Get y value of linear regression plot at xmax

Question

I'm creating a dynamic LaTeX (LuaLaTeX) script, which is creating a plot out of a given CSV file. Settings like xmin, xmax etc. depend on that CSV file.

That CSV file contains the storage utilization of a hard drive, together with date time stamps.

The domain of the plot reaches from two years ago to one year in the future. The black plot shows the CSV data, the thick red like is the linear regression line, expanded in both directions (with the "shorten"-key).
The linear regression is created with this code:

\addplot [line width=10pt, opacity=.3, red, shorten >= -10cm, shorten <= -10cm]  table [
            x index=5,
            y={create col/linear regression={
                x=JulianDayMod,
                y="size",
            }}
        ] {\loadedtable};

Since the CSV has date-formats, I needed to convert it beforehand with this script: Linear regression with dates on x axis in pgfplots

Now I need the y value of the linear regression at xmax. Do you know how to get it?
(its also important to know that xmax is a date as well, like "2022-11-23")

It should be displayed in the legend where I've put x as placeholder.
I already know that you can access the coefficents of the linear regression with \pgfplotstableregressiona and \pgfplotstableregressionb.
And that I can access xmax with \pgfkeysgetvalue{/pgfplots/xmax}{\xmax}

But I couldn't find any solution online for this…

Answer 1

After some trying I found the solution!
(I already had the correct idea in mind but this didn't work in the first run...)

Recap: A linear function has this function: a · x + b

And pgfplotstable lets you access
a with \pgfplotstableregressiona and
b with \pgfplotstableregressionb
of the linear regression plot.

So I used this code to access the value: (xmin was previously defined)

% get xmax (e.g. 2021-11-25)
\pgfkeysgetvalue{/pgfplots/xmax}{\xmax}

% convert xmax (date to julian, which is an integer number)
\newcount\xmaxjulian
\pgfcalendardatetojulian{\xmax}{\xmaxjulian}
\xmaxjulian=\numexpr\xmaxjulian-\xmin % remove offset

% store y value at xmax in \var
\pgfmathsetmacro{\var}{\pgfplotstableregressiona * (\the\xmaxjulian) + \pgfplotstableregressionb}


% print legend:
\addlegendentry{Forecast utilization in one year:
   \luaexec{ tex.sprint ( string.format ( "\%.2f" , \var )  ) } TB}

Note:
That code \luaexec{ tex.sprint ( string.format ( "\%.2f" , \var ) ) } rounds my value to two decimal places. It only works with LuaLaTeX and you need to add \usepackage{luacode} to your code.

Note 2:
You can print the function of the linear regression with this:

Formula of linear regression: 
       $\pgfmathprintnumber{\pgfplotstableregressiona}\cdot x
       \pgfmathprintnumber[print sign]{\pgfplotstableregressionb}$

Note 3:
I added a MWE example here: (you need LuaLaTeX in order to run it)

\documentclass{article}
\usepackage[letterpaper,top=2cm,bottom=2cm,left=3cm,right=3cm,marginparwidth=1.75cm]{geometry}
\usepackage{datatool}
\usepackage{luacode}

\usepackage{pgfplots}
\usepackage{pgfplotstable}
\usepackage{pgfcalendar}
\usepgfplotslibrary{dateplot}
\pgfplotsset{compat=newest}


\begin{filecontents*}{data.csv}
date, size
2021-04-01, 1.42
2021-05-01, 1.46
2021-06-01, 1.58
2021-07-01, 1.55
2021-08-01, 1.69
\end{filecontents*}


\begin{document}
\thispagestyle{empty}
\centering


\pgfplotstableread[col sep=comma]{data.csv}\loadedtable

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% add new column with Julian integer numbers
    \newcount\julianday
    \pgfplotstablecreatecol[
        create col/assign/.code={
            \pgfcalendardatetojulian{\thisrowno{0}}{\julianday}
            \edef\entry{\the\julianday}
            \pgfkeyslet{/pgfplots/table/create col/next content}\entry
        },
    ]{JulianDay}{\loadedtable}
        \pgfplotstablegetelem{0}{JulianDay}\of{\loadedtable}
        \pgfmathtruncatemacro{\xmin}{\pgfplotsretval}
    \pgfplotstablecreatecol[
        expr={\thisrow{JulianDay}-\xmin},
    ]{JulianDayMod}{\loadedtable}
% source: https://tex.stackexchange.com/questions/367339/linear-regression-with-dates-on-x-axis-in-pgfplots


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% compute dates for xmin and xmax

% get last date in file
\DTLloaddb[%
    noheader,%
    keys={date,2}%
    ]{myDB}{data.csv}
\DTLforeach*{myDB}{\CurrentA=date}{%
    \xdef\LastDate{\CurrentA}
}
\newcount\DateOfLastScan
\pgfcalendardatetojulian{\LastDate{}}{\DateOfLastScan}
\pgfcalendarjuliantodate{\DateOfLastScan}{\theyear}{\themonth}{\theday}
\year=\theyear
\month=\themonth
\day=\theday

% get date two years ago
\year=\numexpr\year-2
\edef\twoyearsago{\the\year-\ifnum\the\month<10 0\fi\the\month-\ifnum\the\day<10 0\fi\the\day}
\year=\numexpr\year+2

% get date one year in the future
\year=\numexpr\year+1
\edef\oneyearfuture{\the\year-\ifnum\the\month<10 0\fi\the\month-\ifnum\the\day<10 0\fi\the\day}
\year=\numexpr\year-1


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% print plot

\begin{tikzpicture}
\begin{axis}
[
    date coordinates in=x,
    ylabel={Terabyte}, 
    xticklabel style={rotate=90,anchor=near xticklabel},
    xticklabel=\scriptsize\texttt{\day-\month-\year},
    yticklabel={\luaexec{ tex.sprint ( string.format ( "\%.2f" , \tick )  ) }},
    grid,
    tick align=inside,
    width=\textwidth,
    xmin=\twoyearsago{},
    xmax=\oneyearfuture{},
    ymin=-0.05,
    legend pos = south east,
    legend image post style={only marks, mark=none},
    legend cell align={left},
]


% linear regression
\addplot [line width=10pt, opacity=.3, red, shorten >= -10cm, shorten <= -10cm]  table [
            x index=0,
            % now we can use the newly created column to do the linear regression
            y={create col/linear regression={
                x=JulianDayMod,
                y=size,
            }}
       ] {\loadedtable};
    
% contents from CSV file        
\addplot[thick, no marks, solid] table[col sep=comma, x index=0, y index=1]{\loadedtable};


% get y value at xmax
\pgfkeysgetvalue{/pgfplots/xmax}{\xmax}
\newcount\xmaxjulian
\pgfcalendardatetojulian{\xmax}{\xmaxjulian}
\xmaxjulian=\numexpr\xmaxjulian-\xmin
\pgfmathsetmacro{\var}{\pgfplotstableregressiona * (\the\xmaxjulian) + \pgfplotstableregressionb}

% add legends
\addlegendentry{Forecast utilization in one year: \textbf{\luaexec{% 
   tex.sprint ( string.format ( "\%.2f" , \var )  ) } TB}}
\addlegendentry{Formula of linear regression: 
    $\pgfmathprintnumber{\pgfplotstableregressiona}\cdot x
    \pgfmathprintnumber[print sign]{\pgfplotstableregressionb}$
    }
    
    
% add invisible point at end of linear regression to keep the end of line inside of the plot
\addplot[forget plot,draw=none] coordinates {(\xmax,\var)};


\end{axis}
\end{tikzpicture}
\end{document}

Result: