as the first equation, then it would go off the page margin.

Thanks.

Answer 1

Like this?

\documentclass[fleqn, 12pt]{article} 
\usepackage{amsmath,amsfonts,amssymb}
\usepackage{graphicx}
\graphicspath{ {./images/} }
\setlength{\parskip}{\baselineskip}%
\setlength{\parindent}{0pt}%
\begin{document}
\raggedright

From the model, 
\begin{align}
E( Y_i - \bar{ Y } ) &= E[ ( \beta_0 + \beta_1 X_i ) - ( \beta_0 - \beta_1 \bar{ X } ) ] \nonumber \\
\rlap{(Since the first normal equation gives $Y_i  = \beta_0 + \beta_1 X_i$ and $\bar{Y} = \beta_0 + \beta_1 \bar{X}$)} \phantom{E( Y_i - \bar{ Y } )} \nonumber \\
& = \beta_1( X_i - \bar{X} ) \nonumber
\end{align}
\end{document}

Answer 2

I would put the explanatory text in a \parbox immediately below the material to the right of the first = symbol. That way, it's immediately clear that the explanatory text pertains to the material on the preceding line.

\documentclass[fleqn, 12pt]{article}
\usepackage{amsmath,amsfonts,amssymb}
\DeclareMathOperator{\E}{E} % <-- new (expectation operator)
\setlength{\parskip}{\baselineskip}
\setlength{\parindent}{0pt}

\begin{document}
\raggedright

From the model,
\begin{align*}
\E( Y_i - \bar{Y} ) 
&= \E[(\beta_0+\beta_1 X_i) - (\beta_0-\beta_1\bar{X})]  \\
&\qquad\parbox[t]{0.5\textwidth}{(since the first normal equation gives 
$Y_i = \beta_0 + \beta_1 X_i$ and $\bar{Y} = \beta_0 + \beta_1\bar{X}$)}\\
&= \beta_1(X_i-\bar{X}) \,.
\end{align*}

\end{document}

Answer 3

I would simply set the comment after the display (using “because” instead of “since”). It's more legible and in style with standard mathematical practice; to the contrary, the comment in the middle will raise doubts what it refers to.

Anyway, this is how you can do it; if the comment doesn't fit on one line it will wrap, as shown in the third example.

\documentclass[fleqn, 12pt]{article} 
\usepackage{amsmath,amsfonts,amssymb}
\usepackage{graphicx}
\usepackage{parskip} % \parskip=\baselineskip is HUGE

\makeatletter
\newcommand{\devioustrick}[1]{%
  \ifmeasuring@\else
    \kern-\ifcase\expandafter1\maxcolumn@widths\fi
    \parbox{\dimexpr\linewidth-\mathindent\relax}{#1}%
  \fi
}
\makeatother

\begin{document}

From the model, 
\begin{align*}
E( Y_i - \bar{ Y } ) 
&= E[ ( \beta_0 + \beta_1 X_i ) - ( \beta_0 - \beta_1 \bar{ X } ) ] \\
&= \beta_1( X_i - \bar{X} )
\end{align*}
because the first normal equation gives 
$Y_i  = \beta_0 + \beta_1 X_i$ and 
$\bar{Y} = \beta_0 + \beta_1 \bar{X}$.

From the model, 
\begin{align*}
E( Y_i - \bar{ Y } ) 
={}& E[ ( \beta_0 + \beta_1 X_i ) - ( \beta_0 - \beta_1 \bar{ X } ) ] \\
&\devioustrick{
  (since the first normal equation gives
  $Y_i  = \beta_0 + \beta_1 X_i$ and
  $\bar{Y} = \beta_0 + \beta_1 \bar{X}$)
}\\
={}& \beta_1( X_i - \bar{X} )
\end{align*}

From the model, 
\begin{align*}
E( Y_i - \bar{ Y } ) 
={}& E[ ( \beta_0 + \beta_1 X_i ) - ( \beta_0 - \beta_1 \bar{ X } ) ] \\
&\devioustrick{
  (since the first normal equation gives
  $Y_i  = \beta_0 + \beta_1 X_i$ and
  $\bar{Y} = \beta_0 + \beta_1 \bar{X}$
  and since the definitive answer on life, the universe
  and everything is~$42$)
}\\
={}& \beta_1( X_i - \bar{X} )
\end{align*}

\end{document}

Answer 4

Use \intertext to place text between aligned equations. There is rarely any need to manually align material using 'hard' spaces. The amsmath package provides environments that meet all of the most common requirements.

\documentclass[fleqn, 12pt]{article}
\usepackage{amsmath}
\begin{document}
From the model,
\begin{align*}
E( Y_i - \bar{ Y } ) &= E[ ( \beta_0 + \beta_1 X_i ) - ( \beta_0 - \beta_1 \bar{ X } ) ]  \\
\intertext{Since the first normal equation gives $Y_i  = \beta_0 + \beta_1 X_i$ and $\bar{Y} = \beta_0 + \beta_1 \bar{X}$}
& = \beta_1( X_i - \bar{X} )
\end{align*}

\end{document}

Answer 5

Another solution is to just use \tag. This seems to be appropriate semantically, seeing as the text pertains to the previous equation-line.

From the model,
\begin{align*}
E( Y_i - \bar{ Y } ) &= E[ ( \beta_0 + \beta_1 X_i ) - ( \beta_0 - \beta_1 \bar{ X } ) ]
\tag{since the first normal equation gives $Y_i  = \beta_0 + \beta_1 X_i$ and $\bar{Y} = \beta_0 + \beta_1 \bar{X}$}\\
& = \beta_1( X_i - \bar{X} )
\end{align*}