带残差的三维回归计划

Question

在 R 中，我可以使用以下命令创建带有残差的三维回归平面

scatter3d(prestige ~ income + education, data=Duncan)

具有包scatter3d中的功能car R。

我需要一些提示来制作相同的情节tikz。任何帮助都将不胜感激。谢谢

library(car)
Duncan
                   type income education prestige
accountant         prof     62        86       82
pilot              prof     72        76       83
architect          prof     75        92       90
author             prof     55        90       76
chemist            prof     64        86       90
minister           prof     21        84       87
professor          prof     64        93       93
dentist            prof     80       100       90
reporter             wc     67        87       52
engineer           prof     72        86       88
undertaker         prof     42        74       57
lawyer             prof     76        98       89
physician          prof     76        97       97
welfare.worker     prof     41        84       59
teacher            prof     48        91       73
conductor            wc     76        34       38
contractor         prof     53        45       76
factory.owner      prof     60        56       81
store.manager      prof     42        44       45
banker             prof     78        82       92
bookkeeper           wc     29        72       39
mail.carrier         wc     48        55       34
insurance.agent      wc     55        71       41
store.clerk          wc     29        50       16
carpenter            bc     21        23       33
electrician          bc     47        39       53
RR.engineer          bc     81        28       67
machinist            bc     36        32       57
auto.repairman       bc     22        22       26
plumber              bc     44        25       29
gas.stn.attendant    bc     15        29       10
coal.miner           bc      7         7       15
streetcar.motorman   bc     42        26       19
taxi.driver          bc      9        19       10
truck.driver         bc     21        15       13
machine.operator     bc     21        20       24
barber               bc     16        26       20
bartender            bc     16        28        7
shoe.shiner          bc      9        17        3
cook                 bc     14        22       16
soda.clerk           bc     12        30        6
watchman             bc     17        25       11
janitor              bc      7        20        8
policeman            bc     34        47       41
waiter               bc      8        32       10

scatter3d(prestige ~ income + education, data=Duncan)

scatter3d(prestige ~ income + education | type, data=Duncan)

Answer 1

首先，除了调用 R（一些软件包可以做到）之外，没有基于 tex 的解决方案能够模仿 R 命令的简洁性进行统计分析；这是 R 的强项之一。

话虽如此，这里尝试使用 Asymptote 重做你的第一幅图像（包括统计分析）。请注意，统计分析需要smoothcontour3 包，除非您拥有最新版本的 Asymptote，否则您可能需要手动安装（即将文件复制到您的工作目录中）。

代码假定您的数据（包括标题）已被复制并粘贴到名为的文件中Duncan.dat。（标题不是必需的；只是我明确跳过了第一行。）

\documentclass{standalone}
\usepackage{asypictureB}
\begin{document}
\begin{asypicture}{name=UnifiedRegression}
settings.outformat = "png";
settings.render = 8;
size(10cm);
import graph3;
import smoothcontour3;  // for the leastsquares routine

Billboard.targetsize = true;  // Perspective should not affect the labels.
currentprojection = perspective(60 * (5, 2, 3));

file duncan = input("Duncan.dat");

string headers = duncan;

real[][] independentvars;
real[] dependentvars;

while (!eof(duncan)) {
  string line = duncan;
  string[] entries = split(line);
  if (entries.length < 5) continue;
  string type = entries[1];
  real income = (real)(entries[2]);
  real education = (real)(entries[3]);
  real prestige = (real)(entries[4]);

  // include 1.0 for the residue
  independentvars.push(new real[] {income, education, 1.0});
  dependentvars.push(prestige);
}

real[] coeffs = leastsquares(independentvars, dependentvars, warn=false);
if (coeffs.length == 0) {
  abort("Unable to find regression: independent variables are "
    + "linearly dependent.");
}

real f(pair xy) {
  return coeffs[0] * xy.x  // income
       + coeffs[1] * xy.y  // education
       + coeffs[2];        // residue
}

real xmin = infinity, xmax = -infinity, ymin = infinity, ymax = -infinity;
for (real[] row : independentvars) {
  if (row[0] < xmin) xmin = row[0];
  if (row[0] > xmax) xmax = row[0];
  if (row[1] < ymin) ymin = row[1];
  if (row[1] > ymax) ymax = row[1];
}

// Draw the plane
draw(surface(f, (xmin, ymin), (xmax, ymax)),
     surfacepen=emissive(blue + opacity(0.6)),
     meshpen = blue);

for (int ii = 0; ii < independentvars.length; ++ii) {
  triple pt = (independentvars[ii][0], independentvars[ii][1],
           dependentvars[ii]);
  draw(shift(pt) * unitsphere, material(yellow, emissivepen=0.2*yellow));
  real z = f((pt.x, pt.y));
  if (pt.z > z) draw (pt -- (pt.x, pt.y, z), green);
  else draw(pt -- (pt.x, pt.y, z), red);
}

xaxis3("income", Bounds(Min, Min), InTicks);
yaxis3("education", Bounds(Min, Min), InTicks);
zaxis3("prestige", Bounds(Min, Min), InTicks);
\end{asypicture}
\end{document}

Answer 2

看一下这个pgfplots包。计算回归平面可能最容易，R. 下面是一个最简单的示例（没有修饰）供您入门，其中 try.dat 包含您提供的数据。

\documentclass{article}


\usepackage{pgfplots}

\begin{document}
\begin{tikzpicture}
\begin{axis}
\addplot3[only marks] table[x index=2, y index=3,z index=4]{try.dat};
\end{axis}
\end{tikzpicture}
\end{document}