Notebooks from applied-cs/data-science@e451096c

38e33102 · Christof Kaufmann · b88d83ec · 38e33102 · 38e33102 · 38e33102
Commit 38e33102 authored 1 year ago by Christof Kaufmann
--- a/08-korrelation-und-dimensionsreduktion/01-kovarianz-sol.ipynb
+++ b/08-korrelation-und-dimensionsreduktion/01-kovarianz-sol.ipynb
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Kovarianz\n",
+    "\n",
+    "## Berechnen\n",
+    "\n",
+    "Schreiben Sie eine Funktion `cov`, die zwei Arrays `x` und `y` erhält\n",
+    "und die Kovarianz zurück gibt."
+   ],
+   "id": "0002-0913d59b142f97e01b1f1d202696d848ab5b6e755f3d92df06ee693365f"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "style": "python"
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import pandas as pd"
+   ],
+   "id": "0003-a69527b239a033f8134e8f47e334b1f9486b9076b43570d3fc203164ed0"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Lösung\n",
+    "\n",
+    "Wir ermitteln zunächst die zentrierten x und y-Werte. Dann\n",
+    "multiplizieren wir sie und bilden den Mittelwert."
+   ],
+   "id": "0005-016214def42f652d79a75899e99541de5f9661c91938dffca7490fcc347"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "style": "python"
+   },
+   "outputs": [],
+   "source": [
+    "def cov(x, y):\n",
+    "    x0 = x - np.mean(x)\n",
+    "    y0 = y - np.mean(y)\n",
+    "    return np.mean(x0 * y0)"
+   ],
+   "id": "0006-fadbee38c18d669a38b12077868f7669a98636383c5eb499c50a3a57b9d"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Tests\n",
+    "\n",
+    "Testen Sie die Funktion mit den Beispielen aus den Folien:"
+   ],
+   "id": "0008-1839d17e4e89b5f286b8ba411595b6eadeed6664573c0cae88cf6869b85"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": [
+      "54.875"
+     ]
+    }
+   ],
+   "source": [
+    "df1 = pd.DataFrame({'x': [10, 7, 5, -13, -8, -3, -1, 11], 'y': [8, 10, 3, -9, -1, -7, -1, 13]})\n",
+    "df2 = df1 * [1, -1]\n",
+    "df3 = pd.DataFrame({'x': [14, 10, 4, 2, -1, -1, -9, -11], 'y': [3, 0, 10, -9, 13, -6, 7, -2]})\n",
+    "cov(df1.x, df1.y)"
+   ],
+   "id": "0009-5a9afeeb069c9adcfd985dfa866647c55d0b7afa511f1ab88ce0e3feda9"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": [
+      "-54.875"
+     ]
+    }
+   ],
+   "source": [
+    "cov(df2.x, df2.y)"
+   ],
+   "id": "0010-bcaedf82ed0c414209d4e126ee2fd2013a7f1cd96fb948355bf543c2ce7"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": [
+      "0.0"
+     ]
+    }
+   ],
+   "source": [
+    "cov(df3.x, df3.y)"
+   ],
+   "id": "0011-5530793defbb6ce07fafad4901e5575defa5e0894f0d8b8d206ff56113e"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Erzeugen\n",
+    "\n",
+    "So weit, so gut. Nun drehen wir die Aufgabenstellung um. Versuchen Sie\n",
+    "nun drei Datensätze aus jeweils zwei Samples zu erzeugen:\n",
+    "\n",
+    "**Datensatz 1** soll als Kovarianz 1 besitzen.\n",
+    "\n",
+    "### Lösung\n",
+    "\n",
+    "Ein einfaches Beispiel für zwei Samples mit Kovarianz 1 wäre (0, 0), (2,\n",
+    "2). Der Mittelwert ist (1, 1), somit rechnen wir\n",
+    "$\\frac 1 2 (1 \\cdot 1 + 1 \\cdot 1) = 1$."
+   ],
+   "id": "0016-76dfc0cb6810a254ca36daaf0b86fc5e15a5c807be4f17adf9ff053cfb6"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x = np.array([0, 2])\n",
+    "y = np.array([0, 2])"
+   ],
+   "id": "0017-98190ce71c2abdc19eb7d8ac4354319f0d6acd8d42d0877945777483cda"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Tests"
+   ],
+   "id": "0018-04ac3f4882b3309363456c952768f31a2c708e671a5462093ff68e76a76"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": [
+      "1.0"
+     ]
+    }
+   ],
+   "source": [
+    "cov(x, y)"
+   ],
+   "id": "0019-3ebb3905554befd6e9c90a8161f00000757c58b10e4f248e60f7e1abf9e"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Datensatz 2** soll auch als Kovarianz 1 besitzen, aber mit anderen\n",
+    "Samples als zuvor.\n",
+    "\n",
+    "### Lösung\n",
+    "\n",
+    "Aber die Samples müssen dafür keine Diagonale bilden (Quadrate), sondern\n",
+    "können auch anders liegen (Rechtecke). Wir wählen (0, 0), (1, 4). Der\n",
+    "Mittelwert ist (1, 1), somit rechnen wir\n",
+    "$\\frac 1 2 (\\frac 1 2 \\cdot 2 + \\frac 1 2 \\cdot 2) = 1$."
+   ],
+   "id": "0022-90b5a593898934ee35ed76b5e931784de71996d0e0bf7d5a659d58ea41a"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x = np.array([0, 1])\n",
+    "y = np.array([0, 4])"
+   ],
+   "id": "0023-9ec0433f3ab4acfa7459dc2d56714459dbcbd9078ce19baf91ffb8aa17d"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Tests"
+   ],
+   "id": "0024-503fa0c97971fa858f825b273ceb998780354d5bb183c47acfd4f3507cf"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": [
+      "1.0"
+     ]
+    }
+   ],
+   "source": [
+    "cov(x, y)"
+   ],
+   "id": "0025-3ebb3905554befd6e9c90a8161f00000757c58b10e4f248e60f7e1abf9e"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Datensatz 3** soll als Kovarianz 4 besitzen.\n",
+    "\n",
+    "### Lösung\n",
+    "\n",
+    "Wenn wir die Werte im ersten Beispiel verdoppeln, vervierfacht sich das\n",
+    "Ergebnis. Mit (0, 0), (4, 4) ist die Kovarianz\n",
+    "$\\frac 1 2 (2 \\cdot 2 + 2 \\cdot 2) = 4$."
+   ],
+   "id": "0028-338b5930bf4bafa415d05676a139dfbe8cbce3d950085861e1a4061aa8b"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x = np.array([0, 4])\n",
+    "y = np.array([0, 4])"
+   ],
+   "id": "0029-402124921fd7c721bfaa138f25c8d143eb13fe2aa271ad7473b7126b0ab"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Tests"
+   ],
+   "id": "0030-c36e6e0be7ad3f1dec0afd72fde3a265396ca90bf93c258dbd4e3346cbd"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": [
+      "4.0"
+     ]
+    }
+   ],
+   "source": [
+    "cov(x, y)"
+   ],
+   "id": "0031-3ebb3905554befd6e9c90a8161f00000757c58b10e4f248e60f7e1abf9e"
+  }
+ ],
+ "nbformat": 4,
+ "nbformat_minor": 5,
+ "metadata": {}
+}
+%% Cell type:markdown id:0002-0913d59b142f97e01b1f1d202696d848ab5b6e755f3d92df06ee693365f tags:
+
+# Kovarianz
+
+## Berechnen
+
+Schreiben Sie eine Funktion `cov`, die zwei Arrays `x` und `y` erhält
+und die Kovarianz zurück gibt.
+
+%% Cell type:code id:0003-a69527b239a033f8134e8f47e334b1f9486b9076b43570d3fc203164ed0 tags:
+
+``` 
+import numpy as np
+import pandas as pd
+```
+
+%% Cell type:markdown id:0005-016214def42f652d79a75899e99541de5f9661c91938dffca7490fcc347 tags:
+
+### Lösung
+
+Wir ermitteln zunächst die zentrierten x und y-Werte. Dann
+multiplizieren wir sie und bilden den Mittelwert.
+
+%% Cell type:code id:0006-fadbee38c18d669a38b12077868f7669a98636383c5eb499c50a3a57b9d tags:
+
+``` 
+def cov(x, y):
+    x0 = x - np.mean(x)
+    y0 = y - np.mean(y)
+    return np.mean(x0 * y0)
+```
+
+%% Cell type:markdown id:0008-1839d17e4e89b5f286b8ba411595b6eadeed6664573c0cae88cf6869b85 tags:
+
+### Tests
+
+Testen Sie die Funktion mit den Beispielen aus den Folien:
+
+%% Cell type:code id:0009-5a9afeeb069c9adcfd985dfa866647c55d0b7afa511f1ab88ce0e3feda9 tags:
+
+``` 
+df1 = pd.DataFrame({'x': [10, 7, 5, -13, -8, -3, -1, 11], 'y': [8, 10, 3, -9, -1, -7, -1, 13]})
+df2 = df1 * [1, -1]
+df3 = pd.DataFrame({'x': [14, 10, 4, 2, -1, -1, -9, -11], 'y': [3, 0, 10, -9, 13, -6, 7, -2]})
+cov(df1.x, df1.y)
+```
+
+%% Output
+
+    54.875
+
+%% Cell type:code id:0010-bcaedf82ed0c414209d4e126ee2fd2013a7f1cd96fb948355bf543c2ce7 tags:
+
+``` 
+cov(df2.x, df2.y)
+```
+
+%% Output
+
+    -54.875
+
+%% Cell type:code id:0011-5530793defbb6ce07fafad4901e5575defa5e0894f0d8b8d206ff56113e tags:
+
+``` 
+cov(df3.x, df3.y)
+```
+
+%% Output
+
+    0.0
+
+%% Cell type:markdown id:0016-76dfc0cb6810a254ca36daaf0b86fc5e15a5c807be4f17adf9ff053cfb6 tags:
+
+## Erzeugen
+
+So weit, so gut. Nun drehen wir die Aufgabenstellung um. Versuchen Sie
+nun drei Datensätze aus jeweils zwei Samples zu erzeugen:
+
+**Datensatz 1** soll als Kovarianz 1 besitzen.
+
+### Lösung
+
+Ein einfaches Beispiel für zwei Samples mit Kovarianz 1 wäre (0, 0), (2,
+2). Der Mittelwert ist (1, 1), somit rechnen wir
+$\frac 1 2 (1 \cdot 1 + 1 \cdot 1) = 1$.
+
+%% Cell type:code id:0017-98190ce71c2abdc19eb7d8ac4354319f0d6acd8d42d0877945777483cda tags:
+
+``` 
+x = np.array([0, 2])
+y = np.array([0, 2])
+```
+
+%% Cell type:markdown id:0018-04ac3f4882b3309363456c952768f31a2c708e671a5462093ff68e76a76 tags:
+
+### Tests
+
+%% Cell type:code id:0019-3ebb3905554befd6e9c90a8161f00000757c58b10e4f248e60f7e1abf9e tags:
+
+``` 
+cov(x, y)
+```
+
+%% Output
+
+    1.0
+
+%% Cell type:markdown id:0022-90b5a593898934ee35ed76b5e931784de71996d0e0bf7d5a659d58ea41a tags:
+
+**Datensatz 2** soll auch als Kovarianz 1 besitzen, aber mit anderen
+Samples als zuvor.
+
+### Lösung
+
+Aber die Samples müssen dafür keine Diagonale bilden (Quadrate), sondern
+können auch anders liegen (Rechtecke). Wir wählen (0, 0), (1, 4). Der
+Mittelwert ist (1, 1), somit rechnen wir
+$\frac 1 2 (\frac 1 2 \cdot 2 + \frac 1 2 \cdot 2) = 1$.
+
+%% Cell type:code id:0023-9ec0433f3ab4acfa7459dc2d56714459dbcbd9078ce19baf91ffb8aa17d tags:
+
+``` 
+x = np.array([0, 1])
+y = np.array([0, 4])
+```
+
+%% Cell type:markdown id:0024-503fa0c97971fa858f825b273ceb998780354d5bb183c47acfd4f3507cf tags:
+
+### Tests
+
+%% Cell type:code id:0025-3ebb3905554befd6e9c90a8161f00000757c58b10e4f248e60f7e1abf9e tags:
+
+``` 
+cov(x, y)
+```
+
+%% Output
+
+    1.0
+
+%% Cell type:markdown id:0028-338b5930bf4bafa415d05676a139dfbe8cbce3d950085861e1a4061aa8b tags:
+
+**Datensatz 3** soll als Kovarianz 4 besitzen.
+
+### Lösung
+
+Wenn wir die Werte im ersten Beispiel verdoppeln, vervierfacht sich das
+Ergebnis. Mit (0, 0), (4, 4) ist die Kovarianz
+$\frac 1 2 (2 \cdot 2 + 2 \cdot 2) = 4$.
+
+%% Cell type:code id:0029-402124921fd7c721bfaa138f25c8d143eb13fe2aa271ad7473b7126b0ab tags:
+
+``` 
+x = np.array([0, 4])
+y = np.array([0, 4])
+```
+
+%% Cell type:markdown id:0030-c36e6e0be7ad3f1dec0afd72fde3a265396ca90bf93c258dbd4e3346cbd tags:
+
+### Tests
+
+%% Cell type:code id:0031-3ebb3905554befd6e9c90a8161f00000757c58b10e4f248e60f7e1abf9e tags:
+
+``` 
+cov(x, y)
+```
+
+%% Output
+
+    4.0
--- a/08-korrelation-und-dimensionsreduktion/01-kovarianz.ipynb
+++ b/08-korrelation-und-dimensionsreduktion/01-kovarianz.ipynb
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Kovarianz\n",
+    "\n",
+    "## Berechnen\n",
+    "\n",
+    "Schreiben Sie eine Funktion `cov`, die zwei Arrays `x` und `y` erhält\n",
+    "und die Kovarianz zurück gibt."
+   ],
+   "id": "0002-0913d59b142f97e01b1f1d202696d848ab5b6e755f3d92df06ee693365f"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "style": "python"
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import pandas as pd"
+   ],
+   "id": "0003-a69527b239a033f8134e8f47e334b1f9486b9076b43570d3fc203164ed0"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Tests\n",
+    "\n",
+    "Testen Sie die Funktion mit den Beispielen aus den Folien:"
+   ],
+   "id": "0005-1839d17e4e89b5f286b8ba411595b6eadeed6664573c0cae88cf6869b85"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": [
+      "54.875"
+     ]
+    }
+   ],
+   "source": [
+    "df1 = pd.DataFrame({'x': [10, 7, 5, -13, -8, -3, -1, 11], 'y': [8, 10, 3, -9, -1, -7, -1, 13]})\n",
+    "df2 = df1 * [1, -1]\n",
+    "df3 = pd.DataFrame({'x': [14, 10, 4, 2, -1, -1, -9, -11], 'y': [3, 0, 10, -9, 13, -6, 7, -2]})\n",
+    "cov(df1.x, df1.y)"
+   ],
+   "id": "0006-5a9afeeb069c9adcfd985dfa866647c55d0b7afa511f1ab88ce0e3feda9"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": [
+      "-54.875"
+     ]
+    }
+   ],
+   "source": [
+    "cov(df2.x, df2.y)"
+   ],
+   "id": "0007-bcaedf82ed0c414209d4e126ee2fd2013a7f1cd96fb948355bf543c2ce7"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": [
+      "0.0"
+     ]
+    }
+   ],
+   "source": [
+    "cov(df3.x, df3.y)"
+   ],
+   "id": "0008-5530793defbb6ce07fafad4901e5575defa5e0894f0d8b8d206ff56113e"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Erzeugen\n",
+    "\n",
+    "So weit, so gut. Nun drehen wir die Aufgabenstellung um. Versuchen Sie\n",
+    "nun drei Datensätze aus jeweils zwei Samples zu erzeugen:\n",
+    "\n",
+    "**Datensatz 1** soll als Kovarianz 1 besitzen."
+   ],
+   "id": "0011-5e6f7ee8c09fb3163c75c37ab167a849116ef4505076b2442a9a3e7eb1b"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x = np.array([])\n",
+    "y = np.array([])"
+   ],
+   "id": "0012-1b4ea8eec5f19241e7602ee09cf19927687efc9d38c7d5360c417d2d3ba"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Tests"
+   ],
+   "id": "0013-04ac3f4882b3309363456c952768f31a2c708e671a5462093ff68e76a76"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": [
+      "1.0"
+     ]
+    }
+   ],
+   "source": [
+    "cov(x, y)"
+   ],
+   "id": "0014-3ebb3905554befd6e9c90a8161f00000757c58b10e4f248e60f7e1abf9e"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Datensatz 2** soll auch als Kovarianz 1 besitzen, aber mit anderen\n",
+    "Samples als zuvor."
+   ],
+   "id": "0015-3dbc650c0d3e7b7d38c1256a7a2dc71a13e88a5206c4e416af544e2b775"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x = np.array([])\n",
+    "y = np.array([])"
+   ],
+   "id": "0016-1b4ea8eec5f19241e7602ee09cf19927687efc9d38c7d5360c417d2d3ba"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Tests"
+   ],
+   "id": "0017-503fa0c97971fa858f825b273ceb998780354d5bb183c47acfd4f3507cf"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": [
+      "1.0"
+     ]
+    }
+   ],
+   "source": [
+    "cov(x, y)"
+   ],
+   "id": "0018-3ebb3905554befd6e9c90a8161f00000757c58b10e4f248e60f7e1abf9e"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "**Datensatz 3** soll als Kovarianz 4 besitzen."
+   ],
+   "id": "0019-257f544a893b080f910b0568abdb73110977708806fc07ff2bca207ef7e"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x = np.array([])\n",
+    "y = np.array([])"
+   ],
+   "id": "0020-1b4ea8eec5f19241e7602ee09cf19927687efc9d38c7d5360c417d2d3ba"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "### Tests"
+   ],
+   "id": "0021-c36e6e0be7ad3f1dec0afd72fde3a265396ca90bf93c258dbd4e3346cbd"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": [
+      "4.0"
+     ]
+    }
+   ],
+   "source": [
+    "cov(x, y)"
+   ],
+   "id": "0022-3ebb3905554befd6e9c90a8161f00000757c58b10e4f248e60f7e1abf9e"
+  }
+ ],
+ "nbformat": 4,
+ "nbformat_minor": 5,
+ "metadata": {}
+}
+%% Cell type:markdown id:0002-0913d59b142f97e01b1f1d202696d848ab5b6e755f3d92df06ee693365f tags:
+
+# Kovarianz
+
+## Berechnen
+
+Schreiben Sie eine Funktion `cov`, die zwei Arrays `x` und `y` erhält
+und die Kovarianz zurück gibt.
+
+%% Cell type:code id:0003-a69527b239a033f8134e8f47e334b1f9486b9076b43570d3fc203164ed0 tags:
+
+``` 
+import numpy as np
+import pandas as pd
+```
+
+%% Cell type:markdown id:0005-1839d17e4e89b5f286b8ba411595b6eadeed6664573c0cae88cf6869b85 tags:
+
+### Tests
+
+Testen Sie die Funktion mit den Beispielen aus den Folien:
+
+%% Cell type:code id:0006-5a9afeeb069c9adcfd985dfa866647c55d0b7afa511f1ab88ce0e3feda9 tags:
+
+``` 
+df1 = pd.DataFrame({'x': [10, 7, 5, -13, -8, -3, -1, 11], 'y': [8, 10, 3, -9, -1, -7, -1, 13]})
+df2 = df1 * [1, -1]
+df3 = pd.DataFrame({'x': [14, 10, 4, 2, -1, -1, -9, -11], 'y': [3, 0, 10, -9, 13, -6, 7, -2]})
+cov(df1.x, df1.y)
+```
+
+%% Output
+
+    54.875
+
+%% Cell type:code id:0007-bcaedf82ed0c414209d4e126ee2fd2013a7f1cd96fb948355bf543c2ce7 tags:
+
+``` 
+cov(df2.x, df2.y)
+```
+
+%% Output
+
+    -54.875
+
+%% Cell type:code id:0008-5530793defbb6ce07fafad4901e5575defa5e0894f0d8b8d206ff56113e tags:
+
+``` 
+cov(df3.x, df3.y)
+```
+
+%% Output
+
+    0.0
+
+%% Cell type:markdown id:0011-5e6f7ee8c09fb3163c75c37ab167a849116ef4505076b2442a9a3e7eb1b tags:
+
+## Erzeugen
+
+So weit, so gut. Nun drehen wir die Aufgabenstellung um. Versuchen Sie
+nun drei Datensätze aus jeweils zwei Samples zu erzeugen:
+
+**Datensatz 1** soll als Kovarianz 1 besitzen.
+
+%% Cell type:code id:0012-1b4ea8eec5f19241e7602ee09cf19927687efc9d38c7d5360c417d2d3ba tags:
+
+``` 
+x = np.array([])
+y = np.array([])
+```
+
+%% Cell type:markdown id:0013-04ac3f4882b3309363456c952768f31a2c708e671a5462093ff68e76a76 tags:
+
+### Tests
+
+%% Cell type:code id:0014-3ebb3905554befd6e9c90a8161f00000757c58b10e4f248e60f7e1abf9e tags:
+
+``` 
+cov(x, y)
+```
+
+%% Output
+
+    1.0
+
+%% Cell type:markdown id:0015-3dbc650c0d3e7b7d38c1256a7a2dc71a13e88a5206c4e416af544e2b775 tags:
+
+**Datensatz 2** soll auch als Kovarianz 1 besitzen, aber mit anderen
+Samples als zuvor.
+
+%% Cell type:code id:0016-1b4ea8eec5f19241e7602ee09cf19927687efc9d38c7d5360c417d2d3ba tags:
+
+``` 
+x = np.array([])
+y = np.array([])
+```
+
+%% Cell type:markdown id:0017-503fa0c97971fa858f825b273ceb998780354d5bb183c47acfd4f3507cf tags:
+
+### Tests
+
+%% Cell type:code id:0018-3ebb3905554befd6e9c90a8161f00000757c58b10e4f248e60f7e1abf9e tags:
+
+``` 
+cov(x, y)
+```
+
+%% Output
+
+    1.0
+
+%% Cell type:markdown id:0019-257f544a893b080f910b0568abdb73110977708806fc07ff2bca207ef7e tags:
+
+**Datensatz 3** soll als Kovarianz 4 besitzen.
+
+%% Cell type:code id:0020-1b4ea8eec5f19241e7602ee09cf19927687efc9d38c7d5360c417d2d3ba tags:
+
+``` 
+x = np.array([])
+y = np.array([])
+```
+
+%% Cell type:markdown id:0021-c36e6e0be7ad3f1dec0afd72fde3a265396ca90bf93c258dbd4e3346cbd tags:
+
+### Tests
+
+%% Cell type:code id:0022-3ebb3905554befd6e9c90a8161f00000757c58b10e4f248e60f7e1abf9e tags:
+
+``` 
+cov(x, y)
+```
+
+%% Output
+
+    4.0
--- a/08-korrelation-und-dimensionsreduktion/02-datasaurus-sol.ipynb
+++ b/08-korrelation-und-dimensionsreduktion/02-datasaurus-sol.ipynb
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Datasaurus\n",
+    "\n",
+    "Laden Sie die Daten `datasaurus.csv` und betrachten für beliebige\n",
+    "Datensätze statistische Werte wie\n",
+    "\n",
+    "-   Mittelwerte von x und y\n",
+    "-   Standardabweichungen von x und y\n",
+    "-   Korrelationskoeffizient zwischen x und y\n",
+    "\n",
+    "Was schließen Sie daraus? Was könnten Sie noch machen um ein\n",
+    "Datenverständnis aufzubauen?\n",
+    "\n",
+    "## Lösung\n",
+    "\n",
+    "Wir laden zunächst die Daten."
+   ],
+   "id": "0005-26afc5b4704584feaccf0e55e8a571368fb090c84b1a48d539857d405c9"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "style": "python"
+   },
+   "outputs": [],
+   "source": [
+    "import pandas as pd\n",
+    "df = pd.read_csv('datasaurus.csv')"
+   ],
+   "id": "0006-ec8063a047adadc262ed2fa6a02a175adb276b5352581f5234aae966f7b"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Dann geben wir die Daten mal grob aus:"
+   ],
+   "id": "0007-7706bb8a9163533b90003de7af396b817b9bfd92e413dedc6f55a04d24f"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": [
+      "         dataset          x          y\n",
+      "0           dino  55.384600  97.179500\n",
+      "1           dino  51.538500  96.025600\n",
+      "2           dino  46.153800  94.487200\n",
+      "3           dino  42.820500  91.410300\n",
+      "4           dino  40.769200  88.333300\n",
+      "...          ...        ...        ...\n",
+      "1841  wide_lines  33.674442  26.090490\n",
+      "1842  wide_lines  75.627255  37.128752\n",
+      "1843  wide_lines  40.610125  89.136240\n",
+      "1844  wide_lines  39.114366  96.481751\n",
+      "1845  wide_lines  34.583829  89.588902\n",
+      "\n",
+      "[1846 rows x 3 columns]"
+     ]
+    }
+   ],
+   "source": [
+    "df"
+   ],
+   "id": "0008-0482c68413fbf8290e3b1e49b0a85901cfcd62ab0738760568a2a6e8a57"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Aha, die Datensätze sind also über die Spalte `dataset` getrennt. Das\n",
+    "ist Praktisch, denn damit können wir die Datensätze gruppieren und für\n",
+    "alle den Mittelwert ausgeben:"
+   ],
+   "id": "0009-766eb695b9c56d31ef0e81db1ca96663c9fd98e3e46dd1b6cace938f9ed"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": [
+      "                    x          y\n",
+      "dataset\n",
+      "away        54.266100  47.834721\n",
+      "bullseye    54.268730  47.830823\n",
+      "circle      54.267320  47.837717\n",
+      "dino        54.263273  47.832253\n",
+      "dots        54.260303  47.839829\n",
+      "h_lines     54.261442  47.830252\n",
+      "high_lines  54.268805  47.835450\n",
+      "slant_down  54.267849  47.835896\n",
+      "slant_up    54.265882  47.831496\n",
+      "star        54.267341  47.839545\n",
+      "v_lines     54.269927  47.836988\n",
+      "wide_lines  54.266916  47.831602\n",
+      "x_shape     54.260150  47.839717"
+     ]
+    }
+   ],
+   "source": [
+    "df.groupby('dataset').mean()"
+   ],
+   "id": "0010-b342ee9c963b9fa49a7bea82eefca4c86be18f50947908236381dfc1ad0"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Die Mittelwerte aller Datensätze sind jeweils für x und y nahezu gleich.\n",
+    "Und die Standardabweichungen auch:"
+   ],
+   "id": "0011-5c2541a1ac168b4459987d9491310dcd4abe498e8983f80c18f67a82eac"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": [
+      "                    x          y\n",
+      "dataset\n",
+      "away        16.769825  26.939743\n",
+      "bullseye    16.769239  26.935727\n",
+      "circle      16.760013  26.930036\n",
+      "dino        16.765142  26.935403\n",
+      "dots        16.767735  26.930192\n",
+      "h_lines     16.765898  26.939876\n",
+      "high_lines  16.766704  26.939998\n",
+      "slant_down  16.766759  26.936105\n",
+      "slant_up    16.768853  26.938608\n",
+      "star        16.768959  26.930275\n",
+      "v_lines     16.769959  26.937684\n",
+      "wide_lines  16.770000  26.937902\n",
+      "x_shape     16.769958  26.930002"
+     ]
+    }
+   ],
+   "source": [
+    "df.groupby('dataset').std()"
+   ],
+   "id": "0012-a437abd5ed49b4b3e4e43675df457ff411477c73c3c4aec6d3308b89356"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Was ist mit den Korrelationen zwischen x und y? Der Code ist\n",
+    "kompliziert, weil hier ein Multi-Index ensteht (jeder Dataset enthält\n",
+    "eine Korrelationsmatrix) und wir nur einen Wert davon haben wollen:"
+   ],
+   "id": "0013-d181c960ab516f871d98eadc6493da90b9b4068bccda237e749200efc04"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "stream",
+     "name": "stdout",
+     "text": [
+      "dataset\n",
+      "away         -0.064128\n",
+      "bullseye     -0.068586\n",
+      "circle       -0.068343\n",
+      "dino         -0.064472\n",
+      "dots         -0.060341\n",
+      "h_lines      -0.061715\n",
+      "high_lines   -0.068504\n",
+      "slant_down   -0.068980\n",
+      "slant_up     -0.068609\n",
+      "star         -0.062961\n",
+      "v_lines      -0.069446\n",
+      "wide_lines   -0.066575\n",
+      "x_shape      -0.065583\n",
+      "Name: x, dtype: float64"
+     ]
+    }
+   ],
+   "source": [
+    "df.groupby('dataset').corr()['x'][:, 'y']"
+   ],
+   "id": "0014-8236dab4db77881177f2961943ff03473ddd7fe7c652ac66baea2a09a01"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Also auch die Korrelationswerte sind fast gleich und zwar nahe 0. Hmm…\n",
+    "wir könnten jetzt z. B. den Median anschauen. Der wäre nicht gleich,\n",
+    "aber daraus verstehen wir auch nicht so richtig, was hier los ist.\n",
+    "Scatter-Plots to the rescue!"
+   ],
+   "id": "0015-72d799f9b4a7863ce5a44a0cf48b7da4bce08752c77b2f27f07afecc8be"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "style": "python"
+   },
+   "outputs": [],
+   "source": [
+    "df.groupby('dataset').plot.scatter('x', 'y')"
+   ],
+   "id": "0016-cb4f9080bda8d31054a17b051085cdb7f6f96dc5c873616190c59420579"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Für einen einzelnen Plot können wir natürlich auch nach dem Dataset\n",
+    "filtern:"
+   ],
+   "id": "0017-9bb4b1a268443f12295eac8e102fc5006bcba977410502f17341a4cec57"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "style": "python"
+   },
+   "outputs": [],
+   "source": [
+    "df.loc[df.dataset == 'dino', ['x', 'y']].plot.scatter('x', 'y')"
+   ],
+   "id": "0018-33dd16c34b351bd44e01483365f9c25c16717a4927e3e5f8a46d66ab17a"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Schlussfolgerung: Visualisierung von Daten ist wichtig, aber meistens\n",
+    "nicht so einfach wie hier. Dimensionsreduktionstechniken können dabei\n",
+    "behilflich sein. Statistiken sind nützlich, aber reichen nicht aus um\n",
+    "ein hinreichendes Datenverständnis zu erwerben."
+   ],
+   "id": "0019-9306a8b6383c69b603008b91eefd53d0cbff5ba07be0cdf3b471261b165"
+  }
+ ],
+ "nbformat": 4,
+ "nbformat_minor": 5,
+ "metadata": {}
+}
+%% Cell type:markdown id:0005-26afc5b4704584feaccf0e55e8a571368fb090c84b1a48d539857d405c9 tags:
+
+# Datasaurus
+
+Laden Sie die Daten `datasaurus.csv` und betrachten für beliebige
+Datensätze statistische Werte wie
+
+-   Mittelwerte von x und y
+-   Standardabweichungen von x und y
+-   Korrelationskoeffizient zwischen x und y
+
+Was schließen Sie daraus? Was könnten Sie noch machen um ein
+Datenverständnis aufzubauen?
+
+## Lösung
+
+Wir laden zunächst die Daten.
+
+%% Cell type:code id:0006-ec8063a047adadc262ed2fa6a02a175adb276b5352581f5234aae966f7b tags:
+
+``` 
+import pandas as pd
+df = pd.read_csv('datasaurus.csv')
+```
+
+%% Cell type:markdown id:0007-7706bb8a9163533b90003de7af396b817b9bfd92e413dedc6f55a04d24f tags:
+
+Dann geben wir die Daten mal grob aus:
+
+%% Cell type:code id:0008-0482c68413fbf8290e3b1e49b0a85901cfcd62ab0738760568a2a6e8a57 tags:
+
+``` 
+df
+```
+
+%% Output
+
+             dataset          x          y
+    0           dino  55.384600  97.179500
+    1           dino  51.538500  96.025600
+    2           dino  46.153800  94.487200
+    3           dino  42.820500  91.410300
+    4           dino  40.769200  88.333300
+    ...          ...        ...        ...
+    1841  wide_lines  33.674442  26.090490
+    1842  wide_lines  75.627255  37.128752
+    1843  wide_lines  40.610125  89.136240
+    1844  wide_lines  39.114366  96.481751
+    1845  wide_lines  34.583829  89.588902
+    
+    [1846 rows x 3 columns]
+
+%% Cell type:markdown id:0009-766eb695b9c56d31ef0e81db1ca96663c9fd98e3e46dd1b6cace938f9ed tags:
+
+Aha, die Datensätze sind also über die Spalte `dataset` getrennt. Das
+ist Praktisch, denn damit können wir die Datensätze gruppieren und für
+alle den Mittelwert ausgeben:
+
+%% Cell type:code id:0010-b342ee9c963b9fa49a7bea82eefca4c86be18f50947908236381dfc1ad0 tags:
+
+``` 
+df.groupby('dataset').mean()
+```
+
+%% Output
+
+                        x          y
+    dataset
+    away        54.266100  47.834721
+    bullseye    54.268730  47.830823
+    circle      54.267320  47.837717
+    dino        54.263273  47.832253
+    dots        54.260303  47.839829
+    h_lines     54.261442  47.830252
+    high_lines  54.268805  47.835450
+    slant_down  54.267849  47.835896
+    slant_up    54.265882  47.831496
+    star        54.267341  47.839545
+    v_lines     54.269927  47.836988
+    wide_lines  54.266916  47.831602
+    x_shape     54.260150  47.839717
+
+%% Cell type:markdown id:0011-5c2541a1ac168b4459987d9491310dcd4abe498e8983f80c18f67a82eac tags:
+
+Die Mittelwerte aller Datensätze sind jeweils für x und y nahezu gleich.
+Und die Standardabweichungen auch:
+
+%% Cell type:code id:0012-a437abd5ed49b4b3e4e43675df457ff411477c73c3c4aec6d3308b89356 tags:
+
+``` 
+df.groupby('dataset').std()
+```
+
+%% Output
+
+                        x          y
+    dataset
+    away        16.769825  26.939743
+    bullseye    16.769239  26.935727
+    circle      16.760013  26.930036
+    dino        16.765142  26.935403
+    dots        16.767735  26.930192
+    h_lines     16.765898  26.939876
+    high_lines  16.766704  26.939998
+    slant_down  16.766759  26.936105
+    slant_up    16.768853  26.938608
+    star        16.768959  26.930275
+    v_lines     16.769959  26.937684
+    wide_lines  16.770000  26.937902
+    x_shape     16.769958  26.930002
+
+%% Cell type:markdown id:0013-d181c960ab516f871d98eadc6493da90b9b4068bccda237e749200efc04 tags:
+
+Was ist mit den Korrelationen zwischen x und y? Der Code ist
+kompliziert, weil hier ein Multi-Index ensteht (jeder Dataset enthält
+eine Korrelationsmatrix) und wir nur einen Wert davon haben wollen:
+
+%% Cell type:code id:0014-8236dab4db77881177f2961943ff03473ddd7fe7c652ac66baea2a09a01 tags:
+
+``` 
+df.groupby('dataset').corr()['x'][:, 'y']
+```
+
+%% Output
+
+    dataset
+    away         -0.064128
+    bullseye     -0.068586
+    circle       -0.068343
+    dino         -0.064472
+    dots         -0.060341
+    h_lines      -0.061715
+    high_lines   -0.068504
+    slant_down   -0.068980
+    slant_up     -0.068609
+    star         -0.062961
+    v_lines      -0.069446
+    wide_lines   -0.066575
+    x_shape      -0.065583
+    Name: x, dtype: float64
+
+%% Cell type:markdown id:0015-72d799f9b4a7863ce5a44a0cf48b7da4bce08752c77b2f27f07afecc8be tags:
+
+Also auch die Korrelationswerte sind fast gleich und zwar nahe 0. Hmm…
+wir könnten jetzt z. B. den Median anschauen. Der wäre nicht gleich,
+aber daraus verstehen wir auch nicht so richtig, was hier los ist.
+Scatter-Plots to the rescue!
+
+%% Cell type:code id:0016-cb4f9080bda8d31054a17b051085cdb7f6f96dc5c873616190c59420579 tags:
+
+``` 
+df.groupby('dataset').plot.scatter('x', 'y')
+```
+
+%% Cell type:markdown id:0017-9bb4b1a268443f12295eac8e102fc5006bcba977410502f17341a4cec57 tags:
+
+Für einen einzelnen Plot können wir natürlich auch nach dem Dataset
+filtern:
+
+%% Cell type:code id:0018-33dd16c34b351bd44e01483365f9c25c16717a4927e3e5f8a46d66ab17a tags:
+
+``` 
+df.loc[df.dataset == 'dino', ['x', 'y']].plot.scatter('x', 'y')
+```
+
+%% Cell type:markdown id:0019-9306a8b6383c69b603008b91eefd53d0cbff5ba07be0cdf3b471261b165 tags:
+
+Schlussfolgerung: Visualisierung von Daten ist wichtig, aber meistens
+nicht so einfach wie hier. Dimensionsreduktionstechniken können dabei
+behilflich sein. Statistiken sind nützlich, aber reichen nicht aus um
+ein hinreichendes Datenverständnis zu erwerben.
--- a/08-korrelation-und-dimensionsreduktion/02-datasaurus.ipynb
+++ b/08-korrelation-und-dimensionsreduktion/02-datasaurus.ipynb
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Datasaurus\n",
+    "\n",
+    "Laden Sie die Daten `datasaurus.csv` und betrachten für beliebige\n",
+    "Datensätze statistische Werte wie\n",
+    "\n",
+    "-   Mittelwerte von x und y\n",
+    "-   Standardabweichungen von x und y\n",
+    "-   Korrelationskoeffizient zwischen x und y\n",
+    "\n",
+    "Was schließen Sie daraus? Was könnten Sie noch machen um ein\n",
+    "Datenverständnis aufzubauen?\n",
+    "\n",
+    "Hier Ihr Code:"
+   ],
+   "id": "0004-acee268a50d14b526dc75bb1f3532efe74d442564a65304d69624cfecef"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "style": "python"
+   },
+   "outputs": [],
+   "source": [],
+   "id": "0005-44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855"
+  }
+ ],
+ "nbformat": 4,
+ "nbformat_minor": 5,
+ "metadata": {}
+}
+%% Cell type:markdown id:0004-acee268a50d14b526dc75bb1f3532efe74d442564a65304d69624cfecef tags:
+
+# Datasaurus
+
+Laden Sie die Daten `datasaurus.csv` und betrachten für beliebige
+Datensätze statistische Werte wie
+
+-   Mittelwerte von x und y
+-   Standardabweichungen von x und y
+-   Korrelationskoeffizient zwischen x und y
+
+Was schließen Sie daraus? Was könnten Sie noch machen um ein
+Datenverständnis aufzubauen?
+
+Hier Ihr Code:
+
+%% Cell type:code id:0005-44298fc1c149afbf4c8996fb92427ae41e4649b934ca495991b7852b855 tags:
+
+``` 
+```
--- a/08-korrelation-und-dimensionsreduktion/03-anscombe.ipynb
+++ b/08-korrelation-und-dimensionsreduktion/03-anscombe.ipynb
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Anscombe’s Datasets\n",
+    "\n",
+    "Hier ist der Code um die Statistiken und die Plots aus den Folien zu\n",
+    "erzeugen. Falls Sie möchten, können Sie damit herumspielen."
+   ],
+   "id": "0001-47ec560fa976f47180d8889c9b67b1031223795531ff28c56b723a977ee"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "style": "python"
+   },
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "from numpy.polynomial import Polynomial\n",
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "import seaborn as sns\n",
+    "\n",
+    "df = sns.load_dataset(\"anscombe\")"
+   ],
+   "id": "0002-bbd16bd579840f98abcf3f0f6b704f69373b858aa9b36da508d149f1adf"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "style": "python"
+   },
+   "outputs": [],
+   "source": [
+    "for ds_name, ds in df.groupby('dataset')[['x', 'y']]:\n",
+    "    mean = ds.mean()\n",
+    "    var = ds.var()\n",
+    "    c = ds.corr()\n",
+    "    poly = Polynomial.fit(ds.x, ds.y, deg=1).convert()\n",
+    "    with np.printoptions(precision=2):\n",
+    "        print(f'DS {ds_name:3}: mean (x: {mean.x:.2f}, y: {mean.y:.2f}), var (x: {var.x:.2f}, y: {var.y:.2f}), corr: {c.x.y:.3f}, linear model regression: {poly}')\n",
+    "\n",
+    "sns.lmplot(x=\"x\", y=\"y\", col=\"dataset\", hue=\"dataset\", data=df,\n",
+    "           col_wrap=2, ci=None, palette=\"muted\", height=5,\n",
+    "           line_kws={'color': 'lightgrey'}, scatter_kws={\"s\": 100})\n",
+    "\n",
+    "fig = plt.gcf()\n",
+    "fig.set_size_inches(6.5, 4)\n",
+    "fig.patch.set_alpha(0)\n",
+    "fig.tight_layout()\n",
+    "fig.savefig('anscombe.pdf', pad_inches=0)"
+   ],
+   "id": "0003-b4658e20442bb236c82c49dc2764e6ce9c93c82fe6eb93a5e79ab822189"
+  }
+ ],
+ "nbformat": 4,
+ "nbformat_minor": 5,
+ "metadata": {}
+}
+%% Cell type:markdown id:0001-47ec560fa976f47180d8889c9b67b1031223795531ff28c56b723a977ee tags:
+
+# Anscombe’s Datasets
+
+Hier ist der Code um die Statistiken und die Plots aus den Folien zu
+erzeugen. Falls Sie möchten, können Sie damit herumspielen.
+
+%% Cell type:code id:0002-bbd16bd579840f98abcf3f0f6b704f69373b858aa9b36da508d149f1adf tags:
+
+``` 
+import matplotlib.pyplot as plt
+from numpy.polynomial import Polynomial
+import numpy as np
+import pandas as pd
+import seaborn as sns
+
+df = sns.load_dataset("anscombe")
+```
+
+%% Cell type:code id:0003-b4658e20442bb236c82c49dc2764e6ce9c93c82fe6eb93a5e79ab822189 tags:
+
+``` 
+for ds_name, ds in df.groupby('dataset')[['x', 'y']]:
+    mean = ds.mean()
+    var = ds.var()
+    c = ds.corr()
+    poly = Polynomial.fit(ds.x, ds.y, deg=1).convert()
+    with np.printoptions(precision=2):
+        print(f'DS {ds_name:3}: mean (x: {mean.x:.2f}, y: {mean.y:.2f}), var (x: {var.x:.2f}, y: {var.y:.2f}), corr: {c.x.y:.3f}, linear model regression: {poly}')
+
+sns.lmplot(x="x", y="y", col="dataset", hue="dataset", data=df,
+           col_wrap=2, ci=None, palette="muted", height=5,
+           line_kws={'color': 'lightgrey'}, scatter_kws={"s": 100})
+
+fig = plt.gcf()
+fig.set_size_inches(6.5, 4)
+fig.patch.set_alpha(0)
+fig.tight_layout()
+fig.savefig('anscombe.pdf', pad_inches=0)
+```
--- a/08-korrelation-und-dimensionsreduktion/04-feature-map-sol.ipynb
+++ b/08-korrelation-und-dimensionsreduktion/04-feature-map-sol.ipynb
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Feature-Map\n",
+    "\n",
+    "In dieser Aufgabe wollen wir die Features entsprechend der\n",
+    "Korrelationsmatrix auf einer Karte plotten.\n",
+    "\n",
+    "1.  Laden Sie die Autodaten aus `autos.csv` als DataFrame.\n",
+    "2.  *Bonus: Werfen Sie die Ausreißer raus. Was hat das für Auswirkungen\n",
+    "    auf das Ergebnis.*\n",
+    "3.  Berechnen Sie die Korrelationsmatrix.\n",
+    "4.  Wandeln Sie die Korrelationsmatrix $P$ in eine Distanzmatrix\n",
+    "    $D = \\sqrt{1 - P}$ um. \\*Bonus: Probieren Sie auch\n",
+    "    $D = \\sqrt{1 - |P|}$\n",
+    "5.  Finden Sie mit MDS die Koordinaten zu den Features. Sie benötigen\n",
+    "    `dissimilarity='precomputed'`, damit Sie in `fit` $D$ reingeben\n",
+    "    können.\n",
+    "6.  Plotten Sie das Ergebnis mittels Plotly Express’ Scatter-Plot, denn\n",
+    "    da können Sie an das Argument `text` die Feature-Namen übergeben."
+   ],
+   "id": "0002-8585dc9b0ed930d72556df47900a3e3dae65ea2bd7f244d5822c3bb4206"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "style": "python"
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "import plotly.express as px\n",
+    "from sklearn.manifold import MDS"
+   ],
+   "id": "0003-c1bb0a9ce1897e013bbc5224cd3031da808967b4ce5f467e752db79b3b6"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Lösung\n",
+    "\n",
+    "Hier der Code zur Lösung:"
+   ],
+   "id": "0005-2b2e02f7c099c0b3c2e7ee38e724334b181f374b2f6da5066b33d7489c5"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "style": "python"
+   },
+   "outputs": [],
+   "source": [
+    "df = pd.read_csv('autos.csv').drop(columns=['Marke', 'Modell'])\n",
+    "# df = df[df.Grundpreis < 150_000]  # mit Ausreißern ist der Grundpreis weit weg von den Motordaten\n",
+    "\n",
+    "corr = df.corr()\n",
+    "\n",
+    "dist_corr = np.sqrt(1 - corr)\n",
+    "# dist_corr = np.sqrt(1 - np.abs(corr))  # mit abs rückt die Türanzahl näher an alle anderes\n",
+    "\n",
+    "mds = MDS(dissimilarity='precomputed', normalized_stress='auto')\n",
+    "corr_map = mds.fit_transform(dist_corr)\n",
+    "corr_map = pd.DataFrame(corr_map)\n",
+    "corr_map['feature'] = corr.columns"
+   ],
+   "id": "0006-472ff22b9cdec2be85fd14f451bb4cdea7db8ee3cbf28c128c994cf0453"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Der Grundpreis ist ohne Ausreißer näher an den Motordaten, d.h. der\n",
+    "Preis verhält sich ähnlich. Mit Ausreißer ist der Preis weit weg. Das\n",
+    "lässt sich so interpretieren, dass der Preis für sehr teure Autos nicht\n",
+    "mehr im Verhältnis zum Motor steht."
+   ],
+   "id": "0007-96c5b071fc624449a3bff00f5acf449ff13a3986090c619ea3c40dbebf7"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "px.scatter(corr_map, x=0, y=1, text=corr.columns)"
+   ],
+   "id": "0008-20ca1c79ef727fdf527b2a98d7d6fe563ef6fd9c2b005bb1fdfb364bbbb"
+  }
+ ],
+ "nbformat": 4,
+ "nbformat_minor": 5,
+ "metadata": {}
+}
+%% Cell type:markdown id:0002-8585dc9b0ed930d72556df47900a3e3dae65ea2bd7f244d5822c3bb4206 tags:
+
+# Feature-Map
+
+In dieser Aufgabe wollen wir die Features entsprechend der
+Korrelationsmatrix auf einer Karte plotten.
+
+1.  Laden Sie die Autodaten aus `autos.csv` als DataFrame.
+2.  *Bonus: Werfen Sie die Ausreißer raus. Was hat das für Auswirkungen
+    auf das Ergebnis.*
+3.  Berechnen Sie die Korrelationsmatrix.
+4.  Wandeln Sie die Korrelationsmatrix $P$ in eine Distanzmatrix
+    $D = \sqrt{1 - P}$ um. \*Bonus: Probieren Sie auch
+    $D = \sqrt{1 - |P|}$
+5.  Finden Sie mit MDS die Koordinaten zu den Features. Sie benötigen
+    `dissimilarity='precomputed'`, damit Sie in `fit` $D$ reingeben
+    können.
+6.  Plotten Sie das Ergebnis mittels Plotly Express’ Scatter-Plot, denn
+    da können Sie an das Argument `text` die Feature-Namen übergeben.
+
+%% Cell type:code id:0003-c1bb0a9ce1897e013bbc5224cd3031da808967b4ce5f467e752db79b3b6 tags:
+
+``` 
+import numpy as np
+import pandas as pd
+import plotly.express as px
+from sklearn.manifold import MDS
+```
+
+%% Cell type:markdown id:0005-2b2e02f7c099c0b3c2e7ee38e724334b181f374b2f6da5066b33d7489c5 tags:
+
+## Lösung
+
+Hier der Code zur Lösung:
+
+%% Cell type:code id:0006-472ff22b9cdec2be85fd14f451bb4cdea7db8ee3cbf28c128c994cf0453 tags:
+
+``` 
+df = pd.read_csv('autos.csv').drop(columns=['Marke', 'Modell'])
+# df = df[df.Grundpreis < 150_000]  # mit Ausreißern ist der Grundpreis weit weg von den Motordaten
+
+corr = df.corr()
+
+dist_corr = np.sqrt(1 - corr)
+# dist_corr = np.sqrt(1 - np.abs(corr))  # mit abs rückt die Türanzahl näher an alle anderes
+
+mds = MDS(dissimilarity='precomputed', normalized_stress='auto')
+corr_map = mds.fit_transform(dist_corr)
+corr_map = pd.DataFrame(corr_map)
+corr_map['feature'] = corr.columns
+```
+
+%% Cell type:markdown id:0007-96c5b071fc624449a3bff00f5acf449ff13a3986090c619ea3c40dbebf7 tags:
+
+Der Grundpreis ist ohne Ausreißer näher an den Motordaten, d.h. der
+Preis verhält sich ähnlich. Mit Ausreißer ist der Preis weit weg. Das
+lässt sich so interpretieren, dass der Preis für sehr teure Autos nicht
+mehr im Verhältnis zum Motor steht.
+
+%% Cell type:code id:0008-20ca1c79ef727fdf527b2a98d7d6fe563ef6fd9c2b005bb1fdfb364bbbb tags:
+
+``` 
+px.scatter(corr_map, x=0, y=1, text=corr.columns)
+```
--- a/08-korrelation-und-dimensionsreduktion/04-feature-map.ipynb
+++ b/08-korrelation-und-dimensionsreduktion/04-feature-map.ipynb
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# Feature-Map\n",
+    "\n",
+    "In dieser Aufgabe wollen wir die Features entsprechend der\n",
+    "Korrelationsmatrix auf einer Karte plotten.\n",
+    "\n",
+    "1.  Laden Sie die Autodaten aus `autos.csv` als DataFrame.\n",
+    "2.  *Bonus: Werfen Sie die Ausreißer raus. Was hat das für Auswirkungen\n",
+    "    auf das Ergebnis.*\n",
+    "3.  Berechnen Sie die Korrelationsmatrix.\n",
+    "4.  Wandeln Sie die Korrelationsmatrix $P$ in eine Distanzmatrix\n",
+    "    $D = \\sqrt{1 - P}$ um. \\*Bonus: Probieren Sie auch\n",
+    "    $D = \\sqrt{1 - |P|}$\n",
+    "5.  Finden Sie mit MDS die Koordinaten zu den Features. Sie benötigen\n",
+    "    `dissimilarity='precomputed'`, damit Sie in `fit` $D$ reingeben\n",
+    "    können.\n",
+    "6.  Plotten Sie das Ergebnis mittels Plotly Express’ Scatter-Plot, denn\n",
+    "    da können Sie an das Argument `text` die Feature-Namen übergeben."
+   ],
+   "id": "0002-8585dc9b0ed930d72556df47900a3e3dae65ea2bd7f244d5822c3bb4206"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "style": "python"
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "import plotly.express as px\n",
+    "from sklearn.manifold import MDS"
+   ],
+   "id": "0003-c1bb0a9ce1897e013bbc5224cd3031da808967b4ce5f467e752db79b3b6"
+  }
+ ],
+ "nbformat": 4,
+ "nbformat_minor": 5,
+ "metadata": {}
+}
+%% Cell type:markdown id:0002-8585dc9b0ed930d72556df47900a3e3dae65ea2bd7f244d5822c3bb4206 tags:
+
+# Feature-Map
+
+In dieser Aufgabe wollen wir die Features entsprechend der
+Korrelationsmatrix auf einer Karte plotten.
+
+1.  Laden Sie die Autodaten aus `autos.csv` als DataFrame.
+2.  *Bonus: Werfen Sie die Ausreißer raus. Was hat das für Auswirkungen
+    auf das Ergebnis.*
+3.  Berechnen Sie die Korrelationsmatrix.
+4.  Wandeln Sie die Korrelationsmatrix $P$ in eine Distanzmatrix
+    $D = \sqrt{1 - P}$ um. \*Bonus: Probieren Sie auch
+    $D = \sqrt{1 - |P|}$
+5.  Finden Sie mit MDS die Koordinaten zu den Features. Sie benötigen
+    `dissimilarity='precomputed'`, damit Sie in `fit` $D$ reingeben
+    können.
+6.  Plotten Sie das Ergebnis mittels Plotly Express’ Scatter-Plot, denn
+    da können Sie an das Argument `text` die Feature-Namen übergeben.
+
+%% Cell type:code id:0003-c1bb0a9ce1897e013bbc5224cd3031da808967b4ce5f467e752db79b3b6 tags:
+
+``` 
+import numpy as np
+import pandas as pd
+import plotly.express as px
+from sklearn.manifold import MDS
+```
--- a/08-korrelation-und-dimensionsreduktion/05-reduce-mnist-sol.ipynb
+++ b/08-korrelation-und-dimensionsreduktion/05-reduce-mnist-sol.ipynb
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# MNIST visualisieren\n",
+    "\n",
+    "In dieser Aufgabe wollen wir einen hochdimensionalen Datensatz in 2D\n",
+    "(oder 3D) plotten. Die Daten werden schon geladen."
+   ],
+   "id": "0001-9c88d904212173177e3cd805c405ca6bffb6c39ce47a88ff66351aa9536"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "style": "python"
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import plotly.express as px\n",
+    "from tensorflow.keras.datasets.mnist import load_data\n",
+    "\n",
+    "(x_train, y_train), (x_test, y_test) = load_data()\n",
+    "\n",
+    "# reshape test set to 10 000 x 784\n",
+    "X = x_test.reshape(-1, 28 * 28)"
+   ],
+   "id": "0002-f9e5f87e267af56fbd5014863286132d368c2876d241287b849ceff60cc"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Wenn Sie mögen ist hier ein Plot von verschiedenen Bildern der gleichen\n",
+    "Klasse. So können Sie ein Blick reinwerfen."
+   ],
+   "id": "0003-fef1281e3edb72c906210479c5811c47fe2289914626b2c40534881280c"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "style": "python"
+   },
+   "outputs": [],
+   "source": [
+    "# plot 50 examples for each digit\n",
+    "imgs = np.empty((50, 10, 28, 28))\n",
+    "for j in range(10):\n",
+    "    imgs[:, j] = x_test[y_test == j][:50]\n",
+    "\n",
+    "fig = px.imshow(imgs, animation_frame=0, facet_col=1, facet_col_wrap=5, binary_string=True)\n",
+    "fig.update_xaxes(showticklabels=False)\n",
+    "fig.update_yaxes(showticklabels=False)\n",
+    "fig.show()"
+   ],
+   "id": "0004-c879d58b500c83a0364d8680cc6b05c9cc97d36d3ea3743e112c56644db"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Transformieren Sie die Daten in 2D (ode 3D) und plotten die\n",
+    "Transformierten Daten als Scatter-Plot mit `y_test` als\n",
+    "Farbunterscheidung.\n",
+    "\n",
+    "## Lösung\n",
+    "\n",
+    "Hier der Code zur Lösung:"
+   ],
+   "id": "0007-d262459c63ed3d98add57f2c48715daab6ff8a674c4e923ee87f87f61ad"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "style": "python"
+   },
+   "outputs": [],
+   "source": [
+    "from umap import UMAP\n",
+    "from sklearn.decomposition import PCA\n",
+    "\n",
+    "pca = PCA(n_components=2)\n",
+    "X_pca = pca.fit_transform(X)\n",
+    "\n",
+    "umap = UMAP(n_neighbors=20, metric='manhattan', min_dist=0.1)\n",
+    "X_umap = umap.fit_transform(X)\n",
+    "\n",
+    "scatter1 = px.scatter(X_pca, x=0, y=1, color=y_test)\n",
+    "scatter1.show()\n",
+    "scatter2 = px.scatter(X_umap, x=0, y=1, color=y_test, hover_data={'class': y_test, 'index': np.arange(len(X_umap))})\n",
+    "scatter2.show()"
+   ],
+   "id": "0008-a04806d4df0812cf8fba0aa2e4e76d43ce0a2c8b2e2a9d7c032abc4e78f"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Der Grundpreis ist ohne Ausreißer näher an den Motordaten, d.h. der\n",
+    "Preis verhält sich ähnlich. Mit Ausreißer ist der Preis weit weg. Das\n",
+    "lässt sich so interpretieren, dass der Preis für sehr teure Autos nicht\n",
+    "mehr im Verhältnis zum Motor steht."
+   ],
+   "id": "0009-96c5b071fc624449a3bff00f5acf449ff13a3986090c619ea3c40dbebf7"
+  }
+ ],
+ "nbformat": 4,
+ "nbformat_minor": 5,
+ "metadata": {}
+}
+%% Cell type:markdown id:0001-9c88d904212173177e3cd805c405ca6bffb6c39ce47a88ff66351aa9536 tags:
+
+# MNIST visualisieren
+
+In dieser Aufgabe wollen wir einen hochdimensionalen Datensatz in 2D
+(oder 3D) plotten. Die Daten werden schon geladen.
+
+%% Cell type:code id:0002-f9e5f87e267af56fbd5014863286132d368c2876d241287b849ceff60cc tags:
+
+``` 
+import numpy as np
+import plotly.express as px
+from tensorflow.keras.datasets.mnist import load_data
+
+(x_train, y_train), (x_test, y_test) = load_data()
+
+# reshape test set to 10 000 x 784
+X = x_test.reshape(-1, 28 * 28)
+```
+
+%% Cell type:markdown id:0003-fef1281e3edb72c906210479c5811c47fe2289914626b2c40534881280c tags:
+
+Wenn Sie mögen ist hier ein Plot von verschiedenen Bildern der gleichen
+Klasse. So können Sie ein Blick reinwerfen.
+
+%% Cell type:code id:0004-c879d58b500c83a0364d8680cc6b05c9cc97d36d3ea3743e112c56644db tags:
+
+``` 
+# plot 50 examples for each digit
+imgs = np.empty((50, 10, 28, 28))
+for j in range(10):
+    imgs[:, j] = x_test[y_test == j][:50]
+
+fig = px.imshow(imgs, animation_frame=0, facet_col=1, facet_col_wrap=5, binary_string=True)
+fig.update_xaxes(showticklabels=False)
+fig.update_yaxes(showticklabels=False)
+fig.show()
+```
+
+%% Cell type:markdown id:0007-d262459c63ed3d98add57f2c48715daab6ff8a674c4e923ee87f87f61ad tags:
+
+Transformieren Sie die Daten in 2D (ode 3D) und plotten die
+Transformierten Daten als Scatter-Plot mit `y_test` als
+Farbunterscheidung.
+
+## Lösung
+
+Hier der Code zur Lösung:
+
+%% Cell type:code id:0008-a04806d4df0812cf8fba0aa2e4e76d43ce0a2c8b2e2a9d7c032abc4e78f tags:
+
+``` 
+from umap import UMAP
+from sklearn.decomposition import PCA
+
+pca = PCA(n_components=2)
+X_pca = pca.fit_transform(X)
+
+umap = UMAP(n_neighbors=20, metric='manhattan', min_dist=0.1)
+X_umap = umap.fit_transform(X)
+
+scatter1 = px.scatter(X_pca, x=0, y=1, color=y_test)
+scatter1.show()
+scatter2 = px.scatter(X_umap, x=0, y=1, color=y_test, hover_data={'class': y_test, 'index': np.arange(len(X_umap))})
+scatter2.show()
+```
+
+%% Cell type:markdown id:0009-96c5b071fc624449a3bff00f5acf449ff13a3986090c619ea3c40dbebf7 tags:
+
+Der Grundpreis ist ohne Ausreißer näher an den Motordaten, d.h. der
+Preis verhält sich ähnlich. Mit Ausreißer ist der Preis weit weg. Das
+lässt sich so interpretieren, dass der Preis für sehr teure Autos nicht
+mehr im Verhältnis zum Motor steht.
--- a/08-korrelation-und-dimensionsreduktion/05-reduce-mnist.ipynb
+++ b/08-korrelation-und-dimensionsreduktion/05-reduce-mnist.ipynb
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "# MNIST visualisieren\n",
+    "\n",
+    "In dieser Aufgabe wollen wir einen hochdimensionalen Datensatz in 2D\n",
+    "(oder 3D) plotten. Die Daten werden schon geladen."
+   ],
+   "id": "0001-9c88d904212173177e3cd805c405ca6bffb6c39ce47a88ff66351aa9536"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "style": "python"
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import plotly.express as px\n",
+    "from tensorflow.keras.datasets.mnist import load_data\n",
+    "\n",
+    "(x_train, y_train), (x_test, y_test) = load_data()\n",
+    "\n",
+    "# reshape test set to 10 000 x 784\n",
+    "X = x_test.reshape(-1, 28 * 28)"
+   ],
+   "id": "0002-f9e5f87e267af56fbd5014863286132d368c2876d241287b849ceff60cc"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Wenn Sie mögen ist hier ein Plot von verschiedenen Bildern der gleichen\n",
+    "Klasse. So können Sie ein Blick reinwerfen."
+   ],
+   "id": "0003-fef1281e3edb72c906210479c5811c47fe2289914626b2c40534881280c"
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "style": "python"
+   },
+   "outputs": [],
+   "source": [
+    "# plot 50 examples for each digit\n",
+    "imgs = np.empty((50, 10, 28, 28))\n",
+    "for j in range(10):\n",
+    "    imgs[:, j] = x_test[y_test == j][:50]\n",
+    "\n",
+    "fig = px.imshow(imgs, animation_frame=0, facet_col=1, facet_col_wrap=5, binary_string=True)\n",
+    "fig.update_xaxes(showticklabels=False)\n",
+    "fig.update_yaxes(showticklabels=False)\n",
+    "fig.show()"
+   ],
+   "id": "0004-c879d58b500c83a0364d8680cc6b05c9cc97d36d3ea3743e112c56644db"
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Transformieren Sie die Daten in 2D (ode 3D) und plotten die\n",
+    "Transformierten Daten als Scatter-Plot mit `y_test` als\n",
+    "Farbunterscheidung."
+   ],
+   "id": "0005-9f3a45468236a64a112ad49260df46a53eb308c1c3e503a34d2ae0c353f"
+  }
+ ],
+ "nbformat": 4,
+ "nbformat_minor": 5,
+ "metadata": {}
+}
+%% Cell type:markdown id:0001-9c88d904212173177e3cd805c405ca6bffb6c39ce47a88ff66351aa9536 tags:
+
+# MNIST visualisieren
+
+In dieser Aufgabe wollen wir einen hochdimensionalen Datensatz in 2D
+(oder 3D) plotten. Die Daten werden schon geladen.
+
+%% Cell type:code id:0002-f9e5f87e267af56fbd5014863286132d368c2876d241287b849ceff60cc tags:
+
+``` 
+import numpy as np
+import plotly.express as px
+from tensorflow.keras.datasets.mnist import load_data
+
+(x_train, y_train), (x_test, y_test) = load_data()
+
+# reshape test set to 10 000 x 784
+X = x_test.reshape(-1, 28 * 28)
+```
+
+%% Cell type:markdown id:0003-fef1281e3edb72c906210479c5811c47fe2289914626b2c40534881280c tags:
+
+Wenn Sie mögen ist hier ein Plot von verschiedenen Bildern der gleichen
+Klasse. So können Sie ein Blick reinwerfen.
+
+%% Cell type:code id:0004-c879d58b500c83a0364d8680cc6b05c9cc97d36d3ea3743e112c56644db tags:
+
+``` 
+# plot 50 examples for each digit
+imgs = np.empty((50, 10, 28, 28))
+for j in range(10):
+    imgs[:, j] = x_test[y_test == j][:50]
+
+fig = px.imshow(imgs, animation_frame=0, facet_col=1, facet_col_wrap=5, binary_string=True)
+fig.update_xaxes(showticklabels=False)
+fig.update_yaxes(showticklabels=False)
+fig.show()
+```
+
+%% Cell type:markdown id:0005-9f3a45468236a64a112ad49260df46a53eb308c1c3e503a34d2ae0c353f tags:
+
+Transformieren Sie die Daten in 2D (ode 3D) und plotten die
+Transformierten Daten als Scatter-Plot mit `y_test` als
+Farbunterscheidung.
--- a/08-korrelation-und-dimensionsreduktion/autos.csv
+++ b/08-korrelation-und-dimensionsreduktion/autos.csv
+Marke,Modell,Grundpreis,Leistung_kW,Hubraum,Leergewicht,Verbrauch_kombi,Tueranzahl,Fahrzeugklasse
+Bugatti,Chiron,2856000,1103,7993,2070,22.5,2,6
+Koenigsegg,Agera RS,2112275,865,5032,1395,14.7,2,6
+Lamborghini,Centenario LP770-4,2082500,566,6498,1520,16,2,6
+Lamborghini,Centenario Roadster LP770-4,2082500,566,6498,1570,16,2,6
+smart,forfour BRABUS,21225,80,898,1095,4.6,5,1
+Abarth,595C,21090,107,1368,1150,6.5,2,1
+Abarth,595,18490,107,1368,1110,6,3,1
+VW,up! GTI,16975,85,999,1070,4.8,3,1
+Opel,ADAM ROCKS 1.2,15780,51,1229,1086,5.3,3,1
+Fiat,500C 1.2 8V,15190,51,1242,980,4.9,2,1
+VW,cross up! 1.0 BMT,14500,55,999,1009,4.3,5,1
+Fiat,Panda Cross 1.2 8V,13490,51,1242,1015,5.1,5,1
+Opel,KARL ROCKS 1.0,12800,55,999,939,4.7,5,1
+Peugeot,108 Top! 1.0 VTi 68,12600,51,998,915,4.1,3,1
+Fiat,500 1.2 8V,12590,51,1242,940,4.9,3,1
+Suzuki,Ignis 1.2,12540,66,1242,885,4.6,5,1
+Citroen,C1 Airscape VTi 68,12400,51,998,915,4.1,3,1
+Opel,ADAM 1.2,12135,51,1229,1086,5.3,3,1
+smart,forfour 1.0,11765,52,999,975,4.2,5,1
+Hyundai,i10 1.0,9990,49,998,1008,4.7,5,1
+KIA,Picanto 1.0,9990,49,998,935,4.4,5,1
+Peugeot,108 1.0 VT 68,9990,51,998,915,4.1,3,1
+VW,up! 1.0,9975,44,999,926,4.4,3,1
+Toyota,Aygo 1.0,9950,51,998,915,4.1,3,1
+Fiat,Panda 1.2 8V,9850,51,1242,1015,5.1,5,1
+Skoda,Citigo 1.0,9770,44,999,929,4.4,3,1
+Renault,Twingo SCe 70,9750,51,999,939,5,5,1
+Suzuki,Celerio 1.0,9690,50,998,880,4.3,5,1
+Opel,KARL 1.0,9560,55,999,939,4.5,5,1
+Citroen,C1 VTi 68,9090,51,998,915,4.1,3,1
+SEAT,Mii 1.0,8990,44,999,929,4.4,3,1
+MINI,John Cooper Works Cabrio,34300,170,1998,1385,6.5,2,2
+Nissan,Juke Nismo RS,31915,157,1618,1469,7.3,5,2
+Audi,S1 Sportback,31300,170,1984,1415,7.1,5,2
+Toyota,Yaris GRMN,30800,156,1798,1135,7.5,5,2
+MINI,John Cooper Works,30700,170,1998,1280,6.3,3,2
+Audi,S1,30450,170,1984,1390,7,3,2
+DS Automobiles,DS 3 Performance,26990,153,1598,1250,5.4,3,2
+Opel,Corsa OPC,24930,152,1598,1293,7.5,3,2
+Peugeot,208.,23990,153,1598,1235,5.4,3,2
+VW,Polo GTI,23950,147,1984,1355,5.9,5,2
+Renault,Clio R.S.,23390,147,1618,1279,5.9,5,2
+MINI,One Cabrio,22500,75,1198,1280,5,2,2
+Honda,HR-V 1.5 i-VTEC,20690,96,1498,1312,5.6,5,2
+DS Automobiles,DS 3 Cabrio PureTech 82,19940,60,1199,1110,4.9,2,2
+Jeep,Renegade 1.6 E-torQ,19900,81,1598,1395,6,5,2
+Opel,Mokka X 1.6 Start&Stop,18990,85,1598,1355,6.7,5,2
+Ford,EcoSport 1.0 EcoBoost,18590,92,998,1337,5.2,5,2
+Citroen,C3 Picasso VTi 95,18190,70,1397,1276,5.9,5,2
+Hyundai,i20 Coupee 1.0 T-GDI,18100,88,998,1145,4.8,3,2
+Ford,EcoSport 1.5 Ti-VCT,17990,82,1498,1314,6.3,5,2
+Mazda,CX-3 SKYACTIV-G 120,17990,88,1998,1230,5.9,5,2
+Suzuki,Vitara 1.6,17990,88,1586,1150,5.3,5,2
+Peugeot,2008 PureTech 82,17550,60,1199,1120,4.9,5,2
+Hyundai,Kona 1.0 T-GDI,17500,88,998,1233,5.2,5,2
+MINI,One First,17350,55,1198,1225,5.2,5,2
+Hyundai,i20 Active 1.0 T-GDI blue,17300,74,998,1160,4.5,5,2
+KIA,Soul 1.6 GDI,17240,97,1591,1275,6.5,5,2
+Audi,A1 Sportback 1.0 TFSI ultra,17100,60,999,1135,4.2,5,2
+Fiat,500L 1.4 16V,16990,70,1368,1330,6.2,5,2
+Fiat,500L Wagon 1.4 16V,16990,70,1368,1350,6.1,5,2
+Opel,Crossland X 1.2,16990,60,1199,1136,5.2,5,2
+Ford,B-MAX 1.4,16800,66,1388,1275,6,5,2
+Honda,Jazz 1.3 i-VTEC,16640,75,1318,1138,5,5,2
+Fiat,500L Urban 1.4 16V,16490,70,1368,1320,6.1,5,2
+MINI,One First,16400,55,1198,1165,5.1,3,2
+Fiat,500X 1.6 E-torQ,16290,81,1598,1350,6.4,5,2
+Audi,A1 1.0 TFSI ultra,16250,60,999,1110,4.2,3,2
+DS Automobiles,DS 3 PureTech 82,15990,60,1199,1049,4.6,3,2
+Nissan,Juke 1.6,15990,69,1598,1163,6,5,2
+SEAT,Arona 1.0 EcoTSI,15990,70,999,1165,4.9,5,2
+SsangYong,Tivoli 1.6 e-XGi 160,15990,94,1597,1270,6.6,5,2
+Renault,Captur ENERGY TCe 90,15890,66,898,1259,5.1,5,2
+Hyundai,ix20 1.4 blue,15790,66,1396,1253,5.6,5,2
+KIA,Stonic 1.2,15790,62,1248,1145,5.2,5,2
+Alfa Romeo,MiTo 1.4 8V,15700,57,1368,1155,5.6,3,2
+Suzuki,Jimny 1.3,15590,62,1328,1135,7.1,3,2
+Citroen,C3 Aircross PureTech 82,15290,60,1199,1163,5.1,5,2
+Ford,Tourneo Courier 1.0 EcoBoost,15260,74,998,1260,5.3,5,2
+Ford,Transit Courier Kombi 1.0 EcoBoost,15220,74,998,1260,5.3,4,2
+Fiat,Fiorino Kombi 1.4 8V,15161,57,1368,1255,6.9,4,2
+KIA,Venga 1.4,14890,66,1396,1253,6,5,2
+Citroen,C4 Cactus PureTech 75,13990,55,1199,1040,4.6,5,2
+Suzuki,Swift 1.2 Dualjet,13790,66,1242,915,4.3,5,2
+Suzuki,Baleno 1.2 Dualjet,13790,66,1242,940,4.2,5,2
+Skoda,Fabia Combi 1.0 MPI,13450,55,999,1104,4.8,5,2
+Nissan,Micra 1.0,12990,52,998,977,4.6,5,2
+Renault,Clio Grandtour 1.2 16V 75,12990,54,1149,1141,5.6,5,2
+VW,Polo 1.0 MPI,12975,48,999,1105,4.7,5,2
+Ford,Fiesta 1.1,12950,51,1084,1108,4.7,3,2
+Mazda,2 SKYACTIV-G 75,12890,55,1496,1045,4.7,5,2
+Fiat,Punto 1.2 8V,12790,51,1242,1105,5.4,5,2
+Peugeot,208 1.2 PureTech 68,12750,50,1199,1035,4.7,3,2
+Toyota,Yaris 1.0,12540,51,998,1055,4.3,3,2
+Fiat,Qubo 1.4 8V,12490,57,1368,1255,6.9,5,2
+SEAT,Ibiza 1.0 MPI,12490,48,999,1091,4.9,5,2
+Skoda,Fabia 1.0 MPI,12150,44,999,1080,4.8,5,2
+Opel,Corsa 1.2,12135,51,1229,1120,5.4,3,2
+Hyundai,i20 1.2,12015,55,1248,1055,5.1,5,2
+Citroen,C3 PureTech 68,11990,50,1199,1051,4.7,5,2
+Renault,Clio 1.2 16V 75,11990,54,1149,1134,5.6,5,2
+KIA,Rio 1.2,11690,62,1248,1110,4.8,5,2
+Lada,Kalina Cross 1.6 8V,10200,64,1596,1110,6.6,5,2
+Dacia,Sandero Stepway TCe 90 Start&Stop,9990,66,898,1115,5.1,5,2
+Ford,Ka+ 1.2 Ti-VCT,9990,51,1198,1055,5,5,2
+Mitsubishi,Space Star 1.0,9290,52,999,920,4.2,5,2
+Lada,Kalina Kombi 1.6 8V,8260,64,1596,1110,6.6,5,2
+Lada,Kalina 1.6 8V,7460,64,1596,1080,6.6,5,2
+Dacia,Sandero SCe 75,6990,54,998,1044,5.2,5,2
+smart,fortwo cabrio BRABUS,23675,80,898,1040,4.6,2,1
+smart,fortwo Coupee BRABUS,20415,80,898,995,4.5,3,1
+smart,fortwo cabrio 1.0,14365,52,999,940,4.3,2,1
+smart,fortwo Coupee 1.0,11105,52,999,890,4.1,3,1
+Morgan,Aero Supersports 4.8 V8,168000,270,4799,1220,11.2,2,4
+BMW,M3 CS,117600,338,2979,1660,8.3,4,4
+BMW,M4 CS Coupee,116900,338,2979,1655,8.4,2,4
+Lotus,Evora 400,96000,298,3456,1415,9.7,2,4
+Alfa Romeo,Stelvio Quadrifoglio,89000,375,2891,1905,9,5,4
+Porsche,Macan Turbo,84586,294,3604,2000,9,5,4
+BMW,M4 Cabrio,84500,317,2979,1825,9.1,2,4
+BMW Alpina,B4 S Bi-Turbo Cabrio,81400,324,2979,1915,8.3,2,4
+Audi,RS5 Coupee,80900,331,2894,1730,8.7,2,4
+Audi,RS4 Avant,79800,331,2894,1790,8.8,5,4
+BMW,M4 Coupee,78200,317,2979,1572,8.8,2,4
+BMW,M3,77500,317,2979,1595,8.8,4,4
+Lexus,RC F,75900,351,4969,1840,10.8,3,4
+BMW Alpina,B4 S Bi-Turbo Coupee,75300,324,2979,1690,7.9,2,4
+Lotus,Exige Coupee,75200,258,3456,1110,10.1,2,4
+Lotus,Exige Roadster,75200,258,3456,1110,10.1,2,4
+Porsche,Macan GTS,74828,265,2997,1970,8.9,5,4
+BMW Alpina,B3 S Bi-Turbo Touring,74700,324,2979,1780,8.1,5,4
+BMW Alpina,B3 S Bi-Turbo,72900,324,2979,1705,7.9,4,4
+Alfa Romeo,Giulia Quadrifoglio,72800,375,2891,1670,8.5,4,4
+Cadillac,ATS-V Coupee,72500,346,3564,1775,11.4,3,4
+Alfa Romeo,4C Spider,72000,177,1742,1015,6.9,2,4
+Cadillac,ATS-V,69900,346,3564,1775,11.6,4,4
+Audi,TT RS Roadster,69200,294,2480,1605,8.3,2,4
+Mercedes,C 43 AMG Cabriolet,68455,270,2996,1870,8.3,2,4
+Audi,S5 Cabriolet,68050,260,2995,1915,7.9,2,4
+Morgan,Roadster 3.7 V6,68000,209,3721,950,9.8,2,4
+Audi,TT RS Coupee,66400,294,2480,1515,8.2,3,4
+Mercedes,GLC Coupee 43 AMG,65807,270,2996,1855,8.4,5,4
+Audi,SQ5 TFSI,65400,260,2995,1945,8.3,5,4
+Alfa Romeo,4C,63500,177,1742,970,6.8,2,4
+Audi,S5 Sportback,62750,260,2995,1735,7.5,5,4
+Audi,S5 Coupee,62750,260,2995,1690,7.5,2,4
+Mercedes,GLC 43 AMG,62178,270,2996,1845,8.3,5,4
+Audi,S4 Avant,61900,260,2995,1750,7.7,5,4
+Mercedes,C 43 AMG T-Modell,61850,270,2996,1735,7.9,5,4
+Mercedes,C 43 AMG Coupee,61761,270,2996,1735,7.8,2,4
+Mercedes,C 43 AMG,60184,270,2996,1690,7.8,4,4
+Audi,S4,60050,260,2995,1705,7.5,4,4
+Mercedes,SLC 43 AMG,60036,270,2996,1595,7.8,2,4
+Alpine,A110,58000,185,1798,1178,6.1,2,4
+Land Rover,Range Rover Velar P250,56400,184,1998,1804,7.6,5,4
+Porsche,Macan,56264,185,1984,1845,7.2,5,4
+Audi,TTS Roadster,53350,228,1984,1525,7.3,2,4
+Jaguar,F-Pace 25t,51160,184,1997,1760,7.4,5,4
+Audi,TTS Coupee,50550,228,1984,1440,7.1,3,4
+Audi,Q5 2.0 TFSI,50500,185,1984,1795,6.8,5,4
+BMW,X4 xDrive20i,49850,135,1997,1810,7.2,5,4
+Mercedes,GLC Coupee 250,49837,155,1991,1785,6.9,5,4
+Opel,Insignia Sports Tourer GSi 2.0 DI Turbo Start&Stop,48800,191,1998,1716,8.7,5,4
+Audi,A4 Allroad 2.0 TFSI,48750,185,1984,1655,6.4,5,4
+Volvo,XC60 T5,48650,184,1969,1915,7.4,5,4
+Jeep,Cherokee 3.2 V6 Pentastar,48000,200,3239,2036,9.6,5,4
+Opel,Insignia Grand Sport GSi 2.0 DI Turbo Start&Stop,47800,191,1998,1683,8.6,5,4
+BMW,420i Cabrio,47700,135,1998,1775,6.2,2,4
+Volvo,S60 Cross Country T5,47050,180,1969,1722,7.4,4,4
+Nissan,370Z Nismo,46880,253,3696,1496,10.6,3,4
+Volvo,V60 Cross Country T5,45950,180,1969,1776,7.4,5,4
+Land Rover,Discovery Sport Si4,45750,177,1998,1796,8,5,4
+Mercedes,GLC 250,45315,155,1991,1735,6.5,5,4
+Infiniti,Q50 2.0t,44900,155,1991,1587,6.3,4,4
+Jeep,Wrangler Unlimited 3.6 V6,44900,209,3604,1995,11.4,5,4
+Infiniti,Q60 2.0t,44500,155,1991,1722,6.8,2,4
+BMW,X3 xDrive20i,44400,135,1998,1790,7.1,5,4
+Audi,A5 Cabriolet 2.0 TFSI,44000,140,1984,1675,5.9,2,4
+KIA,Stinger 2.0 T-GDI,43990,188,1998,1717,7.9,5,4
+VW,Passat Alltrack 2.0 TSI BMT,43925,162,1984,1677,6.9,5,4
+Morgan,4/4 1.8 16V,43009,82,1595,800,8.2,2,4
+Mercedes,C 180 Cabriolet,42727,115,1595,1600,6,2,4
+Infiniti,Q50 2.0t,42500,155,1991,1585,6.3,4,4
+Alfa Romeo,Stelvio 2.0 Turbo 16V,42200,147,1995,1735,7,5,4
+Jeep,Wrangler 3.6 V6,41900,209,3604,1828,11,3,4
+Renault,Espace ENERGY TCe 225,40900,165,1798,1685,6.8,5,4
+BMW,420i Coupee,40400,135,1998,1550,5.8,2,4
+BMW,420i Gran Coupee,40400,135,1998,1595,5.8,5,4
+Cadillac,ATS Coupee 2.0 Turbo,40400,203,1998,1591,7.7,3,4
+BMW,320i Gran Turismo,40200,135,1998,1655,6.1,5,4
+Nissan,370Z Roadster,40130,241,3696,1496,11.2,2,4
+DS Automobiles,DS 7 Crossback PureTech 225,38990,165,1598,1500,5.9,5,4
+Alfa Romeo,Giulia 2.0 Turbo 16V,38500,147,1995,1504,6,4,4
+Audi,A5 Sportback 2.0 TFSI,38050,140,1984,1505,5.8,5,4
+Audi,A5 Coupee 2.0 TFSI,38050,140,1984,1465,5.6,2,4
+Cadillac,ATS 2.0 Turbo,37400,203,1998,1593,7.6,4,4
+Jaguar,XE 20t,36960,147,1997,1540,6.3,4,4
+Subaru,Outback 2.5i,36900,129,2498,1582,7,5,4
+Mercedes,C 180 Coupee,36033,115,1595,1475,5.3,2,4
+Audi,TT Roadster 1.8 TFSI,35550,132,1798,1375,5.9,2,4
+Mercedes,SLC 180,35349,115,1595,1435,5.6,2,4
+Skoda,Kodiaq Scout 1.4 TSI ACT,35050,110,1395,1610,6.8,5,4
+Opel,Insignia Country Tourer 1.5 DI Turbo Start&Stop,34885,121,1490,1522,6.4,5,4
+BMW,318i Touring,34550,100,1499,1545,5.4,5,4
+DS Automobiles,DS 5 THP 165 Stop&Start,34390,121,1598,1504,5.9,5,4
+Nissan,370Z Coupee,34130,241,3696,1496,10.6,3,4
+Audi,A4 Avant 1.4 TFSI,33700,110,1395,1445,5.4,5,4
+Mercedes,C 160 T-Modell,33534,95,1595,1470,5.4,5,4
+VW,Sharan 1.4 TSI BMT,33325,110,1395,1703,6.4,5,4
+Ford,Galaxy 1.5 EcoBoost Start/Stopp,33310,118,1498,1708,6.5,5,4
+Audi,TT Coupee 1.8 TFSI,33150,132,1798,1285,5.8,3,4
+BMW,318i,32850,100,1499,1475,5.1,4,4
+Subaru,BRZ 2.0i,32400,147,1998,1243,7.8,2,4
+Skoda,Octavia Scout 1.8 TSI,32110,132,1798,1522,6.8,5,4
+Volvo,V60 T2,32100,90,1498,1680,5.9,5,4
+Mercedes,C 160,31868,95,1595,1395,5.2,4,4
+Audi,A4 1.4 TFSI,31850,110,1395,1395,5.2,4,4
+Skoda,Octavia Combi RS,31590,169,1984,1442,6.5,5,4
+Hyundai,Santa Fe 2.4 GDI,31190,138,2359,1708,9.4,5,4
+Skoda,Octavia RS,30890,169,1984,1420,6.5,5,4
+Peugeot,508 SW THP 165 STOP&START,30850,121,1598,1495,5.8,5,4
+Renault,Talisman Grandtour Energy TCe 150,30800,110,1618,1565,5.8,5,4
+Volvo,S60 T2,30500,90,1498,1632,5.8,4,4
+SEAT,Alhambra 1.4 TSI Start&Stop,30435,110,1395,1703,6.4,5,4
+Ford,S-MAX 1.5 EcoBoost Start/Stopp,30400,118,1498,1645,6.5,5,4
+Subaru,Levorg 1.6 Turbo,29990,125,1600,1537,6.9,5,4
+Toyota,GT86 2.0,29990,147,1998,1305,7.8,2,4
+VW,Tiguan Allspace 1.4 TSI ACT,29975,110,1395,1570,6.1,5,4
+Peugeot,508 THP 165 STOP&START,29800,121,1598,1475,5.8,4,4
+Renault,Talisman Energy TCe 150,29800,110,1618,1505,5.6,4,4
+Toyota,RAV4 2.0,27990,112,1987,1565,6.7,5,4
+VW,Passat Variant 1.4 TSI BMT,27875,92,1395,1394,5.3,5,4
+Opel,Cascada 1.4 Turbo,27545,88,1364,1701,6.7,2,4
+Ford,Mondeo Turnier 1.0 EcoBoost,26990,92,998,1476,5.3,5,4
+VW,Passat 1.4 TSI BMT,26800,92,1395,1367,5.3,4,4
+Opel,Insignia Sports Tourer 1.5 DI Turbo Start&Stop,26730,103,1490,1487,6,5,4
+Skoda,Kodiaq 1.4 TSI,26150,92,1395,1502,6,5,4
+Ford,Mondeo 1.0 EcoBoost,25990,92,998,1455,5.2,5,4
+KIA,Optima Sportswagon 2.0,25990,120,1999,1550,7.6,5,4
+Subaru,Forester 2.0X,25900,110,1995,1478,6.9,5,4
+Mazda,6 SKYACTIV-G 145 i-ELOOP,25890,107,1998,1375,5.5,4,4
+Mazda,6 Kombi SKYACTIV-G 145 i-ELOOP,25890,107,1998,1380,5.6,5,4
+Toyota,Avensis Touring Sports 1.6,25740,97,1598,1460,6.2,5,4
+Opel,Insignia Grand Sport 1.5 DI Turbo Start&Stop,25630,103,1490,1441,5.9,5,4
+Hyundai,i40 Kombi 1.6 GDI blue,25490,99,1591,1503,6.1,5,4
+Nissan,X-Trail 1.6 DIG-T,25440,120,1618,1505,6.2,5,4
+KIA,Optima 2.0,25090,120,1999,1530,7.4,4,4
+Nissan,X-Trail 1.6 DIG-T,24990,120,1618,1505,6.2,5,4
+Peugeot,5008 1.2 PureTech 130,24900,96,1199,1385,5.1,5,4
+Toyota,Avensis 1.6,24740,97,1598,1430,6.1,4,4
+Honda,CR-V 2.0,23990,114,1997,1531,7.2,5,4
+Mitsubishi,Outlander 2.0 ClearTec,21990,110,1998,1497,6.7,5,4
+Nissan,Evalia 16V 110,20690,81,1598,1386,7.3,5,4
+Nissan,NV200 Kombi 16V 110,19921,81,1598,1351,7.3,5,4
+Skoda,Octavia Combi 1.2 TSI,18150,63,1197,1247,4.8,5,4
+Skoda,Octavia 1.2 TSI,17450,63,1197,1225,4.8,5,4
+Nissan,GT-R Nismo,184950,441,3799,1800,11.8,3,5
+Jaguar,F-Type SVR Cabriolet 5.0 V8 Kompressor,146400,423,5000,1720,11.3,2,5
+Jaguar,F-Type SVR Coupee 5.0 V8 Kompressor,139400,423,5000,1705,11.3,3,5
+Porsche,Cayenne Turbo,138850,404,3996,2250,11.9,5,5
+Porsche,Cayenne Turbo,132781,382,4806,2260,11.2,5,5
+BMW,X6 M,124200,423,4395,2265,11.1,5,5
+Mercedes,CLS 63 AMG Shooting Brake,122630,410,5461,2025,10.6,5,5
+Audi,RS7 performance cod Sportback,122200,445,3993,2005,9.5,5,5
+BMW,X5 M,120700,423,4395,2350,11.1,5,5
+BMW,M5,117900,441,4395,1930,10.5,4,5
+Mercedes,CLS 63 AMG Coupee,116918,410,5461,1870,9.9,4,5
+BMW Alpina,B5 Bi-Turbo Touring,115300,447,4395,2120,10.4,5,5
+Audi,RS6 cod Avant,112000,412,3993,2025,9.8,5,5
+BMW Alpina,B5 Bi-Turbo,112000,447,4395,2015,10.3,4,5
+Porsche,Cayenne GTS,102555,324,3604,2185,9.8,5,5
+Lexus,GS F,100500,351,4969,1865,11.2,4,5
+Nissan,GT-R,99900,419,3799,1827,11.8,3,5
+Cadillac,CTS-V,98900,477,6162,1925,13,4,5
+Dodge,Charger SRT 392,85900,362,6417,2000,15.5,4,5
+Audi,S7 cod Sportback,84600,331,3993,2030,9.3,5,5
+Dodge,Challenger SRT 392,82900,362,6417,2000,15.5,2,5
+Audi,S6 cod Avant,80150,331,3993,2035,9.4,5,5
+Mercedes,E 43 AMG T-Modell,78177,295,2996,1930,8.6,5,5
+Porsche,718 Boxster GTS,78160,269,2497,1450,9,2,5
+Audi,S6 cod,77650,331,3993,1970,9.2,4,5
+Mercedes,GLE Coupee 43 AMG,77469,270,2996,2240,8.9,5,5
+Porsche,718 Cayman GTS,76137,269,2497,1450,9,2,5
+Maserati,Levante,76000,257,2979,2109,10.7,4,5
+Mercedes,E 43 AMG,75387,295,2996,1840,8.2,4,5
+Porsche,Cayenne,74828,250,2995,1985,9,5,5
+BMW,X6 xDrive35i,72000,225,2979,2100,8.5,5,5
+Mercedes,GLE 43 AMG,70746,270,2996,2180,8.6,5,5
+Maserati,Ghibli,70250,257,2979,1810,8.9,4,5
+Maserati,Ghibli,69200,243,2979,1810,8.9,4,5
+Mercedes,GLE Coupee 400,68306,245,2996,2180,8.7,5,5
+BMW,X5 xDrive35i,66400,225,2979,2105,8.5,5,5
+Jaguar,F-Type Cabriolet P300,66200,221,1997,1545,7.2,2,5
+Mercedes,CLS 400 Shooting Brake,65212,245,3498,1845,7.3,5,5
+Mercedes,CLS 400 Coupee,63427,245,3498,1775,7.4,4,5
+BMW,630i Gran Turismo,62300,190,1998,1720,6.2,5,5
+Dodge,RAM 1500 Quad Cab 5.7 V8,61900,295,5700,2556,12.8,4,5
+Mercedes,GLE 400,61583,245,2996,2130,8.5,5,5
+Infiniti,Q70 3.7,60750,235,3696,1826,10.8,4,5
+Volvo,XC90 T5,59850,184,1969,2112,7.8,5,5
+Jaguar,F-Type Coupee P300,59200,221,1997,1525,7.2,3,5
+Volvo,V90 Cross Country T5,57800,184,1969,1937,7.3,5,5
+Porsche,718.,54717,220,1988,1410,7.4,2,5
+Land Rover,Discovery Si4,54700,221,1997,2093,9.4,5,5
+Mercedes,E 200 Cabriolet,54228,135,1991,1755,6.2,3,5
+Infiniti,QX70 3.7,53800,235,3696,2012,12.1,5,5
+Porsche,718.,52694,220,1988,1410,7.4,2,5
+Jeep,Grand Cherokee 3.6 V6,51900,213,3604,2266,10,5,5
+Jaguar,XF Sportbrake 25t,51060,184,1997,1760,6.8,5,5
+Lexus,RX 200t,49900,175,1998,1885,7.8,5,5
+Cadillac,XT5 3.6 V6,49300,231,3649,1954,10,5,5
+BMW,520i Touring,49100,135,1998,1705,5.8,5,5
+Mercedes,E 200 T-Modell,48903,135,1991,1705,6.2,5,5
+Chevrolet,Camaro Cabriolet 2.0 Turbo,48000,202,1998,1659,8.1,2,5
+BMW,520i,46600,135,1998,1605,5.4,4,5
+Mercedes,E 200 Coupee,46494,135,1991,1645,6.5,3,5
+Cadillac,CTS 2.0 Turbo,45350,203,1998,1659,7.8,4,5
+Audi,A6 Avant 1.8 TFSI ultra,45200,140,1798,1710,5.9,5,5
+Jaguar,XF 20t,45060,147,1997,1635,6.8,4,5
+Volvo,V90 T4,44900,140,1969,1851,6.9,5,5
+VW,T6 California 2.0 TSI BMT,44833,110,1984,2264,9.5,4,5
+Ford,Mustang Convertible 2.3 EcoBoost,43500,213,2261,1715,9.1,2,5
+Volvo,S90 T4,43450,140,1969,1800,6.7,4,5
+Mercedes,E 200,43019,135,1991,1575,6.1,4,5
+Audi,A6 1.8 TFSI ultra,42700,140,1798,1645,5.7,4,5
+Ford,Mustang Convertible 2.3 EcoBoost,42500,233,2261,1715,8.2,2,5
+Chevrolet,Camaro Coupee 2.0 Turbo,40400,202,1998,1539,8,2,5
+Ford,Mustang Fastback 2.3 EcoBoost,39000,213,2261,1655,9,2,5
+VW,T6 Caravelle 2.0 TSI BMT,38645,110,1984,1862,9.1,4,5
+Ford,Mustang Fastback 2.3 EcoBoost,38000,233,2261,1655,8,2,5
+VW,T6 Multivan 2.0 TSI BMT,36902,110,1984,2007,9.2,4,5
+VW,Arteon 1.5 TSI ACT,35325,110,1498,1504,5.1,5,5
+VW,T6 Transporter Kombi 2.0 TSI BMT Normaldach,33832,110,1984,1862,9.1,4,5
+Skoda,Superb Combi 1.4 TSI,26750,92,1395,1395,5.6,5,5
+Skoda,Superb 1.4 TSI,25750,92,1395,1375,5.6,5,5
+Mercedes,Maybach G 650,749700,463,5980,2580,17,5,6
+Ford,GT,500000,475,3497,1385,14.9,2,6
+Rolls-Royce,Phantom 6.8 V12,446250,420,6749,2560,13.9,4,6
+Lamborghini,Aventador S Roadster LP740-4,373262,544,6498,1625,16.9,2,6
+Mercedes,Maybach S 650 Cabriolet,357000,463,5980,2115,12,2,6
+Lamborghini,Aventador S LP740-4,335055,544,6498,1575,16.9,2,6
+Rolls-Royce,Dawn 6.6 V12,329630,420,6592,2560,14.2,2,6
+Bentley,Mulsanne,297191,377,6752,2685,15,4,6
+Bentley,Continental Supersports Convertible,291253,522,5998,2455,15.9,2,6
+Rolls-Royce,Wraith 6.6 V12,285898,465,6592,2435,14.3,2,6
+Porsche,911 GT2 RS,285220,515,3800,1545,11.8,2,6
+Ferrari,812.,282934,588,6496,1630,14.9,2,6
+Rolls-Royce,Ghost 6.6 V12,277657,420,6592,2435,14.3,4,6
+Aston Martin,Vanquish Volante,268995,424,5935,1919,12.8,3,6
+Bentley,Continental Supersports,264775,522,5998,2280,15.7,2,6
+Mercedes,S 65 AMG Cabriolet,257457,463,5980,2255,12,2,6
+Aston Martin,Vanquish,253995,424,5935,1814,12.8,3,6
+McLaren,720S,247350,527,3994,1322,10.7,2,6
+Ferrari,F488 Spider,236750,493,3902,1525,11.4,2,6
+Mercedes,G 500 4x4,231693,310,3982,3021,13.8,5,6
+Ferrari,GTC4Lusso T,226246,449,3855,1870,11.6,2,6
+Ferrari,F488 GTB,212653,493,3902,1475,11.4,2,6
+McLaren,570S Spider,208975,419,3799,1573,10.7,2,6
+Bentley,Bentayga W12,208488,447,5950,2440,12.8,5,6
+Lamborghini,Urus,204000,478,3996,2200,12.7,5,6
+Aston Martin,DB11 Volante V8,199000,375,3982,1870,9.9,3,6
+Bentley,Continental GT W12,198492,467,5950,2244,12.2,2,6
+Lamborghini,Huracn Spyder LP580-2,196350,426,5204,1509,12.1,2,6
+McLaren,570GT,195350,419,3799,1515,10.7,2,6
+Aston Martin,Rapide S,193995,411,5935,2065,12.9,5,6
+Aston Martin,V12 Vantage S Roadster,192741,421,5935,1745,14.7,3,6
+Bentley,Continental GT Convertible V8,192066,373,3993,2470,10.9,2,6
+Porsche,911 Turbo Cabriolet,190020,397,3800,1740,9.3,2,6
+Mercedes,S 63 AMG Cabriolet,190013,430,5461,2185,10.4,2,6
+Porsche,911.,189544,368,3996,1445,13.3,2,6
+McLaren,570S,185400,419,3799,1515,10.7,2,6
+Ferrari,California T,184689,412,3855,1730,10.7,2,6
+Aston Martin,DB11 V8,184000,375,3982,1760,9.9,3,6
+Bentley,Flying Spur V8,183855,373,3993,2417,10.9,4,6
+Donkervoort,D8 GTO-RS,182070,284,2480,695,8,2,6
+Aston Martin,V12 Vantage S,179950,421,5935,1680,17,3,6
+Lamborghini,Huracn LP580-2,178500,426,5204,1389,11.9,2,6
+Mercedes,S 63 AMG Coupee,177310,450,3982,2080,9.3,2,6
+Porsche,911 Turbo Coupee,176930,397,3800,1670,9.1,2,6
+Mercedes,S 63 AMG Coupee,175436,430,5461,2070,10.1,2,6
+Bentley,Continental GT V8,174573,373,3993,2370,10.6,2,6
+McLaren,540C,163200,397,3799,1446,10.7,2,6
+Mercedes,SL 63 AMG,161959,430,5461,1845,9.8,2,6
+Mercedes,S 63 AMG,160293,450,3982,2070,8.9,4,6
+Porsche,Panamera Sport Turismo Turbo,158604,404,3996,2110,9.4,5,6
+Porsche,Panamera Turbo,155748,404,3996,2070,9.3,5,6
+Audi,R8 Spyder 5.2 FSI V10,153000,397,5204,1755,12.6,2,6
+Porsche,911.,152416,368,3996,1488,12.9,2,6
+BMW Alpina,B7 Bi-Turbo,149400,447,4395,2110,10.4,4,6
+Porsche,911.,146228,331,2981,1660,9.7,2,6
+Mercedes,G 63 AMG,145359,420,5461,2550,13.8,5,6
+Maserati,GranCabrio Sport,144320,338,4691,1980,14.5,2,6
+Jaguar,XJR575,143900,423,5000,1875,11.1,4,6
+Mercedes,S 500 Cabriolet,140545,335,4663,2115,8.5,2,6
+Audi,R8 Coupee 5.2 FSI V10,140000,397,5204,1665,12.4,2,6
+Mercedes,Maybach S 560,139700,345,3982,2240,8.8,4,6
+Porsche,911 Carrera Cabriolet,138850,331,2981,1595,9.4,2,6
+Donkervoort,D8 GTO-S,138040,254,2480,740,8,2,6
+BMW,M6 Cabrio,137200,412,4395,2055,10.3,2,6
+BMW Alpina,B6 Bi-Turbo Cabriolet,137200,441,4395,2095,9.6,2,6
+BMW Alpina,B6 Bi-Turbo Gran Coupee,135800,441,4395,2030,10.4,4,6
+Aston Martin,V8 Vantage S Roadster,135520,321,4735,1710,13.8,2,6
+Mercedes,GLS 63 AMG,135482,430,5461,2580,12.3,5,6
+BMW,M6 Gran Coupee,134500,412,4395,1950,9.9,4,6
+Land Rover,Range Rover Sport SVR,132200,423,5000,2310,12.8,5,6
+BMW,M6 Coupee,129600,412,4395,1925,9.9,2,6
+Land Rover,Range Rover Sport SVR,129600,405,5000,2330,12.8,5,6
+BMW Alpina,B6 Bi-Turbo Coupee,129200,441,4395,1940,9.4,2,6
+Mercedes,AMG GT Roadster,129180,350,3982,1670,9.4,2,6
+Maserati,GranTurismo Sport,129020,338,4691,1880,14.3,2,6
+Aston Martin,V8 Vantage AMR,126995,320,4735,1610,13.8,3,6
+Porsche,911 Carrera Coupee,125760,331,2981,1525,9.4,2,6
+Chevrolet,Corvette Z06 Cabriolet,124700,485,6162,1734,12.7,2,6
+Land Rover,Range Rover 5.0 V8 SC,121800,375,5000,2336,12.8,5,6
+Chevrolet,Corvette Z06 Coupee,119700,485,6162,1734,12.7,3,6
+Audi,S8 cod,118500,382,3993,2050,9.4,4,6
+Porsche,911.,118382,272,2981,1645,8.9,2,6
+Mercedes,AMG GT Coupee,117280,350,3982,1615,9.3,2,6
+Porsche,911 Carrera Cabriolet,111004,272,2981,1575,8.5,2,6
+Porsche,911 Carrera T Coupee,107553,272,2981,1500,9.5,2,6
+Mercedes,G 500,106701,310,3982,2595,12.3,5,6
+Audi,A8 4.0 TFSI cod,104400,320,3993,1955,8.9,4,6
+Mercedes,S 450 Coupee,101656,270,2996,2050,8.9,2,6
+Chevrolet,Corvette Grand Sport Cabriolet 6.2 V8,100900,343,6162,1614,12.3,2,6
+Mercedes,S 400 Coupee,100561,270,2996,2035,8.3,2,6
+Cadillac,Escalade 6.2 V8,99900,313,6162,2710,12.6,5,6
+Mercedes,SL 400,99341,270,2996,1735,7.7,2,6
+Porsche,911 Carrera Coupee,97914,272,2981,1505,8.3,2,6
+Porsche,Panamera Sport Turismo 4,97557,243,2995,1955,7.8,5,6
+Maserati,Quattroporte,97430,257,2979,1860,9.1,4,6
+Chevrolet,Corvette Grand Sport Coupe 6.2 V8,95900,343,6162,1588,12.3,3,6
+Land Rover,Range Rover Sport 5.0 V8 SC,94900,375,5000,2306,12.8,5,6
+Jaguar,XJ 3.0 V6 Kompressor,93800,250,2995,1865,9.8,4,6
+BMW,740i,93000,240,2998,1800,6.8,4,6
+Mercedes,S 450,92255,270,2987,1995,6.6,4,6
+Porsche,Panamera,90655,243,2995,1890,7.5,5,6
+BMW,640i Cabrio,90600,235,2979,1895,7.7,2,6
+Chevrolet,Corvette Stingray Cabriolet 6.2 V8,85400,343,6162,1664,12.3,2,6
+BMW,640i Gran Coupe,83900,235,2979,1825,7.6,4,6
+BMW,640i Coupe,81900,235,2979,1760,7.6,2,6
+Chevrolet,Corvette Stingray Coupe 6.2 V8,80400,343,6162,1614,12.3,3,6
+Mercedes,GLS 400,77029,245,2996,2435,8.9,5,6
+Cadillac,CT6 3.0 V6,73500,307,2997,1879,9.6,4,6
+Land Rover,Range Rover Sport 2.0 Si4,65600,221,1997,2083,9.2,5,6
+Land Rover,Range Rover Evoque Coupe Si4,62200,213,1998,1833,7.6,3,3
+BMW,M2 Coupe,59500,272,2979,1570,8.5,2,3
+Mercedes,CLA 45 AMG Shooting Brake,57804,280,1991,1615,6.9,5,3
+Mercedes,CLA 45 AMG,57209,280,1991,1585,6.9,4,3
+Mercedes,GLA 45 AMG,56852,280,1991,1585,7.4,5,3
+Audi,RS3 Limousine,55900,294,2480,1590,8.3,4,3
+Land Rover,Range Rover Evoque Cabriolet Si4,55300,177,1998,2013,8.2,2,3
+Audi,RS3 Sportback,54600,294,2480,1585,8.3,5,3
+Mercedes,A 45 AMG,51527,280,1991,1555,6.9,5,3
+Audi,S3 Cabriolet,51150,228,1984,1710,6.7,2,3
+VW,Golf R Variant,45350,228,1984,1593,7.1,5,3
+Subaru,Impreza WRX STi 2.5,44500,221,2457,1527,10.9,4,3
+Land Rover,Range Rover Evoque Si4,43850,177,1998,1752,8.2,5,3
+Audi,S3 Limousine,43250,228,1984,1505,7,4,3
+Audi,S3 Sportback,42350,228,1984,1505,7,5,3
+Jaguar,E-Pace P250,42350,183,1998,1832,7.7,5,3
+Subaru,Impreza WRX STi 2.5,41550,221,2457,1575,10.4,4,3
+Audi,S3,41450,228,1984,1480,7,3,3
+VW,Golf R,41175,228,1984,1483,7.8,3,3
+Ford,Focus RS,40675,257,2261,1560,7.7,5,3
+Infiniti,QX30 2.0t,40150,155,1991,1542,6.7,5,3
+Lotus,Elise,39900,100,1598,876,6.3,2,3
+MINI,John Cooper Works Countryman,39500,170,1998,1615,7.4,5,3
+BMW,X2 sDrive20i,39200,141,1998,1535,5.5,5,3
+MINI,John Cooper Works Clubman,36800,170,1998,1550,7.4,5,3
+Opel,Astra OPC,36360,206,1998,1550,7.8,3,3
+Honda,Civic Type R,36050,235,1996,1380,7.7,5,3
+SEAT,Leon ST Cupra 300,35930,221,1984,1440,7,5,3
+Peugeot,308.,35350,200,1598,1280,6,5,3
+SEAT,Leon Cupra 300,34730,221,1984,1395,6.9,5,3
+SEAT,Leon SC Cupra 300,34340,221,1984,1375,6.9,3,3
+VW,Touran 1.2 TSI BMT,34300,81,1197,1436,5.5,5,3
+BMW,218i Cabrio,34200,100,1499,1575,5.5,2,3
+VW,Golf Alltrack 1.8 TSI BMT,34125,132,1798,1537,6.7,5,3
+Mazda,CX-5 SKYACTIV-G 160,32190,118,1998,1495,6.8,5,3
+BMW,X1 sDrive18i,31700,103,1499,1475,5.5,5,3
+Audi,A3 Cabriolet 1.4 TFSI,31450,85,1395,1430,5.3,2,3
+Volvo,XC40 T3,31350,114,1498,1725,6.8,5,3
+Ford,Focus Turnier ST 2.0 EcoBoost Start/Stopp,30550,184,1999,1461,6.8,5,3
+VW,Golf GTI,30425,169,1984,1364,6.4,3,3
+Mercedes,CLA 180 Shooting Brake,30274,90,1595,1430,5.5,5,3
+Mazda,MX-5 RF SKYACTIV-G 160,29890,118,1998,1120,6.9,2,3
+BMW,218i Coupe,29750,100,1499,1420,5.1,2,3
+Hyundai,i30 N,29700,184,1998,1475,7,5,3
+Mercedes,CLA 180,29679,90,1595,1395,5.4,4,3
+Ford,Focus ST 2.0 EcoBoost Start/Stopp,29600,184,1999,1437,6.8,5,3
+Mercedes,GLA 180,28941,90,1595,1395,5.7,5,3
+Audi,Q3 1.4 TFSI,28700,92,1395,1460,5.8,5,3
+BMW,216i Gran Tourer,28600,75,1499,1475,5.3,5,3
+Volvo,V40 Cross Country T3,28280,112,1969,1569,5.6,5,3
+BMW,216i Active Tourer,27350,75,1499,1415,5.4,5,3
+VW,Tiguan 1.4 TSI,26975,92,1395,1490,6.1,5,3
+Mercedes,B 160,26638,75,1595,1395,5.5,5,3
+Audi,A3 Limousine 1.0 TFSI,25550,85,999,1260,4.4,4,3
+Honda,Civic Limousine 1.5 Turbo,25520,134,1498,1321,5.7,4,3
+DS Automobiles,DS 4 Crossback PureTech 130 Stop&Start,25490,96,1199,1330,4.9,5,3
+KIA,pro_ceed GT,25390,150,1591,1395,7.4,3,3
+KIA,ceed GT,25390,150,1591,1382,7.4,5,3
+Fiat,124 Spider 1.4 Multiair Turbo,24990,103,1368,1125,6.4,2,3
+Fiat,124 Spider 1.4 Multiair Turbo,24990,103,1368,1125,6.4,2,3
+Hyundai,Veloster 1.6 Turbo,24990,137,1591,1333,6.9,4,3
+SEAT,Leon X-PERIENCE 1.4 TSI Start&Stop,24950,92,1395,1263,5.3,5,3
+VW,Scirocco 1.4 TSI BMT,24950,92,1395,1280,5.4,3,3
+Jeep,Compass 1.4 Multiair 140,24900,103,1368,1505,6.2,5,3
+Volvo,V40 T2,24850,90,1969,1546,5.6,5,3
+VW,Caddy Alltrack 1.2 TSI BMT,24782,62,1197,1350,6.1,5,3
+BMW,116i,24700,80,1499,1375,5.3,3,3
+Mercedes,A 160,24681,75,1595,1370,5.4,5,3
+Audi,A3 Sportback 1.0 TFSI,24650,85,999,1255,4.5,5,3
+Honda,Civic Tourer 1.8,24590,104,1798,1355,6.2,5,3
+Skoda,Karoq 1.0 TSI,24290,85,999,1340,5.1,5,3
+Infiniti,Q30 1.6t,24200,90,1595,1407,5.7,5,3
+MINI,One Countryman,24000,75,1499,1440,5.5,5,3
+DS Automobiles,DS 4 PureTech 130 Stop&Start,23990,96,1199,1330,4.9,5,3
+KIA,pro_ceed 1.0 T-GDI 120 ISG,23990,88,998,1271,4.9,3,3
+Opel,Zafira 1.4 Turbo,23950,88,1364,1628,6.8,5,3
+Audi,A3 1.0 TFSI,23750,85,999,1225,4.5,3,3
+Opel,Grandland X 1.2 DI Turbo Start&Stop,23700,96,1199,1350,5.4,5,3
+Renault,Grand Sconic ENERGY TCe 115,23690,85,1197,1505,6.1,5,3
+VW,Beetle Cabriolet 1.2 TSI BMT,23450,77,1197,1395,5.4,2,3
+Audi,Q2 1.0 TFSI ultra,23400,85,999,1280,5.1,5,3
+Ford,Kuga 1.5 EcoBoost Start/Stopp,23300,88,1498,1579,6.3,5,3
+Peugeot,3008 1.2 PureTech 130,23250,96,1199,1325,5.1,5,3
+Mazda,MX-5 SKYACTIV-G 131,22990,96,1496,1050,6,2,3
+Subaru,XV 1.6i,22980,84,1600,1408,6.4,5,3
+VW,Caddy Beach 1.2 TSI BMT,22943,62,1197,1350,6.1,5,3
+MINI,One Clubman,22850,75,1499,1375,5.1,5,3
+Hyundai,Tucson 1.6 GDI blue    ,22740,97,1591,1454,6.3,5,3
+Hyundai,i30 Fastback 1.0 T-GDI,22200,88,  998,1460,5.2,5,3
+Toyota,C-HR 1.2 T,21990,85,1197,1320,5.9,5,3
+Subaru,Impreza 1.6i,21980,84,1600,1359,6.2,5,3
+VW,Golf Variant 1.0 TSI BMT,21850,81,999,1295,4.9,5,3
+Mazda,3 SKYACTIV-G 120,21790,88,1998,1280,5.1,4,3
+Toyota,Verso 1.6,21765,97,1598,1505,6.8,5,3
+Alfa Romeo,Giulietta 1.4 TB 16V,21500,88,1368,1355,6.2,5,3
+Opel,Astra GTC 1.4 Turbo,21360,88,1364,1437,6.3,3,3
+Toyota,Corolla 1.6,21220,97,1598,1270,6,4,3
+Citroen,Grand C4 Picasso PureTech 130 Stop&Start,20990,96,1199,1370,5,5,3
+Ford,Grand C-MAX 1.0 EcoBoost Start/Stopp,20850,74,998,1493,5.2,5,3
+Nissan,Qashqai 1.2 DIG-T,20490,85,1197,1350,5.6,5,3
+VW,Golf Sportsvan 1.0 TSI,20475,63,999,1335,4.9,5,3
+VW,Golf Sportsvan 1.2 TSI BMT,20475,63,1197,1320,5,5,3
+VW,T-Roc 1.0 TSI,20390,85,999,1270,5.1,5,3
+Ford,Tourneo Connect 1.0 EcoBoost Start/Stopp,20249,74,998,1474,5.6,5,3
+Opel,Astra 1.6,20220,85,1598,1405,6.8,4,3
+Honda,Civic 1.0 Turbo,19990,95,988,1229,4.8,5,3
+KIA,Carens 1.6 GDI,19990,99,1591,1458,6.5,5,3
+KIA,Sportage 1.6 GDI,19990,97,1591,1397,6.7,5,3
+Mercedes,Citan Tourer lang 112,19990,84,1192,1440,6.2,5,3
+Renault,Sconic ENERGY TCe 115,19990,85,1197,1503,5.8,5,3
+Renault,Kadjar ENERGY TCe 130,19990,96,1197,1381,5.7,5,3
+SEAT,Ateca 1.0 TSI Ecomotive,19990,85,999,1280,5.2,5,3
+SsangYong,Korando 2.0 e-XGi 200,19990,110,1998,1612,7.5,5,3
+Subaru,XV 1.6i,19990,84,1600,1370,6.5,5,3
+Peugeot,308 SW 1.2 PureTech 110,19800,81,1199,1265,4.7,5,3
+Suzuki,SX4 S-Cross 1.0 Boosterjet,19790,82,998,1165,5,5,3
+Citroen,C4 Picasso PureTech 110 Stop&Start,18990,81,1199,1355,5.1,5,3
+Mitsubishi,ASX 1.6 ClearTec,18990,86,1590,1335,5.7,5,3
+Ford,Focus 1.0 EcoBoost Start/Stopp,18700,74,998,1303,4.8,4,3
+Peugeot,308 1.2 PureTech 110,18700,81,1199,1155,4.6,5,3
+Subaru,Impreza 1.6i,18600,84,1600,1380,6.2,5,3
+Opel,Astra Sports Tourer 1.4,18550,74,1399,1273,5.7,5,3
+VW,Caddy 1.2 TSI BMT,18528,62,1197,1350,6.1,4,3
+Mitsubishi,Lancer 1.6 ClearTec,18490,86,1590,1305,5.5,4,3
+Mitsubishi,Lancer Sportback 1.6 ClearTec,18490,86,1590,1345,5.5,5,3
+Renault,Megane Grandtour ENERGY TCe 100,18490,74,1197,1366,5.4,5,3
+Hyundai,i30 Kombi 1.4,18450,74,1368,1285,5.6,5,3
+VW,Caddy Kombi 1.2 TSI BMT,18445,62,1197,1350,6.1,4,3
+Nissan,Pulsar 1.2 DIG-T,18270,85,1197,1265,5,5,3
+Ford,C-MAX 1.6 Ti-VCT,18250,63,1596,1374,6.4,5,3
+Mazda,3 SKYACTIV-G 100,18190,74,1496,1260,5.1,5,3
+VW,Golf 1.0 TSI BMT,18075,63,999,1206,4.8,3,3
+Fiat,DoblKombi 1.4 16V,17990,70,1368,1370,7.4,5,3
+SEAT,Toledo 1.2 TSI,17990,66,1197,1156,4.7,5,3
+Citroen,Berlingo Kombi VTi 95,17850,72,1598,1395,6.4,4,3
+Peugeot,Partner Tepee VTi 98,17850,72,1598,1550,6.4,4,3
+Ford,Focus Turnier 1.6 Ti-VCT,17700,63,1596,1300,6,5,3
+Toyota,Auris Touring Sports 1.33,17690,73,1329,1250,5.6,5,3
+Opel,Astra 1.4,17550,74,1399,1244,5.5,5,3
+Renault,Megane ENERGY TCe 100,17490,74,1197,1280,5.4,5,3
+SsangYong,XLV 1.6 e-XGi 160,17490,94,1597,1390,7.1,5,3
+Hyundai,i30 1.4,17450,74,1368,1244,5.4,5,3
+Citroen,C4 PureTech 110,17240,81,1199,1275,4.8,5,3
+Renault,Kangoo ENERGY TCe 115,17150,84,1197,1395,6.2,4,3
+SEAT,Leon ST 1.2 TSI,16640,63,1197,1233,5.1,5,3
+Toyota,Auris 1.33,16490,73,1329,1225,5.5,5,3
+Fiat,Tipo Kombi 1.4 16V,16450,70,1368,1280,5.7,5,3
+Ford,Focus 1.6 Ti-VCT,16450,63,1596,1264,5.9,5,3
+KIA,ceed Sportswagon 1.4,16190,73,1368,1279,6,5,3
+Skoda,Rapid 1.0 TSI,15890,70,999,1170,4.4,5,3
+Skoda,Rapid Spaceback 1.0 TSI,15790,70,999,1165,4.4,5,3
+SEAT,Leon 1.2 TSI,15490,63,1197,1188,5.1,5,3
+Fiat,Tipo 1.4 16V,15450,70,1368,1270,5.7,5,3
+Opel,Combo Combi 1.4,15110,70,1364,1445,7.4,5,3
+SEAT,Leon SC 1.2 TSI,14990,63,1197,1168,5.1,3,3
+KIA,ceed 1.4,14490,73,1368,1254,6,5,3
+Fiat,Tipo 1.4 16V,14450,70,1368,1225,5.7,4,3
+Dacia,Lodgy Stepway TCe 115 Start&Stop,14200,85,1197,1278,5.6,5,3
+Dacia,Dokker Stepway TCe 115 Start&Stop,13600,85,1197,1280,5.7,5,3
+Citroen,C-Elysee PureTech 82,12990,60,1199,1055,4.8,4,3
+Lada,Vesta 1.6 16V,12740,78,1596,1250,6.1,4,3
+Dacia,Logan MCV Stepway TCe 90 Start&Stop,12200,66,898,1165,5.1,5,3
+Lada,Urban 1.7,11990,61,1690,1285,9.5,3,3
+Dacia,Duster SCe 115,11290,84,1598,1262,6.6,5,3
+Lada,Taiga 1.7,10790,61,1690,1285,9.5,3,3
+Dacia,Duster SCe 115 Start&Stop,10690,84,1598,1165,6.4,5,3
+Dacia,Lodgy SCe 100 Start&Stop,9990,75,1598,1211,6.1,5,3
+Dacia,Dokker SCe 100 Start&Stop,8990,75,1598,1239,6.2,4,3
+Lada,Granta 1.6 8V,8500,64,1596,1080,6.6,5,3
+Dacia,Logan MCV SCe 75,7990,54,998,1091,5.4,5,3
+Lada,Granta 1.6 8V,7260,64,1596,1080,6.6,4,3
\ No newline at end of file
--- a/08-korrelation-und-dimensionsreduktion/datasaurus.csv
+++ b/08-korrelation-und-dimensionsreduktion/datasaurus.csv
+dataset,x,y
+dino,55.3846,97.1795
+dino,51.5385,96.0256
+dino,46.1538,94.4872
+dino,42.8205,91.4103
+dino,40.7692,88.3333
+dino,38.7179,84.8718
+dino,35.641,79.8718
+dino,33.0769,77.5641
+dino,28.9744,74.4872
+dino,26.1538,71.4103
+dino,23.0769,66.4103
+dino,22.3077,61.7949
+dino,22.3077,57.1795
+dino,23.3333,52.9487
+dino,25.8974,51.0256
+dino,29.4872,51.0256
+dino,32.8205,51.0256
+dino,35.3846,51.4103
+dino,40.2564,51.4103
+dino,44.1026,52.9487
+dino,46.6667,54.1026
+dino,50,55.2564
+dino,53.0769,55.641
+dino,56.6667,56.0256
+dino,59.2308,57.9487
+dino,61.2821,62.1795
+dino,61.5385,66.4103
+dino,61.7949,69.1026
+dino,57.4359,55.2564
+dino,54.8718,49.8718
+dino,52.5641,46.0256
+dino,48.2051,38.3333
+dino,49.4872,42.1795
+dino,51.0256,44.1026
+dino,45.3846,36.4103
+dino,42.8205,32.5641
+dino,38.7179,31.4103
+dino,35.1282,30.2564
+dino,32.5641,32.1795
+dino,30,36.7949
+dino,33.5897,41.4103
+dino,36.6667,45.641
+dino,38.2051,49.1026
+dino,29.7436,36.0256
+dino,29.7436,32.1795
+dino,30,29.1026
+dino,32.0513,26.7949
+dino,35.8974,25.2564
+dino,41.0256,25.2564
+dino,44.1026,25.641
+dino,47.1795,28.718
+dino,49.4872,31.4103
+dino,51.5385,34.8718
+dino,53.5897,37.5641
+dino,55.1282,40.641
+dino,56.6667,42.1795
+dino,59.2308,44.4872
+dino,62.3077,46.0256
+dino,64.8718,46.7949
+dino,67.9487,47.9487
+dino,70.5128,53.718
+dino,71.5385,60.641
+dino,71.5385,64.4872
+dino,69.4872,69.4872
+dino,46.9231,79.8718
+dino,48.2051,84.1026
+dino,50,85.2564
+dino,53.0769,85.2564
+dino,55.3846,86.0256
+dino,56.6667,86.0256
+dino,56.1538,82.9487
+dino,53.8462,80.641
+dino,51.2821,78.718
+dino,50,78.718
+dino,47.9487,77.5641
+dino,29.7436,59.8718
+dino,29.7436,62.1795
+dino,31.2821,62.5641
+dino,57.9487,99.4872
+dino,61.7949,99.1026
+dino,64.8718,97.5641
+dino,68.4615,94.1026
+dino,70.7692,91.0256
+dino,72.0513,86.4103
+dino,73.8462,83.3333
+dino,75.1282,79.1026
+dino,76.6667,75.2564
+dino,77.6923,71.4103
+dino,79.7436,66.7949
+dino,81.7949,60.2564
+dino,83.3333,55.2564
+dino,85.1282,51.4103
+dino,86.4103,47.5641
+dino,87.9487,46.0256
+dino,89.4872,42.5641
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