{ "cells": [ { "cell_type": "code", "execution_count": 1, "id": "17766d32-3ca5-4ad8-8eb5-7cb7aac5c532", "metadata": { "tags": [ "remove-cell" ] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "---------------------------------\n", "Working on the host: Joachims-MacBook-Pro.local\n", "\n", "---------------------------------\n", "Python version: 3.10.2 | packaged by conda-forge | (main, Feb 1 2022, 19:30:18) [Clang 11.1.0 ]\n", "\n", "---------------------------------\n", "Python interpreter: /opt/miniconda3/envs/srh/bin/python\n" ] } ], "source": [ "%matplotlib inline\n", "# Load the \"autoreload\" extension\n", "%load_ext autoreload\n", "# always reload modules\n", "%autoreload 2\n", "# black formatter for jupyter notebooks\n", "#%load_ext nb_black\n", "# black formatter for jupyter lab\n", "%load_ext lab_black\n", "\n", "%run ../../src/notebook_env.py" ] }, { "cell_type": "markdown", "id": "9cfda20a-5051-427d-aaff-9212b6808eb9", "metadata": {}, "source": [ "# Lineare Regression" ] }, { "cell_type": "code", "execution_count": 2, "id": "f23d2d6f-c5cf-4d78-9718-929ba0494d74", "metadata": {}, "outputs": [], "source": [ "import math\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "from scipy.stats import linregress\n", "import statsmodels.api as sm" ] }, { "cell_type": "markdown", "id": "1d92b3b1-511c-4cf7-ad7c-40bffcc9d972", "metadata": {}, "source": [ "Die Regressionsanalyse ist ein statistisches Verfahren zur Schätzung der Beziehungen zwischen zwei oder mehr Variablen. Die Beziehung wird als $y \\sim x$ oder $y=f(x)$ modelliert. Beide Modellbeschreibungen besagen, dass die Variable $y$ eine Funktion von $x$ ist. Daher wird die Variable $y$ als **Antwortvariable** oder **abhängige Variable** bezeichnet, während die Variable $x$ als **Prädikatorvariable** oder **unabhängige Variable** bezeichnet wird." ] }, { "cell_type": "markdown", "id": "7ee29b8c-4285-4b37-88d1-d82c1b208099", "metadata": {}, "source": [ "## Einfache lineare Regression" ] }, { "cell_type": "markdown", "id": "d4addbfe-8867-4bb3-8888-639bfd948515", "metadata": {}, "source": [ "In diesem Abschnitt wird eine spezielle Art der Regression behandelt, die als einfache lineare Regression bezeichnet wird. In diesem speziellen Fall der Regressionsanalyse wird die Beziehung zwischen der Antwortvariablen $y$ und der Prädikatorvariablen $x$ in Form einer **linearen** Gleichung dargestellt" ] }, { "cell_type": "markdown", "id": "c23f7e2e-a8a4-477e-9a95-afb165ffae23", "metadata": {}, "source": [ "$$y= a + bx\\text{,}$$" ] }, { "cell_type": "markdown", "id": "9c173282-2658-4b65-81d1-06364363fb4e", "metadata": {}, "source": [ "wobei $a$ und $b$ Konstanten sind. Die Zahl $a$ wird als **Achsenabschnitt** bezeichnet und definiert den Schnittpunkt der Regressionslinie mit der $y$-Achse ($x=0$). Die Zahl $b$ wird als **Regressionskoeffizient** bezeichnet. Er ist ein Maß für die Steigung der **Regressionsgeraden**. So gibt $b$ an, um wie viel sich der $y$-Wert ändert, wenn sich der $x$-Wert um $1$ Einheit erhöht. Das Adjektiv **einfach** bezieht sich auf die Tatsache, dass die Ergebnisvariable mit einem einzigen Vorhersagewert verknüpft ist. Das Modell wird als **deterministisches Modell** betrachtet, da es eine genaue Beziehung zwischen $x$ und $y$ herstellt.\n", "\n", "Lassen Sie uns ein einfaches Beispiel betrachten. Gegeben ist eine Grundgesamtheit von $n=3$ Punkten mit kartesischen Koordinaten ($x_i,y_i$) von ($1,6$), ($2,8$) und ($3,10$). Diese Punkte liegen auf einer Geraden und können daher durch ein lineares Gleichungsmodell in der Form $y=a+bx$ beschrieben werden, wobei der Schnittpunkt $a=4$ und $b=2$ ist." ] }, { "cell_type": "code", "execution_count": 3, "id": "c275450a-1570-4d17-94d5-9239dae0e3d1", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Abhängige Variable')" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "fig, ax = plt.subplots()\n", "points = [(1, 6), (2, 8), (3, 10)]\n", "for xy in points:\n", " ax.plot(xy[0], xy[1], \"o\", color=\"C0\", markersize=12)\n", "ax.axhline(0, color=\"k\", linestyle=\"dashed\")\n", "ax.axvline(0, color=\"k\", linestyle=\"dashed\")\n", "xaxis = np.linspace(-3, 6, 100)\n", "y = 2 * xaxis + 4\n", "ax.plot(xaxis, y)\n", "\n", "xaxis = np.linspace(2, 3, 10)\n", "y = [8] * 10\n", "ax.plot(xaxis, y, color=\"C0\", linestyle=\"dashed\")\n", "\n", "yaxis = np.linspace(8, 10, 10)\n", "x = [3] * 10\n", "ax.plot(x, yaxis, color=\"C0\", linestyle=\"dashed\")\n", "\n", "ax.annotate(\n", " r\"$y = a + bx = 4 + 2x$\",\n", " xy=(-1, 2.2),\n", " xytext=(-1.2, 6.3),\n", " arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n", " size=18,\n", " horizontalalignment=\"center\",\n", ")\n", "\n", "ax.arrow(x=2, y=7, dx=0.8, dy=0, head_width=0.5, head_length=0.2, color=\"k\")\n", "\n", "ax.arrow(\n", " x=3.2, y=8, dx=0, dy=1.5, head_width=0.15, head_length=0.5, color=\"k\", width=0.0125\n", ")\n", "\n", "ax.arrow(\n", " x=0.1,\n", " y=3,\n", " dx=0,\n", " dy=-2.3,\n", " head_width=0.15,\n", " head_length=0.5,\n", " color=\"k\",\n", " width=0.0125,\n", ")\n", "\n", "ax.arrow(\n", " x=0.1,\n", " y=1,\n", " dx=0,\n", " dy=2.5,\n", " head_width=0.15,\n", " head_length=0.5,\n", " color=\"k\",\n", " width=0.0125,\n", ")\n", "\n", "ax.text(s=\"$a=4$\", x=0.25, y=2, size=16)\n", "ax.text(s=\"Zuhnahme um\\n1 Einheit\", x=2, y=5.2, size=16)\n", "ax.text(s=\"Zuhnahme um\\n2 Einheiten (b=2)\", x=3.35, y=8.2, size=16)\n", "ax.grid()\n", "ax.set_xlim(-2.5, 5.5)\n", "ax.set_ylim(-2.5, 14)\n", "ax.set_xlabel(\"Unabhängige Variable\")\n", "ax.set_ylabel(\"Abhängige Variable\")" ] }, { "cell_type": "markdown", "id": "86efee92-5576-4c9d-bb2c-f557779f8586", "metadata": {}, "source": [ "In vielen Fällen ist die Beziehung zwischen zwei Variablen $x$ und $y$ jedoch nicht exakt. Das liegt daran, dass die Antwortvariable $y$ von anderen unbekannten und/oder zufälligen Prozessen beeinflusst wird, die von der Prädikatorvariable $x$ nicht vollständig erfasst werden. In einem solchen Fall liegen die Datenpunkte nicht auf einer Geraden. Die Daten können jedoch immer noch einer zugrunde liegenden linearen Beziehung folgen. Um diese Unbekannten zu berücksichtigen, wird der linearen Modellgleichung ein **Zufallsfehlerterm**, bezeichnet mit $\\epsilon$, hinzugefügt, was im Gegensatz zum oben beschriebenen deterministischen Modell zu einem **probabilistischen Modell** führt." ] }, { "cell_type": "markdown", "id": "26c2370a-cb5a-4bd7-b982-cefbb464b10d", "metadata": {}, "source": [ "$$y = a + b x + \\epsilon$$" ] }, { "cell_type": "markdown", "id": "047a613f-5ae5-47f9-8bd9-a0da06971404", "metadata": {}, "source": [ "wobei angenommen wird, dass der Fehlerterm $\\epsilon_i$ aus unabhängigen normalverteilten Werten besteht, $\\epsilon_i \\sim N(0,\\sigma^2)$.\n", "\n", "Bei der linearen Regressionsmodellierung werden folgende Annahmen über das Modell getroffen ({cite:t}`fahrmeirstatistik` s.439, {cite:t}`Frost2018`).\n", "\n", "- Der zufällige Fehlerterm $\\epsilon$ hat für jedes $x$ einen Mittelwert gleich Null.\n", "- Die mit verschiedenen Beobachtungen verbundenen Fehler sind unabhängig.\n", "- Für jedes gegebene $x$ ist die Verteilung der Fehler normal.\n", "- Die Verteilung der Fehler für jedes $x$ hat die gleiche (konstante) Standardabweichung, die mit $\\sigma_\\epsilon$ bezeichnet wird." ] }, { "cell_type": "markdown", "id": "94dd2a3d-0462-4387-9e7d-8246dae1ba39", "metadata": {}, "source": [ "Betrachten wir ein weiteres Beispiel. Diesmal nehmen wir eine Zufallsstichprobe mit dem Stichprobenumfang $n=8$ aus einer Grundgesamtheit. Um zu betonen, dass die Werte des Abschnitts und der Steigung aus Stichprobendaten berechnet werden, werden $a$ und $b$ mit $\\beta_0$ bzw. $\\beta_1$ bezeichnet. Außerdem wird der Fehlerterm $\\epsilon$ als $e$ bezeichnet. $\\beta_0$, $\\beta_1$ und $e$ sind also Schätzungen auf der Grundlage von Stichprobendaten für die Grundgesamtheitsparameter $a$, $b$ und $\\epsilon$." ] }, { "cell_type": "markdown", "id": "51b44194-3be7-4609-b1e9-cc3dac40a416", "metadata": {}, "source": [ "$$\\hat y = \\beta_0 + \\beta_1 x + e \\text{,}$$" ] }, { "cell_type": "markdown", "id": "3e2162d2-65aa-4bd8-b8b5-2d332221b801", "metadata": {}, "source": [ "wobei $\\hat y$ der **geschätzte oder vorhergesagte Wert** von $y$ für einen bestimmten Wert von $x$ ist." ] }, { "cell_type": "code", "execution_count": 4, "id": "d1e4b94f-ce45-4064-af68-082adae3de05", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Abhängige Variable')" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "np.random.seed(12)\n", "n = 12\n", "a = 3\n", "b = 2.5\n", "x = np.random.uniform(2, 8, n)\n", "y = a + b * (x + np.random.uniform(-3, 3, n))\n", "\n", "fig, ax = plt.subplots()\n", "\n", "\n", "for xy in zip(x, y):\n", " yhat = a + b * xy[0]\n", " # ax.plot((xy), (xy[0], yhat))\n", " ax.plot((xy[0], xy[0]), (xy[1], yhat), color=\"k\")\n", "ax.scatter(x=x, y=y, s=100)\n", "xaxis = np.linspace(-1, 10, 100)\n", "regline = a + b * xaxis\n", "ax.plot(xaxis, regline)\n", "\n", "ax.annotate(\n", " r\"$\\hat y = \\beta_0 + \\beta_1x$\",\n", " xy=(6, 18),\n", " xytext=(8, 12),\n", " arrowprops=dict(headwidth=15, headlength=30, width=4, color=\"k\"),\n", " size=18,\n", " horizontalalignment=\"center\",\n", ")\n", "\n", "ax.text(s=\"$(x_i, y_i)$\", x=2.9, y=17.8, size=16)\n", "ax.text(s=\"$e_i = y_i - \\hat y_1$\", x=1.6, y=13.8, size=16)\n", "\n", "ax.set_xlim(-0.5, 9.5)\n", "ax.grid()\n", "ax.set_xlabel(\"Unabhängige Variable\")\n", "ax.set_ylabel(\"Abhängige Variable\")" ] }, { "cell_type": "markdown", "id": "23abdbc4-1628-4741-8b87-4433e858a16c", "metadata": {}, "source": [ "Der Fehler $e_i$ für jedes einzelne Wertepaar ($x_i,y_i$), auch **Residuum** genannt, wird aus der Differenz zwischen dem beobachteten Wert $y_i$ und dem durch $\\hat{y}_i$ gegebenen vorhergesagten Wert errechnet." ] }, { "cell_type": "markdown", "id": "51b954dc-2836-425c-a6f0-157abaa9c369", "metadata": {}, "source": [ "$$e_i = y_i - \\hat y_i$$" ] }, { "cell_type": "markdown", "id": "0371df93-2cc5-4e59-9873-87ca7e0900af", "metadata": {}, "source": [ "Je nach Datenlage ist $e_i$ eine negative Zahl, wenn $y_i$ unterhalb der Regressionslinie liegt, oder eine positive Zahl, wenn $y_i$ oberhalb der Regressionslinie liegt." ] }, { "cell_type": "markdown", "id": "0a43f666-dfb7-433c-969d-f85a936c51ea", "metadata": { "tags": [] }, "source": [ "## Parameterschätzung - Methode der gewöhnlichen kleinsten Quadrate (OLS)" ] }, { "cell_type": "markdown", "id": "8533bd50-c9ff-4d23-b2a4-b582b0f6bb37", "metadata": {}, "source": [ "Da wir nun die Beschränkungen des deterministischen Modells gelockert und einen Fehlerterm $\\epsilon$ eingeführt haben, stoßen wir auf ein weiteres Problem. Es gibt unendlich viele Regressionsgeraden, die die Spezifikationen des probabilistischen Modells erfüllen." ] }, { "cell_type": "code", "execution_count": 5, "id": "cd49302e-18e1-4d55-9bd0-a7b802a221bb", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'Abhängige Variable')" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "np.random.seed(12)\n", "n = 12\n", "a = 3\n", "b = 2.5\n", "x = np.random.uniform(2, 8, n)\n", "y = a + b * (x + np.random.uniform(-3, 3, n))\n", "\n", "fig, ax = plt.subplots()\n", "xaxis = np.linspace(-1, 10, 100)\n", "n = 3\n", "_b = np.random.uniform(b - 3, b + 3, n)\n", "_a = np.random.uniform(a - 5, a + 5, n)\n", "for e, (__a, __b) in enumerate(zip(_a, _b)):\n", " regline = __a + __b * xaxis\n", " ax.plot(xaxis, regline, color=f\"C{e+1}\")\n", "\n", "# [(6.161682980460268, 1.3593855069401755),\n", "# (0.8958678353055358, 3.5287158712720164),\n", "# (5.331259776126706, 2.3273786695000847)]\n", "\n", "ax.text(s=r\"$\\hat y = 0.90 + 3.53x+e$\", x=3, y=22, size=18)\n", "ax.text(s=r\"$\\hat y = 5.336 + 2.33x+e$\", x=6.5, y=19, size=18)\n", "ax.text(s=r\"$\\hat y = 6.16 + 1.36x+e$\", x=6.5, y=13, size=18)\n", "\n", "ax.scatter(x=x, y=y, s=100)\n", "\n", "\n", "ax.set_xlim(-0.5, 9.5)\n", "ax.set_ylim(0, 28)\n", "ax.grid()\n", "ax.set_xlabel(\"Unabhängige Variable\")\n", "ax.set_ylabel(\"Abhängige Variable\")" ] }, { "cell_type": "markdown", "id": "5cefa177-f9fd-47cd-80df-fcffd689be87", "metadata": {}, "source": [ "Offensichtlich brauchen wir eine Strategie, um diejenige Regressionsgerade auszuwählen, die das beste Modell zur Beschreibung der Daten darstellt. In diesem Abschnitt befassen wir uns mit einer der gängigsten Methoden zur Erfüllung dieser Aufgabe, der so genannten Methode der gewöhnlichen kleinsten Quadrate (englisch ordinary least squares, kurz: $OLS$).\n", "\n", "Wie im vorigen Abschnitt erwähnt, wird für jedes bestimmte Wertepaar ($x_1,y_1$)\n", "wird der Fehler $e_i$ durch $y_1-\\hat y$ berechnet. Um die beste Anpassungsgerade für die gegebenen Daten zu erhalten, wird die **Summe der Fehlerquadrate**, bezeichnet als $SSE$, minimiert." ] }, { "cell_type": "markdown", "id": "21bf8dbd-7bc9-496c-9f64-9f4dbffa1962", "metadata": {}, "source": [ "$$min\\; SSE = \\sum_{i=1}^n e_i^2=\\sum_{i=1}^n (y - \\hat y)^2$$" ] }, { "cell_type": "markdown", "id": "f0019e43-93e5-459d-8f82-9075498461b7", "metadata": {}, "source": [ "Für das einfache lineare Modell gibt es eine analytische Lösung für $\\beta_1$" ] }, { "cell_type": "markdown", "id": "ac4d51d0-6ed1-40a4-92b7-405567dc58d3", "metadata": {}, "source": [ "$$\\hat{\\beta_1} = \\frac{\\sum_{i=1}^n ((x_i- \\bar x) (y_i-\\bar y))}{\\sum_{i=1}^n (x_i-\\bar x)^2} = \\frac{cov(x,y)}{var(x)}\\text{,}$$" ] }, { "cell_type": "markdown", "id": "46d354be-eeff-494a-8880-dee4ccb0ea7d", "metadata": {}, "source": [ "und $\\beta_0$:" ] }, { "cell_type": "markdown", "id": "d5509c8d-5c22-492c-98f6-cdf7729e3708", "metadata": {}, "source": [ "$$\\hat{\\beta_0} = \\bar y -\\hat{\\beta_1} \\bar x$$" ] }, { "cell_type": "markdown", "id": "8d0c6910-422f-47e6-99da-2bff196c735d", "metadata": {}, "source": [ "Die $OLS$ liefert die Maximum-Likelihood-Schätzung für $\\hat \\beta$, wenn die Parameter die gleiche Varianz haben und unkorreliert sind und die Residuen $\\epsilon$ unkorreliert sind und einer Gaußschen Verteilung folgen (Homoskedastizität)." ] }, { "cell_type": "markdown", "id": "6491f5c7-71f3-4e9e-9630-816520078745", "metadata": {}, "source": [ "## Einfache lineare Regression - Ein Beispiel" ] }, { "cell_type": "markdown", "id": "0638c0ee-93ef-48f4-a32e-eed92a4122a7", "metadata": {}, "source": [ "Um einige praktische Erfahrungen zu sammeln, wenden wir die einfache lineare Regression in einer Übung an. Dazu laden wir den `students` Datensatz. Sie können die Datei `students.csv` hier herunterladen. Importieren Sie den Datensatz und geben Sie ihm einen passenden Namen." ] }, { "cell_type": "code", "execution_count": 6, "id": "f6345041-8ad7-442d-9fec-848741fb928a", "metadata": {}, "outputs": [], "source": [ "# Lese Datei students.csv als Dataframe ein\n", "students = pd.read_csv(\"../../data/students.csv\")" ] }, { "cell_type": "markdown", "id": "be221ef5-3593-46e4-8093-0d376813d09d", "metadata": {}, "source": [ "Der `students` Datensatz besteht aus $8239$ Zeilen, von denen jede einen bestimmten Studenten repräsentiert, und $16$ Spalten, von denen jede einer Variable/einem Merkmal entspricht, das sich auf diesen bestimmten Studenten bezieht. Diese selbsterklärenden Variablen sind: `stud_id`, `name`, `gender`, `age`, `height`, `weight`, `religion`, `nc_score`, `semester`, `major`, `minor`, `score1`, `score2`, `online_tutorial`, `graduated`, `salary`." ] }, { "cell_type": "markdown", "id": "a238156f-adb1-495e-8b63-1993279e50ce", "metadata": {}, "source": [ "Um die **einfache lineare Regression** zu veranschaulichen, untersuchen wir die Beziehung zwischen zwei Variablen, `height` der Studenten als Prädiktorvariable und `weight` der Studierenden als Antwortvariable." ] }, { "cell_type": "markdown", "id": "74a9fc66-5ca6-4b94-86e7-a032281a1b96", "metadata": {}, "source": [ "### Vorbereitung der Daten" ] }, { "cell_type": "markdown", "id": "f8daa022-3676-43d3-ab8e-c4ee86596876", "metadata": {}, "source": [ "Zur Datenaufbereitung ziehen wir eine Zufallsstichprobe von $12$ Studenten aus dem Datensatz und erstellen einen Datensatz mit den zwei Variablen von Interesse (`height` und `weight`). Außerdem stellen wir die Daten in Form eines Streudiagramms dar, um die zugrunde liegende lineare Beziehung zwischen den beiden Variablen zu visualisieren." ] }, { "cell_type": "code", "execution_count": 7, "id": "69eaf959-f46c-42f2-8cbe-89cfe7941f96", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n = 12\n", "data = students[[\"weight\", \"height\"]].sample(n, random_state=2).sort_index()\n", "\n", "fig, ax = plt.subplots()\n", "ax.scatter(data[\"height\"], data[\"weight\"])" ] }, { "cell_type": "markdown", "id": "7aa8e93f-1a65-4844-b54b-a5c473223e05", "metadata": {}, "source": [ "Die visuelle Inspektion bestätigt unsere Vermutung, dass die Beziehung zwischen der Größe und der Gewichtsvariable ungefähr linear ist. Mit anderen Worten: Mit zunehmender Größe neigt der einzelne Studierende dazu, ein höheres Gewicht zu haben." ] }, { "cell_type": "markdown", "id": "466c74f3-814c-444c-a07c-a6401d1863a6", "metadata": {}, "source": [ "### Schätzung der Parameter" ] }, { "cell_type": "markdown", "id": "d9466e4d-b1db-4bf8-901c-ae678f8d4373", "metadata": {}, "source": [ "#### Lösen für $\\beta_0$ und $\\beta_1$ analytisch in Python" ] }, { "cell_type": "markdown", "id": "f018d495-5684-46cf-854b-d61361f0d610", "metadata": {}, "source": [ "Wie im vorherigen Abschnitt gezeigt, können die Parameter $\\beta_0$ und $\\beta_1$ eines einfachen linearen Modells analytisch berechnet werden. Erinnern Sie sich an die Gleichung für ein lineares Modell aus Stichprobendaten" ] }, { "cell_type": "markdown", "id": "b8ba347d-982b-4f3c-a928-2a051d712c34", "metadata": {}, "source": [ "$$\\hat y = \\beta_0 + \\beta_1 x + e \\text{,}$$" ] }, { "cell_type": "markdown", "id": "b212ec50-5372-4868-96a4-c0d9ca43e22c", "metadata": {}, "source": [ "für $\\beta_1$" ] }, { "cell_type": "markdown", "id": "45fc132d-29ec-4caf-9cc3-28765659d73a", "metadata": {}, "source": [ "$$\\hat{\\beta_1} = \\frac{\\sum_{i=1}^n ((x_i- \\bar x) (y_i-\\bar y))}{\\sum_{i=1}^n (x_i-\\bar x)^2} = \\frac{cov(x,y)}{var(x)}\\text{,}$$" ] }, { "cell_type": "markdown", "id": "6572b10c-3e54-49fa-8287-1c55a11ab1bf", "metadata": {}, "source": [ "und für $\\beta_0$" ] }, { "cell_type": "markdown", "id": "759a4ccc-cc2c-44c6-a9f9-e8b4003c4824", "metadata": {}, "source": [ "$$\\hat{\\beta_0} = \\bar y -\\hat{\\beta_1} \\bar x$$" ] }, { "cell_type": "markdown", "id": "cdec4a52-c758-4d78-bbf1-9745b4d9b955", "metadata": {}, "source": [ "Zum besseren Verständnis verwenden wir Python, um die einzelnen Terme zu berechnen" ] }, { "cell_type": "code", "execution_count": 8, "id": "b4fe47cd-cf03-4aa8-aa4e-08f32ca7754b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.6507615230460924" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Berechne b1\n", "x = data[\"height\"]\n", "y = data[\"weight\"]\n", "x_bar = np.mean(x)\n", "y_bar = np.mean(y)\n", "\n", "b1 = np.sum((x - x_bar) * (y - y_bar)) / np.sum((x - x_bar) ** 2)\n", "b1" ] }, { "cell_type": "markdown", "id": "7eaf037c-89f5-49d5-bf98-eb102c8b86de", "metadata": {}, "source": [ "Die Steigung des Regressionsmodells beträgt ungefähr $0,65$. Zur Überprüfung der Korrektheit berechnen wir das Verhältnis der Kovarianz von $x$ und $y$ mit der Funktion `cov()` und die Varianz von $x$ mit der Funktion `var()` und vergleichen es mit dem Ergebnis von oben." ] }, { "cell_type": "code", "execution_count": 9, "id": "3e745bf1-ada6-4102-b160-4316cf537c5b", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.6507615230460924" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.cov(x, y, ddof=0)[0][1] / np.var(x)" ] }, { "cell_type": "markdown", "id": "ff048971-779c-492b-9915-84f63d42f2df", "metadata": {}, "source": [ "Eine perfekte Übereinstimmung!\n", "\n", "Weiter berechnen wir $\\beta_0$." ] }, { "cell_type": "code", "execution_count": 10, "id": "866a3ad1-4042-4bba-82f0-df7de54d299a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-39.443206412825674" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Berechne b0\n", "b0 = y_bar - b1 * x_bar\n", "b0" ] }, { "cell_type": "markdown", "id": "bb181305-e0b6-46c8-b8f3-473fd4090231", "metadata": {}, "source": [ "Der Achsenabschnitt $\\beta_0$ des Regressionsmodells beträgt ungefähr $-39,44$.\n", "\n", "Wir können also das Regressionsmodell aufschreiben" ] }, { "cell_type": "markdown", "id": "d6a465c4-3796-4cec-847c-c3105f1dde0f", "metadata": {}, "source": [ "$$\\text{Gewicht} = -39,44 + 0,65 \\times \\text{Höhe}$$" ] }, { "cell_type": "markdown", "id": "48ffe19f-47e6-4ec3-b08b-34bab70f4b7b", "metadata": {}, "source": [ "Auf der Grundlage dieser Gleichung können wir nun das Gewicht eines Studenten anhand seiner Größe bestimmen. Lassen Sie uns zum Spaß das Gewicht von Studierenden mit einer Größe von $156$, $178$ und $192$ cm vorhersagen." ] }, { "cell_type": "markdown", "id": "b714b921-9b3d-43f4-8b3b-a13dd12f39e5", "metadata": {}, "source": [ "$$\\text{Gewicht}_{156} = -39,44 + 0,65 \\times \\text{156} \\approx 62 \\ \\text{kg}$$" ] }, { "cell_type": "markdown", "id": "f5a393f8-6d04-40a9-a097-379bf5cb0209", "metadata": {}, "source": [ "$$\\text{Gewicht}_{178} = -39,44 + 0,65 \\times \\text{178} \\approx 76 \\ \\text{kg}$$" ] }, { "cell_type": "markdown", "id": "b8d32a0b-d856-4e01-b561-46224ae30c39", "metadata": {}, "source": [ "$$\\text{Gewicht}_{192} = -39,44 + 0,65 \\times \\text{192} \\approx 85 \\ \\text{kg}$$" ] }, { "cell_type": "markdown", "id": "e6671ae9-d3e5-495e-bf2b-dd0fffbc9909", "metadata": { "tags": [] }, "source": [ "#### Verwenden Sie die Funktion `linregress()` bzw `OLS()` in Python, um $\\beta_0$ zu berechnen und $\\beta_1$" ] }, { "cell_type": "markdown", "id": "966f8a70-1445-466b-b012-bae511245dd9", "metadata": {}, "source": [ "Zum einen können wir die Funktion `linregress()` nutzen um $\\beta_0$ und $\\beta_1$ zu berechnen." ] }, { "cell_type": "code", "execution_count": 11, "id": "0fa76c3a-76ec-4e34-a929-8b51dc358212", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "beta_0 = -39.44320641282566\n", "beta_1 = 0.6507615230460922\n" ] } ], "source": [ "gradient, intercept, r_value, p_value, stderr = linregress(\n", " data[\"height\"], data[\"weight\"]\n", ")\n", "print(f\"beta_0 = {intercept}\")\n", "print(f\"beta_1 = {gradient}\")" ] }, { "cell_type": "markdown", "id": "0b85a5fa-ae87-42d9-8d76-730bd591070c", "metadata": {}, "source": [ "Eine andere Möglichkeit ist es das Paket [`statsmodels`](https://www.statsmodels.org/stable/index.html) und die Funktion `OLS()` zu nutzen, die zusätzlich zur Berechnung von $\\beta_0 , \\beta_1$ viele weitere Möglichkeiten bietet" ] }, { "cell_type": "code", "execution_count": 12, "id": "4076cff7-b0fe-4069-b60a-6f9bbbf52b0c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "const -39.443206\n", "height 0.650762\n", "dtype: float64" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = sm.add_constant(x)\n", "model = sm.OLS(y, x).fit()\n", "\n", "model.params" ] }, { "cell_type": "markdown", "id": "9484e252-e170-4b1c-bd49-f87eb34206a0", "metadata": {}, "source": [ "Die Ausgabe über die Methode `params` liefert den Achsenabschnitt und den Regressionskoeffizienten. Weiters kann die Methode `summary()` nützlich sein, wenn Sie auf andere Eigenschaft des Modellobjekts zugreifen möchten." ] }, { "cell_type": "code", "execution_count": 13, "id": "b7db01e3-f0a1-4207-a7c6-e0afda2c08b7", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/opt/miniconda3/envs/srh/lib/python3.10/site-packages/scipy/stats/_stats_py.py:1477: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=12\n", " warnings.warn(\"kurtosistest only valid for n>=20 ... continuing \"\n" ] }, { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: weight R-squared: 0.921
Model: OLS Adj. R-squared: 0.913
Method: Least Squares F-statistic: 115.9
Date: Sun, 03 Jul 2022 Prob (F-statistic): 8.05e-07
Time: 17:23:34 Log-Likelihood: -22.602
No. Observations: 12 AIC: 49.20
Df Residuals: 10 BIC: 50.17
Df Model: 1
Covariance Type: nonrobust
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
const -39.4432 10.057 -3.922 0.003 -61.851 -17.036
height 0.6508 0.060 10.766 0.000 0.516 0.785
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 2.161 Durbin-Watson: 1.778
Prob(Omnibus): 0.339 Jarque-Bera (JB): 0.923
Skew: 0.110 Prob(JB): 0.630
Kurtosis: 1.659 Cond. No. 3.33e+03


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 3.33e+03. This might indicate that there are
strong multicollinearity or other numerical problems." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: weight R-squared: 0.921\n", "Model: OLS Adj. R-squared: 0.913\n", "Method: Least Squares F-statistic: 115.9\n", "Date: Sun, 03 Jul 2022 Prob (F-statistic): 8.05e-07\n", "Time: 17:23:34 Log-Likelihood: -22.602\n", "No. Observations: 12 AIC: 49.20\n", "Df Residuals: 10 BIC: 50.17\n", "Df Model: 1 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "const -39.4432 10.057 -3.922 0.003 -61.851 -17.036\n", "height 0.6508 0.060 10.766 0.000 0.516 0.785\n", "==============================================================================\n", "Omnibus: 2.161 Durbin-Watson: 1.778\n", "Prob(Omnibus): 0.339 Jarque-Bera (JB): 0.923\n", "Skew: 0.110 Prob(JB): 0.630\n", "Kurtosis: 1.659 Cond. No. 3.33e+03\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 3.33e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.summary()" ] }, { "cell_type": "markdown", "id": "632d922b-3a4e-43dd-8431-1d5e646bbb8b", "metadata": {}, "source": [ "Die Methode `conf_int()` gibt das Konfidenzintervall für die Modellkoeffizienten für ein bestimmtes Konfidenzniveau zurück (Standardeinstellung entspricht $\\alpha = 0,05$." ] }, { "cell_type": "code", "execution_count": 14, "id": "939135c1-ab4b-4821-98a6-98e8b2539ff8", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
\n", "\n", "\n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", " \n", "
01
const-61.850735-17.035678
height0.5160810.785442
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" ], "text/plain": [ " 0 1\n", "const -61.850735 -17.035678\n", "height 0.516081 0.785442" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.conf_int(alpha=0.05)" ] }, { "cell_type": "markdown", "id": "dbdbfc98-7e77-4c5b-b020-74faeb851021", "metadata": {}, "source": [ "Eine weitere nützliche Extraktormethode ist die Funktion `resid()`." ] }, { "cell_type": "code", "execution_count": 15, "id": "ed9bbbcd-ac0c-49a9-ae9f-635364a9bd44", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "339 0.815271\n", "2124 -1.037014\n", "2388 1.218317\n", "2727 -1.527876\n", "2767 -1.035491\n", "3594 1.164509\n", "4152 2.655371\n", "4433 2.072124\n", "5100 -1.038537\n", "7099 -2.438537\n", "7136 0.930501\n", "8170 -1.778637\n", "dtype: float64" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.resid" ] }, { "cell_type": "markdown", "id": "9d053377-a7bd-42b3-ba9c-66af620b980d", "metadata": {}, "source": [ "Wir können sofort überprüfen, ob die Summe der Residuen ($\\sum e$) nahe bei Null liegt." ] }, { "cell_type": "code", "execution_count": 16, "id": "877e46d9-2ff3-4088-bc97-63f096430398", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "-6.394884621840902e-14" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sum(model.resid)" ] }, { "cell_type": "markdown", "id": "f444c319-59ad-41b9-8f2c-bd88781514c4", "metadata": {}, "source": [ "Cool, nahe an Null!\n", "\n", "Um die erhaltene Regressionslinie zu zeichnen, verwenden wir die Funktion $y = \\beta_0 + \\beta_1 x$, die Linien auf der Grundlage des Achsenabschnitts ($\\beta_0$) und der Steigung ($\\beta_1$) zeichnet. Wir verwenden den Syntax `plot([x_1,x_2],[y_1,y_2])` um die Regressionsgerade zu plotten." ] }, { "cell_type": "markdown", "id": "6e52b51e-c554-460f-8869-2093fb04f8b2", "metadata": {}, "source": [ "Eine weitere besonders interessante Extraktormethode ist `predict()`. Wenn sie nicht spezifiziert ist, gibt die Methode `predict()` $\\hat y_i$ für jedes einzelne $x_i$ zurück; ähnlich wie die Methode `fittedvalues`. Man kann jedoch auch neue Daten angeben und die Funktion `predict()` wird $\\hat y_i$ für jedes gegebene $x_i$ vorhersagen. Beachten Sie, dass die neuen Daten ein Data-Frame-Objekt oder eine Liste sein müssen." ] }, { "cell_type": "code", "execution_count": 17, "id": "693b6136-a48a-4ee9-948a-dfae30f47ca9", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "339 69.884729\n", "2124 71.837014\n", "2388 67.281683\n", "2727 64.027876\n", "2767 70.535491\n", "3594 70.535491\n", "4152 78.344629\n", "4433 64.027876\n", "5100 73.138537\n", "7099 73.138537\n", "7136 56.869499\n", "8170 64.678637\n", "dtype: float64\n" ] } ], "source": [ "print(model.predict(x))" ] }, { "cell_type": "code", "execution_count": 18, "id": "087915dd-5471-4430-96d0-d071cd6481bf", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "339 69.884729\n", "2124 71.837014\n", "2388 67.281683\n", "2727 64.027876\n", "2767 70.535491\n", "3594 70.535491\n", "4152 78.344629\n", "4433 64.027876\n", "5100 73.138537\n", "7099 73.138537\n", "7136 56.869499\n", "8170 64.678637\n", "dtype: float64" ] }, "execution_count": 18, "metadata": {}, "output_type": "execute_result" } ], "source": [ "model.fittedvalues" ] }, { "cell_type": "code", "execution_count": 19, "id": "59929ae2-d61e-4c1d-ada1-5058b5702725", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "ax.scatter(data[\"height\"], data[\"weight\"], label=\"Datapoints\")\n", "ax.scatter(data[\"height\"], model.fittedvalues, label=\"Fitted values\")\n", "# create regression line\n", "x_axis = np.linspace(140, 190, 100)\n", "_x_axis = sm.add_constant(x_axis)\n", "ax.plot(x_axis, model.predict(_x_axis))\n", "\n", "ax.set_ylabel(\"Gewicht\")\n", "ax.set_xlabel(\"Körpergrösse\")\n", "ax.legend()" ] }, { "cell_type": "markdown", "id": "7c3d27d6-4201-4a22-becb-176a539cc4bf", "metadata": {}, "source": [ "Darüber hinaus bietet Python einen einfachen Ansatz zur Erstellung von Fehlerbereichen um die angepasste Regressionslinie. Es gibt zwei Arten von Bändern, die als *schmale* und *breite* Bänder bezeichnet werden. Die schmalen Bänder, die so genannten Konfidenzbänder, spiegeln die Unsicherheit über die Linie selbst wider. Die Bänder sind schmal, wenn es viele Beobachtungen gibt, und spiegeln eine gut bestimmte Linie wider. Die breiten Banden, die so genannten Prognosebänder ({cite:t}`Frost2018` s.27), beinhalten die Unsicherheit über zukünftige Beobachtungen. Diese Bänder erfassen die Mehrheit der beobachteten Punkte und fallen nicht zu einer Linie zusammen, wenn die Anzahl der Beobachtungen zunimmt.\n", "\n", "Um diese Unsicherheitsbänder zu berechnen, wenden wir die Methode `get_prediction()` an und fügen die Methode `summary_frame()` hinzu, um den Vektor der vorhergesagten Werte zu erhalten, der mit Grenzwerten ergänzt wird." ] }, { "cell_type": "code", "execution_count": 20, "id": "9ead8b43-89f1-47c6-a292-14df6877ba1a", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pred = np.linspace(140, 190)\n", "pred = sm.add_constant(pred)\n", "model_predictions = model.get_prediction(pred).summary_frame()\n", "\n", "fig, ax = plt.subplots()\n", "ax.scatter(data[\"height\"], data[\"weight\"], label=\"Beobachtungen\")\n", "\n", "# create regression line\n", "x_axis = np.linspace(140, 190)\n", "\n", "ax.plot(x_axis, model_predictions[\"mean\"], label=\"Regressionslinie\")\n", "ax.fill_between(\n", " x_axis,\n", " model_predictions[\"obs_ci_lower\"],\n", " model_predictions[\"obs_ci_upper\"],\n", " alpha=0.1,\n", " label=\"Prognoseinterval\",\n", ")\n", "\n", "ax.fill_between(\n", " x_axis,\n", " model_predictions[\"mean_ci_lower\"],\n", " model_predictions[\"mean_ci_upper\"],\n", " alpha=0.5,\n", " label=\"Konvidenzinterval\",\n", ")\n", "\n", "ax.set_ylabel(\"Gewicht\")\n", "ax.set_xlabel(\"Körpergrösse\")\n", "ax.legend()" ] }, { "cell_type": "markdown", "id": "c03e9984-a1e4-460c-aee2-718ca7d4cd64", "metadata": {}, "source": [ "Es gibt viele weitere Attribute und Methoden eines `OLS`-Objekts auf die zugegriffen werden kann. Die Funktion `dir()` gibt einen Überblick über die Struktur des Modellobjekts." ] }, { "cell_type": "code", "execution_count": 21, "id": "bd3e04b8-dd20-41b2-9870-97c29f52f6c5", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "['HC0_se',\n", " 'HC1_se',\n", " 'HC2_se',\n", " 'HC3_se',\n", " '_HCCM',\n", " '__class__',\n", " '__delattr__',\n", " '__dict__',\n", " '__dir__',\n", " '__doc__',\n", " '__eq__',\n", " '__format__',\n", " '__ge__',\n", " '__getattribute__',\n", " '__gt__',\n", " '__hash__',\n", " '__init__',\n", " '__init_subclass__',\n", " '__le__',\n", " '__lt__',\n", " '__module__',\n", " '__ne__',\n", " '__new__',\n", " '__reduce__',\n", " '__reduce_ex__',\n", " '__repr__',\n", " '__setattr__',\n", " '__sizeof__',\n", " '__str__',\n", " '__subclasshook__',\n", " '__weakref__',\n", " '_abat_diagonal',\n", " '_cache',\n", " '_data_attr',\n", " '_data_in_cache',\n", " '_get_robustcov_results',\n", " '_is_nested',\n", " '_use_t',\n", " '_wexog_singular_values',\n", " 'aic',\n", " 'bic',\n", " 'bse',\n", " 'centered_tss',\n", " 'compare_f_test',\n", " 'compare_lm_test',\n", " 'compare_lr_test',\n", " 'condition_number',\n", " 'conf_int',\n", " 'conf_int_el',\n", " 'cov_HC0',\n", " 'cov_HC1',\n", " 'cov_HC2',\n", " 'cov_HC3',\n", " 'cov_kwds',\n", " 'cov_params',\n", " 'cov_type',\n", " 'df_model',\n", " 'df_resid',\n", " 'diagn',\n", " 'eigenvals',\n", " 'el_test',\n", " 'ess',\n", " 'f_pvalue',\n", " 'f_test',\n", " 'fittedvalues',\n", " 'fvalue',\n", " 'get_influence',\n", " 'get_prediction',\n", " 'get_robustcov_results',\n", " 'info_criteria',\n", " 'initialize',\n", " 'k_constant',\n", " 'llf',\n", " 'load',\n", " 'model',\n", " 'mse_model',\n", " 'mse_resid',\n", " 'mse_total',\n", " 'nobs',\n", " 'normalized_cov_params',\n", " 'outlier_test',\n", " 'params',\n", " 'predict',\n", " 'pvalues',\n", " 'remove_data',\n", " 'resid',\n", " 'resid_pearson',\n", " 'rsquared',\n", " 'rsquared_adj',\n", " 'save',\n", " 'scale',\n", " 'ssr',\n", " 'summary',\n", " 'summary2',\n", " 't_test',\n", " 't_test_pairwise',\n", " 'tvalues',\n", " 'uncentered_tss',\n", " 'use_t',\n", " 'wald_test',\n", " 'wald_test_terms',\n", " 'wresid']" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dir(model)" ] }, { "cell_type": "markdown", "id": "2bd4bc15-1019-44be-9c5c-82b7c9bea457", "metadata": {}, "source": [ "## Modelldiagnose" ] }, { "cell_type": "markdown", "id": "aa240f5d-24ea-46cc-a63e-d913d03e3de7", "metadata": {}, "source": [ "Regressionsdiagnostik beinhaltet eine Reihe von Verfahren, die zur Bewertung der numerischen Ergebnisse einer Regressionsanalyse angewandt werden. Die Verfahren umfassen Methoden der grafischen und quantitativen Analyse oder formale statistische Hypothesentests. In diesem Abschnitt konzentrieren wir uns auf die beiden wichtigsten Methoden, die grafische und die quantitative Analyse. Statistische Hypothesentests für Regressionsprobleme finden Sie im Abschnitt über *Hypothesentests*." ] }, { "cell_type": "markdown", "id": "0333d895-60d5-4348-82d2-2bf8d7e162b2", "metadata": {}, "source": [ "### Bestimmheitsmaß" ] }, { "cell_type": "markdown", "id": "5316e156-381e-4411-b285-7d61523b823f", "metadata": {}, "source": [ "Der Bestimmtheitsmaß, auch als $R^2$ bezeichnet, ist der Anteil der Variation der beobachteten Werte, der durch die Regressionsgleichung erklärt wird. Mit anderen Worten: $R^2$ ist ein statistisches Maß dafür, wie gut die Regressionsgerade die realen Datenpunkte annähert; es ist also ein Maß für die Anpassungsfähigkeit des Modells.\n", "\n", "Die Gesamtvariation der Antwortvariablen $y$\n", "basiert auf der Abweichung jedes beobachteten Wertes $y_i$ vom Mittelwert $\\bar y$. Diese Größe wird als **Gesamtsumme der Quadrate, $SST$**, bezeichnet und ist gegeben durch" ] }, { "cell_type": "markdown", "id": "0f971ad9-d49c-44f7-879a-092cd5e028d4", "metadata": {}, "source": [ "$$SST = \\sum (y_i - \\bar y)^2\\text{.}$$" ] }, { "cell_type": "markdown", "id": "702e4d2d-9fed-41a0-94d4-7c731b8e768a", "metadata": {}, "source": [ "Diese Gesamtsumme der Quadrate ($SST$) kann in zwei Teile zerlegt werden: die durch die Regressionslinie erklärte Abweichung $\\hat y_i- \\bar y$ und die verbleibende unerklärte Abweichung $y_i-\\hat y_i$. Folglich wird der Anteil der Variation, der durch die Regression erklärt wird, als **Summe der Quadrate aufgrund der Regression**, $SSR$, bezeichnet und ist gegeben durch" ] }, { "cell_type": "markdown", "id": "4bc22e06-b5de-4586-8793-2d9542dbc177", "metadata": {}, "source": [ "$$SSR = \\sum (\\hat y_i- \\bar y)^2\\text{.}$$" ] }, { "cell_type": "markdown", "id": "68c4d989-7cac-4346-bc8f-65214750ab48", "metadata": {}, "source": [ "Das Verhältnis zwischen der Summe der Quadrate aufgrund der Regression ($SSR$) und der Gesamtsumme der Quadrate ($SST$) wird als Bestimmtheitsmaß bezeichnet und mit $R^2$ angegeben." ] }, { "cell_type": "markdown", "id": "2dd5c82c-7ef5-458f-8543-a2905f801b8f", "metadata": {}, "source": [ "$$R^2 = \\frac{SSR}{SST}$$" ] }, { "cell_type": "markdown", "id": "89256a2e-1f0a-4cf7-b8cc-1a41354e792a", "metadata": {}, "source": [ "$R^2$ liegt zwischen $0$ und $1$. Ein Wert nahe $0$ deutet darauf hin, dass die Regressionsgleichung nicht in der Lage ist, die Daten zu erklären. Ein $R^2$ von $1$ zeigt an, dass die Regressionsgerade perfekt zu den Daten passt.\n", "\n", "Der Vollständigkeit halber wird die Variation in den beobachteten Werten der Reaktionsvariablen, die nicht durch die Regression erklärt wird, als **Summe der quadrierten Fehler der Vorhersage** ($SSE$) bezeichnet und ist gegeben durch" ] }, { "cell_type": "markdown", "id": "59c86e39-73fc-4d7c-b534-476850860796", "metadata": {}, "source": [ "$$SSE = \\sum (y_i-\\hat y_i)^2\\text{.}$$" ] }, { "cell_type": "markdown", "id": "7575b6b8-cfe2-4bbc-8c4d-018156fb37a9", "metadata": {}, "source": [ "Erinnern Sie sich, dass die $SSE$-Größe minimiert wird, um die beste Regressionslinie zur Beschreibung der Daten zu erhalten, auch bekannt als die Methode der gewöhnlichen kleinsten Quadrate ($OLS$)." ] }, { "cell_type": "markdown", "id": "bf7f91bb-4d86-4cce-9c97-58c7b65fe67c", "metadata": {}, "source": [ "### Die Methode `summary()`" ] }, { "cell_type": "markdown", "id": "386c64bd-dd29-4c70-87ab-f5d6817092ed", "metadata": {}, "source": [ "Eine grundlegendes Mittel für die Regressionsdiagnose in Python ist die Methode `summary()`. Die Funktion `OLS()` gibt ein Modellobjekt zurück. Dieses `OLS()`-Objekt enthält die Modelleigenschaften, die durch Anwendung der Methode `summary()` untersucht werden können.\n", "\n", "Zu Demonstrationszwecken wird dasselbe Modell wie im vorherigen Abschnitt verwendet." ] }, { "cell_type": "code", "execution_count": 22, "id": "f9da9cf2-6282-4a99-b5a1-49a3aac2b751", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/opt/miniconda3/envs/srh/lib/python3.10/site-packages/scipy/stats/_stats_py.py:1477: UserWarning: kurtosistest only valid for n>=20 ... continuing anyway, n=12\n", " warnings.warn(\"kurtosistest only valid for n>=20 ... continuing \"\n" ] }, { "data": { "text/html": [ "\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
OLS Regression Results
Dep. Variable: weight R-squared: 0.921
Model: OLS Adj. R-squared: 0.913
Method: Least Squares F-statistic: 115.9
Date: Sun, 03 Jul 2022 Prob (F-statistic): 8.05e-07
Time: 17:23:35 Log-Likelihood: -22.602
No. Observations: 12 AIC: 49.20
Df Residuals: 10 BIC: 50.17
Df Model: 1
Covariance Type: nonrobust
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
coef std err t P>|t| [0.025 0.975]
const -39.4432 10.057 -3.922 0.003 -61.851 -17.036
height 0.6508 0.060 10.766 0.000 0.516 0.785
\n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "\n", " \n", "\n", "
Omnibus: 2.161 Durbin-Watson: 1.442
Prob(Omnibus): 0.339 Jarque-Bera (JB): 0.923
Skew: 0.110 Prob(JB): 0.630
Kurtosis: 1.659 Cond. No. 3.33e+03


Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 3.33e+03. This might indicate that there are
strong multicollinearity or other numerical problems." ], "text/plain": [ "\n", "\"\"\"\n", " OLS Regression Results \n", "==============================================================================\n", "Dep. Variable: weight R-squared: 0.921\n", "Model: OLS Adj. R-squared: 0.913\n", "Method: Least Squares F-statistic: 115.9\n", "Date: Sun, 03 Jul 2022 Prob (F-statistic): 8.05e-07\n", "Time: 17:23:35 Log-Likelihood: -22.602\n", "No. Observations: 12 AIC: 49.20\n", "Df Residuals: 10 BIC: 50.17\n", "Df Model: 1 \n", "Covariance Type: nonrobust \n", "==============================================================================\n", " coef std err t P>|t| [0.025 0.975]\n", "------------------------------------------------------------------------------\n", "const -39.4432 10.057 -3.922 0.003 -61.851 -17.036\n", "height 0.6508 0.060 10.766 0.000 0.516 0.785\n", "==============================================================================\n", "Omnibus: 2.161 Durbin-Watson: 1.442\n", "Prob(Omnibus): 0.339 Jarque-Bera (JB): 0.923\n", "Skew: 0.110 Prob(JB): 0.630\n", "Kurtosis: 1.659 Cond. No. 3.33e+03\n", "==============================================================================\n", "\n", "Notes:\n", "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n", "[2] The condition number is large, 3.33e+03. This might indicate that there are\n", "strong multicollinearity or other numerical problems.\n", "\"\"\"" ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Lese Datei students.csv als Dataframe ein; Indexspalte wird übersprungen\n", "students = pd.read_csv(\"../../data/students.csv\", index_col=0)\n", "\n", "n = 12\n", "\n", "data = students[[\"height\", \"weight\"]].sample(n, random_state=2)\n", "x = data[\"height\"]\n", "y = data[\"weight\"]\n", "\n", "x = sm.add_constant(x)\n", "model = sm.OLS(y, x).fit()\n", "predictions = model.predict(x) # make the predictions by the model\n", "\n", "# Lese Modellwerte aus\n", "model.summary()" ] }, { "cell_type": "markdown", "id": "4ef94d2d-abca-48cc-800d-c8ce110c376b", "metadata": {}, "source": [ "- Die Ausgabe der Methode `summary()` beginnt mit einer Wiederholung der abhängigen Variable und der angewandten Methode (in diesem Fall $OLS$).\n", "\n", "- Die nächste Zeile zeigt $R^2$, den quadrierten Pearson Korrelationskoeffizienten, auch bekannt als Bestimmtheitsmaß und das angepasste $R^2$, ein statistisches Maß, das für die Merkmalsauswahl bei der Regressionsanalyse mit mehreren Prädiktoren (multiple Regression) verwendet werden kann.\n", "\n", "- Die darauf folgenden Zeilen zeigen die $F$-Statistik, die Anzahl der Beobachtungen (Datenpunkte) und Freiheitsgrade.\n", "\n", "- In den nächsten Zeilen werden der Regressionskoeffizient (unter `height`) und der Achsenabschnitt (unter `const`) angegeben, außerdem für jeden von ihnen der Standardfehler, die $t$-Werte und die $p$-Werte.\n" ] }, { "cell_type": "markdown", "id": "c156b35a-8b36-444d-90e4-1098c3d57986", "metadata": {}, "source": [ "### Diagnostische Plots" ] }, { "cell_type": "markdown", "id": "2e470649-94f6-4918-8920-495fa9525301", "metadata": {}, "source": [ "Es ist wichtig zu wissen, dass Sie eine lineare Regressionsanalyse mit dem Softwarepaket Python oder einer anderen Statistiksoftware durchführen können, die eine Reihe von Zahlen, einschließlich eines $p$-Werts, ergibt, so dass Sie sofort feststellen können, ob die Ergebnisse signifikant waren (oder nicht). Sind wir mit der Angabe der Signifikanz der Ergebnisse fertig?\n", "\n", "Nehmen wir einen sehr berühmten Datensatz, das so genannte Anscombe-Quartett. Das Anscombe-Quartett besteht aus vier Datensätzen und hat die folgende Form:" ] }, { "cell_type": "markdown", "id": "051f8ce9-2e90-4134-8f53-1785c1f9ae8e", "metadata": {}, "source": [ "|||||||||\n", "|--- |--- |--- |--- |--- |--- |--- |--- |\n", "|x1|y1|x2|y2|x3|y3|x4|y4|\n", "|10 |8,04|10|9,14|10|7,46|8|6,58|\n", "|8|6,95|8|8,14|8|6,77|8|5,76|\n", "|13|7,58|13|8,74|13|12,74|8|7,71|\n", "|9|8,81|9|8,77|9|7,11|8|8,84|\n", "|11|8,33|11|9,26|11|7,81|8|8,47|\n", "|14|9,96|14|8,1|14|8,84|8|7,04|\n", "|6|7,24|6|6,13|6|6,08|8|5,25|\n", "|4|4,26|4|3,1|4|5,39|19|12,5|\n", "|12|10,84|12|9,13|12|8,15|8|5,56|\n", "|7|4,82|7|7,26|7|6,42|8|7,91|\n", "|5|5,68|5|4,74|5|5,73|8 |6,89|" ] }, { "cell_type": "markdown", "id": "1c684cc6-ff06-4a7d-8bfe-4db21de377db", "metadata": {}, "source": [ "Das Anscombe-Quartett wird oft verwendet um die Unterschiede zwischen grafischer und statistischer Auswertung hervorzuheben. Wir geben den Datensatz in Python ein." ] }, { "cell_type": "code", "execution_count": 23, "id": "b5eb0faa-2287-46eb-9751-a1da0823e615", "metadata": {}, "outputs": [], "source": [ "x1 = [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5]\n", "y1 = [8.04, 6.95, 7.58, 8.81, 8.33, 9.96, 7.24, 4.26, 10.84, 4.82, 5.68]\n", "\n", "x2 = [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5]\n", "y2 = [9.14, 8.14, 8.74, 8.77, 9.26, 8.10, 6.13, 3.10, 9.13, 7.26, 4.74]\n", "\n", "x3 = [10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5]\n", "y3 = [7.46, 6.77, 12.74, 7.11, 7.81, 8.84, 6.08, 5.39, 8.15, 6.42, 5.73]\n", "\n", "x4 = [8, 8, 8, 8, 8, 8, 8, 19, 8, 8, 8]\n", "y4 = [6.58, 5.76, 7.71, 8.84, 8.47, 7.04, 5.25, 12.50, 5.56, 7.91, 6.89]\n", "\n", "X = [x1, x2, x3, x4]\n", "Y = [y1, y2, y3, y4]" ] }, { "cell_type": "markdown", "id": "0e306425-9c5c-41ed-8e5f-76c1b0b22eca", "metadata": {}, "source": [ "Nun berechnen wir einige deskriptive statistische Maße für jedes der vier $(x,y)$-Paare. Zunächst berechnen wir den Mittelwert für jedes einzelne $x$ und $y$ im Datensatz." ] }, { "cell_type": "code", "execution_count": 24, "id": "9d36aac8-a408-4d8d-99dd-eb0cea41df03", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "mean x1: 9.0 | mean y1: 7.501\n", "mean x2: 9.0 | mean y2: 7.501\n", "mean x3: 9.0 | mean y3: 7.5\n", "mean x4: 9.0 | mean y4: 7.501\n" ] } ], "source": [ "for e, (x, y) in enumerate(zip(X, Y)):\n", " print(f\"mean x{e+1}: {round(np.mean(x),3)} | mean y{e+1}: {round(np.mean(y),3)}\")" ] }, { "cell_type": "markdown", "id": "e57eaf94-1416-4908-be3a-dbaca458f7b4", "metadata": {}, "source": [ "Die Werte stimmen entweder perfekt überein oder liegen sehr nahe beieinander!!\n", "\n", "Jetzt berechnen wir die Varianz jedes $(x,y)$ Paares." ] }, { "cell_type": "code", "execution_count": 25, "id": "ad4f642d-7ab2-456f-bcac-bec044e61d2f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "variance x1: 10.0 | variance y1: 3.752\n", "variance x2: 10.0 | variance y2: 3.752\n", "variance x3: 10.0 | variance y3: 3.748\n", "variance x4: 10.0 | variance y4: 3.748\n" ] } ], "source": [ "for e, (x, y) in enumerate(zip(X, Y)):\n", " print(\n", " f\"variance x{e+1}: {round(np.var(x),3)} | variance y{e+1}: {round(np.var(y),3)}\"\n", " )" ] }, { "cell_type": "markdown", "id": "3c797e41-bba5-48a8-ac30-31153a5a4e07", "metadata": {}, "source": [ "Sie sind zwar nicht exakt gleich, aber definitiv sehr nahe beieinander. Schließlich erstellen wir mit der Funktion `linregress()` ein lineares Modell für jede Teilmenge und berechnen die Koeffizienten des Modells und $R^2$, das Bestimmtheitsmaß." ] }, { "cell_type": "code", "execution_count": 26, "id": "f477c448-6e97-435c-99aa-fa9dd219070f", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1: 0.5x + 3.0, p-value: 0.00217, Pearson correlation coefficient: 0.816, Standard error of the estimated slope: 0.1179\n", "2: 0.5x + 3.0, p-value: 0.00218, Pearson correlation coefficient: 0.816, Standard error of the estimated slope: 0.118\n", "3: 0.5x + 3.0, p-value: 0.00218, Pearson correlation coefficient: 0.816, Standard error of the estimated slope: 0.1179\n", "4: 0.5x + 3.0, p-value: 0.00216, Pearson correlation coefficient: 0.817, Standard error of the estimated slope: 0.1178\n" ] } ], "source": [ "for e, (x, y) in enumerate(zip(X, Y)):\n", " slope, intercept, r_value, p_value, std_err = linregress(x, y)\n", " print(\n", " f\"{e+1}: {round(slope,2)}x + {round(intercept,2)}, p-value: {round(p_value,5)}, Pearson correlation coefficient: {round(r_value,3)}, Standard error of the estimated slope: {round(std_err,4)}\"\n", " )" ] }, { "cell_type": "markdown", "id": "088fcc6a-b3ce-4fb7-8efb-f3ab3d099010", "metadata": {}, "source": [ "Erstaunlich! Sie sind fast identisch! Und jetzt $R^2$:" ] }, { "cell_type": "code", "execution_count": 27, "id": "e33b80f5-4dda-4cc1-8286-584abbcfe413", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "r2: 0.667\n", "r2: 0.666\n", "r2: 0.666\n", "r2: 0.667\n" ] } ], "source": [ "for e, (x, y) in enumerate(zip(X, Y)):\n", " _, _, r_value, _, _ = linregress(x, y)\n", " print(\n", " f\"r2: {round(r_value**2,3)}\",\n", " )" ] }, { "cell_type": "markdown", "id": "7ece7840-8e33-4f86-939a-cd0fde0ee0d3", "metadata": {}, "source": [ "Wow, was für eine Analyse! Wir haben eine Menge verschiedener statistischer Methoden auf die vier Datensätze angewandt, und ehrlich gesagt, sie sehen einander sehr ähnlich.\n", "\n", "Sind wir jetzt mit unserer Analyse fertig? Nein, noch nicht! Egal was wir tun, wir sollten immer überprüfen, ob das Modell für die Daten gut funktioniert. Eine einfache Möglichkeit, dies zu tun, ist die Visualisierung der Daten. Lassen Sie uns den Anscombe-Datensatz einschließlich der Regressionslinie grafisch darstellen." ] }, { "cell_type": "code", "execution_count": 28, "id": "209b807a-38dd-4220-98cc-3a7f38681ad8", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(ncols=2, nrows=2)\n", "ax = np.ravel(ax)\n", "xaxis = np.linspace(0, 20, 100)\n", "for e, (x, y) in enumerate(zip(X, Y)):\n", " slope, intercept, _, _, _ = linregress(x, y)\n", " regline = intercept + slope * xaxis\n", " ax[e].plot(xaxis, regline, color=f\"C{e+1}\")\n", " ax[e].scatter(x, y, color=f\"C{e+1}\")\n", " ax[e].set_title(f\"Anscombe's Datensatz #{e+1}\")\n", " ax[e].text(s=f\"y={round(intercept,2)}+{round(slope,3)}x\", x=1, y=11, size=16)\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "id": "5f6bd4d8-135a-49bb-9f30-381a1690283b", "metadata": { "tags": [] }, "source": [ "Was für eine Überraschung! Das wichtigste Ergebnis der Übung ist die Erkenntnis, dass wir auf viele verschiedene Arten prüfen müssen, ob ein Modell für Daten gut funktioniert. Wir achten auf Regressionsergebnisse wie Steigungskoeffizienten, $p$-Werte oder $R^2$, die uns sagen, wie gut ein Modell die gegebenen Daten darstellt. Das ist jedoch nicht die ganze Geschichte. Wir müssen auch visuelle Diagnosen anwenden. Die visuelle Inspektion hilft bei der Bewertung, ob die Annahmen der linearen Regression erfüllt sind, oder bei der Ermittlung von Ausreißern und/oder statistisch bedeutsame Beobachtungen und so genannten Hebelwerte, die das numerische Ergebnis der Regressionsanalyse beeinflussen." ] }, { "cell_type": "markdown", "id": "1222b921-db3d-4831-aed6-161392789641", "metadata": {}, "source": [ "### Analyse der Residuen" ] }, { "cell_type": "markdown", "id": "4196e517-c69d-4860-9f6a-e512f2ba29d9", "metadata": {}, "source": [ "Ein Residuum eines beobachteten Wertes ist die Differenz zwischen dem beobachteten Wert und dem geschätzten Wert $(y_i- \\hat y_i)$. Es handelt sich um die Residuen, die nach der Anpassung eines Modells an die Daten übrig bleiben. Die **Summe der quadrierten Vorhersagefehler** ($SSE$), auch bekannt als die **Summe der quadrierten Residuen** oder die **Fehlersumme der Quadrate**, ist ein Indikator dafür, wie gut ein Modell die Daten darstellt.\n", "\n", "Wenn die absoluten Residuen, definiert für die Beobachtung $x_i$ als $e_i=y_i- \\hat y_i$ definiert sind, ungewöhnlich groß sind, kann es sein, dass die Beobachtung aus einer anderen Grundgesamtheit stammt oder dass bei der Durchführung oder Aufzeichnung der Beobachtung ein Fehler aufgetreten ist." ] }, { "cell_type": "code", "execution_count": 29, "id": "b1f3e990-785d-4ff0-a6ab-9b895c5a577c", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(ncols=2)\n", "xaxis = np.linspace(0, 20, 100)\n", "colors = [\"C1\", \"C3\"]\n", "for e, (x, y) in enumerate(zip((X[0], X[2]), (Y[0], Y[2]))):\n", " slope, intercept, _, _, _ = linregress(x, y)\n", " regline = intercept + slope * xaxis\n", " ax[e].plot(xaxis, regline, color=colors[e])\n", " ax[e].scatter(x, y, s=90, color=colors[e])\n", " for _x, _y in zip(x, y):\n", " yhat = intercept + slope * _x\n", " ax[e].plot((_x, _x), (_y, yhat), color=\"k\")\n", " ax[e].set_title(f\"Anscombe's Datensatz #{colors[e][1:]}\")\n", "fig.tight_layout()" ] }, { "cell_type": "markdown", "id": "f7280741-d166-4ccf-b49b-1d54454c0cc8", "metadata": {}, "source": [ "Die beiden obigen Diagramme zeigen, dass ein Datenpunkt in Anscombes Datensatz Nr. $3$ (rechtes Diagramm) ein ungewöhnlich großes Residuum aufweist. Ein solcher Datenpunkt erfordert besondere Aufmerksamkeit, da er die Regressionsanalyse beeinflusst. Es gibt keine allgemeingültige Regel, wie mit Ausreißern umzugehen ist, aber je nach den Fachkenntnissen des Forschers kann es Fälle geben, in denen man beschließt, einen solchen Ausreißer aus der Analyse auszuschließen.\n", "\n", "Darüber hinaus können wir die Residuen analysieren, um zu prüfen, ob die Annahmen der linearen Regression erfüllt sind. Regressionsresiduen sollten annähernd normalverteilt sein, d. h. die Regression sollte die Struktur erklären, und was übrig bleibt, sollte nur Rauschen sein, das durch Messfehler oder viele kleine unkorrelierte Faktoren verursacht wird. Die Normalität der Residuen kann grafisch überprüft werden, indem man die Residuen gegen die Werte der Prädiktorvariablen aufträgt. In einem solchen **Residuen-Plot** sollten die Residuen zufällig um $0$ streuen\n", "und die Variation um $0$ sollte gleich sein.\n", "\n", "Vor der Darstellung der Residuen ist es üblich, die Residuen zu standardisieren. Python bietet die Möglichkeit mit `get_influence()` auf die standardisierten Residuen zuzugreifen (`influence = model.get_influence()\n", "` und `standardized_residuals = influence.resid_studentized_internal`) und alternativ kann man mit `stud_res = model.outlier_test()` die studentisierten Residuen ({cite:t}`fahrmeirstatistik` s.152) berechnen.\n", "\n", "Wenn die Annahmen für Regressionsschlussfolgerungen erfüllt sind, sollten die folgenden zwei Bedingungen gelten ({cite:t}`fahrmeirstatistik` s.443):\n", "- Eine Darstellung der Residuen (Residuenplot) gegen die Werte der Prädiktorvariablen sollte ungefähr in ein horizontales Band fallen, das um die $x$-Achse zentriert und symmetrisch ist.\n", "\n", "- Eine Normalwahrscheinlichkeitsdarstellung der Residuen sollte in etwa linear sein." ] }, { "cell_type": "code", "execution_count": 30, "id": "a26dfe01-c25f-4f12-9204-b499d4a0d2f5", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "n = 200\n", "toy_x = np.random.uniform(-100, 100, n)\n", "toy1_y = 5 * toy_x + np.random.normal(0, 25, n)\n", "toy2_y = toy_x**2 + np.random.normal(0, 25**2, n)\n", "eps = 100 + 5 * (toy_x) ** 2\n", "toy3_y = 4 * np.abs(toy_x) + np.random.normal(25, eps, n)\n", "\n", "toys = [toy1_y, toy2_y, toy3_y]\n", "titles = [\n", " \"Keine Verletzung\",\n", " \"Verletzung der Linearität\",\n", " \"Verletzung der konstanten Standardabweichung (Heteroskedastizität)\",\n", "]\n", "x = sm.add_constant(toy_x)\n", "\n", "fig, ax = plt.subplots(nrows=len(toys))\n", "for e, toy in enumerate(toys):\n", "\n", " _model = sm.OLS(toy, toy_x).fit()\n", " influence = _model.get_influence()\n", " standardized_residuals = influence.resid_studentized_internal\n", "\n", " ax[e].scatter(toy_x, standardized_residuals)\n", " ax[e].set_title(titles[e])\n", " ax[e].set_xticks([])\n", " ax[e].set_ylim(-4.5, 4.5)\n", " ax[e].axhline(0, color=\"k\")\n", "fig.tight_layout()\n", "fig.suptitle(\"Residuen-Plots\", size=28)\n", "fig.subplots_adjust(top=0.85)" ] }, { "cell_type": "markdown", "id": "a3a95790-a7d3-4c17-9213-bbe6619fa3ad", "metadata": {}, "source": [ "Nur in der obersten Grafik sind die Residuen relativ gut um den Nullpunkt verteilt, während dies in den beiden unteren Grafiken nicht der Fall ist, was darauf hindeutet, dass die linearen Modellannahmen für dieses Modell nicht erfüllt sind." ] }, { "cell_type": "code", "execution_count": 31, "id": "bafcfdd4-4644-4adb-8d57-1755a6964b3b", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "toys = [toy1_y, toy2_y, toy3_y]\n", "titles = [\n", " \"Keine Verletzung\",\n", " \"Verletzung der Linearität\",\n", " \"Heteroskedastizität\",\n", "]\n", "fig, ax = plt.subplots(ncols=len(toys))\n", "for e, toy in enumerate(toys):\n", " _model = sm.OLS(toy, toy_x).fit()\n", " influence = _model.get_influence()\n", " standardized_residuals = influence.resid_studentized_internal\n", " sm.qqplot(standardized_residuals, line=\"s\", ax=ax[e])\n", " ax[e].set_title(titles[e])\n", "\n", "fig.tight_layout()\n", "fig.suptitle(\"Q-Q-Diagramm\", size=28)\n", "fig.subplots_adjust(top=0.85)" ] }, { "cell_type": "markdown", "id": "3874a8c0-a216-4d9f-a1a6-47546c85d405", "metadata": {}, "source": [ "Die Normalwahrscheinlichkeitsdiagramme, die oft als Q-Q-Diagramme bezeichnet werden, zeigen, dass nur im linken Diagramm die Datenpunkte in etwa auf eine gerade Linie fallen. Dies ist bei den anderen Diagrammen nicht der Fall, was darauf hindeutet, dass die Annahmen des linearen Modells nicht erfüllt sind." ] }, { "cell_type": "markdown", "id": "61bf77ee-3995-47e1-8a1d-311228df09e8", "metadata": {}, "source": [ "### Ausreißer und einflußreiche Beobachtungen" ] }, { "cell_type": "markdown", "id": "66228652-5d20-42bf-b4dd-266bf0afcc99", "metadata": {}, "source": [ "**Ausreißer** sind Punkte, die aus der Wolke der Datenpunkte herausfallen. Ausreißer, die horizontal von der Mitte der Wolke wegfallen und die Neigung der Regressionslinie nicht beeinflussen, werden als **Leverage-Werte** (Hebelwerte) bezeichnet. Ausreißer, die die Steigung der Regressionsgeraden tatsächlich beeinflussen, werden als **einflußreiche Beobachtungen** bezeichnet, bei denen es sich in der Regel um hohe Leverage-Punkte handelt.\n", "\n", "Wir wollen einen Beispielsdatensatz erstellen, um das Konzept der statistisch bedeutsamen Beobachtungen zu untersuchen." ] }, { "cell_type": "code", "execution_count": 32, "id": "13e9731d-8b89-4239-967f-a7214c114014", "metadata": { "tags": [ "hide-input" ] }, "outputs": [ { "data": { "text/plain": [ "(-1.65, 12.65, -23.52561113057294, 125.83725556438257)" ] }, "execution_count": 32, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "np.random.seed(110) # seede zufallswerte\n", "\n", "# Erzeuge Zufallswerte\n", "n = 100\n", "beta0 = 5\n", "beta1 = 2.5\n", "\n", "x = np.random.uniform(0, 10, n)\n", "y = beta0 + beta1 * x + np.random.normal(loc=0, scale=12, size=n) # add random noise\n", "\n", "# Erzeuge Hebelwerte\n", "n_lev = math.floor(n * 0.05)\n", "x_lev = np.random.uniform(0, 8, n_lev)\n", "y_lev = (\n", " beta0**1.5 + beta1**3 * x_lev + np.random.normal(loc=0, scale=12, size=n_lev)\n", ") # add random noise\n", "\n", "# Erzeuge einflußreiche Beobachtungen\n", "n_inf = math.floor(n * 0.02)\n", "x_inf = np.random.uniform(10, 15, n_inf)\n", "y_inf = beta0 + beta1**2.5 * x_inf + np.random.normal(loc=0, scale=12, size=n_inf)\n", "\n", "\n", "# Baue Datensätze\n", "x_full = np.hstack([x, x_inf, x_lev])\n", "y_full = np.hstack([y, y_inf, y_lev])\n", "\n", "# Fitte lineares Modell\n", "base_model = sm.OLS(y, sm.add_constant(x)).fit()\n", "lev_model = sm.OLS(np.hstack([y, y_lev]), sm.add_constant(np.hstack([x, x_lev]))).fit()\n", "inf_model = sm.OLS(np.hstack([y, y_inf]), sm.add_constant(np.hstack([x, x_inf]))).fit()\n", "full_model = sm.OLS(y_full, sm.add_constant(x_full)).fit()\n", "\n", "\n", "fig, ax = plt.subplots()\n", "ax.scatter(x, y, label=\"Datenpunkte ohne Ausreisser\")\n", "ax.scatter(x_lev, y_lev, label=\"Hebelpunkte\")\n", "ax.scatter(x_inf, y_inf, label=\"Aussreisser mit Einfluss\")\n", "\n", "xaxis = np.linspace(-1, 12, 100)\n", "for _model in [base_model, lev_model, inf_model]:\n", " pred = _model.predict(sm.add_constant(xaxis))\n", " plt.plot(xaxis, pred, linestyle=\"dashed\")\n", "pred_full = full_model.predict(sm.add_constant(xaxis))\n", "plt.plot(xaxis, pred_full)\n", "ax.legend()\n", "ax.axis(\"off\")" ] }, { "cell_type": "markdown", "id": "2bc5dad4-36a7-4f4c-8acf-e43c2ad6a3a4", "metadata": {}, "source": [ "Die obige Abbildung zeigt deutlich die Auswirkungen der verschiedenen Arten von Ausreißern. Die blaue gestrichelte Linie zeigt die Regressionslinie ohne Ausreißer, die orange gestrichelte Linie zeigt die Regressionslinie, wenn die orangen Hebelpunkte enthalten sind, die grüne gestrichelte Linie zeigt die Regressionslinie, wenn die grünen Ausreisser enthalten sind, und die rote Linie zeigt die Regressionslinie, wenn alle Daten enthalten sind. Offensichtlich haben die grünen Punkte den größten Einfluss auf die Steigung der Regressionslinie!" ] }, { "cell_type": "markdown", "id": "4631f618-1e08-4a06-88b1-8f72eb371d0f", "metadata": {}, "source": [ "#### Leverage" ] }, { "cell_type": "markdown", "id": "b380d0e8-15f2-4a20-a899-87e03b8f404c", "metadata": {}, "source": [ "Die Leverage einer Beobachtung zeigt an, ob sie das Regressionsmodell beeinflussen kann. Diese Beobachtungen sind nicht notwendigerweise ein Fehler, aber sie sollten identifiziert und überprüft werden. Die Leverage wird durch den **$H$-Wert** gemessen, der den Gesamteinfluss einer einzelnen Beobachtung auf die Modellvorhersagen misst. Der $H$-Wert nimmt Werte zwischen $0$ und $1$ an. Ein Punkt mit einer Hebelwirkung von Null hat keinen Einfluss auf das Regressionsmodell. Je höher der $H$-Wert ist, desto größer ist der Einfluss des betreffenden Punktes auf das Regressionsmodell.\n" ] }, { "cell_type": "markdown", "id": "347d55f7-06d6-47fb-afcb-a3fee74f3e46", "metadata": { "tags": [] }, "source": [ "#### Cook-Abstand" ] }, { "cell_type": "markdown", "id": "1ba2128f-24f0-4321-9f94-cd7d67307def", "metadata": {}, "source": [ "Eine weitere Methode zur Erfassung einflussreicher Ausreißer ist der Cook-Abstand. Das Maß ist eine Kombination aus Leverage und Residuen der einzelnen Beobachtungen. Je höher die Hebelwirkung und der Rückstand, desto größer ist der Cook-Abstand. Normalerweise werden Punkte mit einem Cook-Abstand von mehr als $1$ als einflussreich eingestuft. In Python wird der Cook-Abstand mit dem Attribut `cooks.distance` berechnet." ] }, { "cell_type": "markdown", "id": "a349c78a-e067-4115-8aa1-7b65b2ace4c0", "metadata": {}, "source": [ "#### Andere nützliche Regressionsdiagnosen" ] }, { "cell_type": "markdown", "id": "c80dc3be-4b2e-4d20-a15c-437631e30266", "metadata": {}, "source": [ "Weitere nützliche Werkzeuge für die Regressionsanalysediagnose sind DFFITS (\"difference in fit(s)\"), die angibt, wie sehr eine Beobachtung den zugehörigen angepassten Wert beeinflusst, und die DFBETAS, die die Änderung der geschätzten Parameter angibt, wenn eine Beobachtung im Verhältnis zu ihrem Standardfehler ausgeschlossen wird." ] }, { "cell_type": "markdown", "id": "ca4f5d9a-b487-4056-a229-5a525ea93a1f", "metadata": {}, "source": [ "In Paket statsmodels kann auf diese die genanten und weitere diagnostische Verfahren sehr leicht über die Methdode `get_influence().summary_frame()`zurückgegriffen werden. " ] }, { "cell_type": "code", "execution_count": 33, "id": "837fd749-8598-4209-84c3-a5bdc77d79df", "metadata": {}, "outputs": [ { "data": { "text/html": [ "
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dfb_constdfb_x1cooks_dstandard_residhat_diagdffits_internalstudent_residdffits
17-0.008556-0.0066830.000378-0.2745030.009938-0.027502-0.273291-0.027380
5-0.0002630.0096730.0001580.1526580.0133450.0177540.1519460.017671
190.066637-0.0220270.0042800.9248060.0099080.0925150.9241630.092451
86-0.0758900.0314100.004754-0.9498550.010429-0.097511-0.949408-0.097465
390.003107-0.0020120.0000060.0271350.0148130.0033270.0270060.003311
820.023955-0.0918900.009254-1.0289800.017179-0.136041-1.029271-0.136080
210.027092-0.0976690.010127-1.0618360.017647-0.142317-1.062488-0.142404
360.040591-0.0334270.0008330.2363720.0289420.0408070.2353060.040623
64-0.0689530.0233270.004514-0.9480470.009946-0.095021-0.947586-0.094975
690.009371-0.0063110.0000490.0778620.0158720.0098880.0774930.009841
470.039709-0.0285730.0008390.2995740.0183540.0409630.2982720.040785
130.125702-0.1055630.0079400.6964750.0317010.1260180.6947570.125708
\n", "
" ], "text/plain": [ " dfb_const dfb_x1 cooks_d standard_resid hat_diag dffits_internal \\\n", "17 -0.008556 -0.006683 0.000378 -0.274503 0.009938 -0.027502 \n", "5 -0.000263 0.009673 0.000158 0.152658 0.013345 0.017754 \n", "19 0.066637 -0.022027 0.004280 0.924806 0.009908 0.092515 \n", "86 -0.075890 0.031410 0.004754 -0.949855 0.010429 -0.097511 \n", "39 0.003107 -0.002012 0.000006 0.027135 0.014813 0.003327 \n", "82 0.023955 -0.091890 0.009254 -1.028980 0.017179 -0.136041 \n", "21 0.027092 -0.097669 0.010127 -1.061836 0.017647 -0.142317 \n", "36 0.040591 -0.033427 0.000833 0.236372 0.028942 0.040807 \n", "64 -0.068953 0.023327 0.004514 -0.948047 0.009946 -0.095021 \n", "69 0.009371 -0.006311 0.000049 0.077862 0.015872 0.009888 \n", "47 0.039709 -0.028573 0.000839 0.299574 0.018354 0.040963 \n", "13 0.125702 -0.105563 0.007940 0.696475 0.031701 0.126018 \n", "\n", " student_resid dffits \n", "17 -0.273291 -0.027380 \n", "5 0.151946 0.017671 \n", "19 0.924163 0.092451 \n", "86 -0.949408 -0.097465 \n", "39 0.027006 0.003311 \n", "82 -1.029271 -0.136080 \n", "21 -1.062488 -0.142404 \n", "36 0.235306 0.040623 \n", "64 -0.947586 -0.094975 \n", "69 0.077493 0.009841 \n", "47 0.298272 0.040785 \n", "13 0.694757 0.125708 " ] }, "execution_count": 33, "metadata": {}, "output_type": "execute_result" } ], "source": [ "full_model.get_influence().summary_frame().sample(12)" ] }, { "cell_type": "markdown", "id": "2e6dc3ac-6350-4fef-8890-d6ef3c0b1879", "metadata": {}, "source": [ "Ebenso stehen Visualisierungsmethoden zur Auswahl." ] }, { "cell_type": "code", "execution_count": 34, "id": "4281e6e5-6035-4a8b-8230-c6f9fe4e3aa9", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "_ = sm.graphics.influence_plot(full_model, criterion=\"cooks\")" ] }, { "cell_type": "code", "execution_count": 35, "id": "f3bed7c7-25ae-4a3c-ad7c-80d1eeaea2b3", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
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