如何绘制线性回归的一般形式

Question

我尝试使用 Mathcha（一个可帮助构建拓扑图和绘图的在线网站）并且也尝试使用 Sage，以便绘制下面显示的线性回归图，但是我所有的尝试都没有得到下面这张图：

Answer 1

你可以尝试这样的事情，用 pgfplots：

\documentclass[border=2mm]{standalone}    
\usepackage {pgfplots}
\pgfplotsset{compat=1.17}

\def\func(#1){0.75*#1+0.58}  % Linear regression function
\pgfmathsetmacro\y{\func(2)} % \alpha x_1 + \beta

\begin{document}
\begin{tikzpicture}[line cap=round, mark options={mark size=1.5pt,fill=white}]
  \begin{axis}
    [
      xmin=0,
      xmax=4,
      ymin=0,
      ymax=4,
      domain=0.25:3.75,
      axis lines=center,
      xlabel=$x$,
      ylabel=$y$,      
      xtick={2},
      xticklabels={$x_1$},
      ytick=\empty
    ]
    \addplot [thick, blue]             {(\func(x))};
    \addplot [dashed, red] coordinates {(2,0) (2,2.44)};
    \addplot [mark=*, red] coordinates {(2,\y)};
    \addplot [only marks]  coordinates {(0.5,0.80) (1,1.57)   (1.5,1.34)
                                        (2,2.44)   (2.5,2.48) (3,2.66)
                                        (3.5,3.17)};
    \node       at (2,2.44) [left]  {$y_1$};
    \node[red]  at (2,\y)   [right] {$\alpha x_1+\beta$};
    \node[blue] at (2.6,3.1)        {$y=\alpha x+\beta$};
  \end{axis}
 \end{tikzpicture}
\end{document}

您将得到下图：

Answer 2

虽然很晚了，但这是 TIKZ 唯一的尝试：

\documentclass[tikz,border=3.5mm]{standalone}
\usepackage{pgfplots}
\usetikzlibrary{plotmarks}
\usetikzlibrary{decorations.pathreplacing}

\begin{document}
    
    \begin{tikzpicture}
        \pgfsetplotmarksize{0.4ex}

        \draw[->] (0,0) -- (4,0) node[xshift=0.25cm]{$x$};
        \draw[->] (0,0) -- (0,4) node[xshift=0.25cm]{$y$};
        \draw[-,blue] (0.5,0.5) -- (3.5,3.5);
        
        \foreach \b  in {1,1.5,...,3}{
        \node[black] at (\b+rnd-rnd,\b+rnd-rnd){\pgfuseplotmark{o}};
        \b
        }
    
        \node[inner sep=0,black, label={[below, yshift=-0.2cm]$x_1$}] (n1)at (2,0){};
        \node[inner sep=0,black, label={[above]$y_1$}](n2) at (2,2.5){\pgfuseplotmark{o}};
        \path[draw,dashed,red] (n1)--(n2);
        \node[red,fill=white,inner sep=0.35ex, label={[right,xshift=0.2cm]$\alpha x_1+\beta$}] at (2,2){\pgfuseplotmark{o}};
        \node[inner sep=0,blue] (n1)at (1.5,3.5){$y=\alpha x_1+\beta$};     
    
    \end{tikzpicture}
    
\end{document}