diff --git a/Aufgaben/01 - linear regression - 1 feature.ipynb b/Aufgaben/01 - linear regression - 1 feature.ipynb
index 937e5f7..b555913 100644
--- a/Aufgaben/01 - linear regression - 1 feature.ipynb	
+++ b/Aufgaben/01 - linear regression - 1 feature.ipynb	
@@ -1066,7 +1066,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.12"
+   "version": "3.12.8"
   },
   "varInspector": {
    "cols": {
diff --git a/Aufgaben/05 - lineare regression - sklearn.ipynb b/Aufgaben/05 - lineare regression - sklearn.ipynb
new file mode 100644
index 0000000..81a6be4
--- /dev/null
+++ b/Aufgaben/05 - lineare regression - sklearn.ipynb	
@@ -0,0 +1,381 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "f19ad4d1",
+   "metadata": {},
+   "source": [
+    "# Lineare Regression mit scikit-learn"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "fca110ae",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "# plotting settings\n",
+    "pd.plotting.register_matplotlib_converters()\n",
+    "import matplotlib.pyplot as plt\n",
+    "%matplotlib inline\n",
+    "import seaborn as sns\n",
+    "from sklearn.linear_model import LinearRegression"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "6edf6b65",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>BuildingArea</th>\n",
+       "      <th>Rooms</th>\n",
+       "      <th>Price</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>79.0</td>\n",
+       "      <td>2</td>\n",
+       "      <td>1035000.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>150.0</td>\n",
+       "      <td>3</td>\n",
+       "      <td>1465000.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>142.0</td>\n",
+       "      <td>4</td>\n",
+       "      <td>1600000.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>6</th>\n",
+       "      <td>210.0</td>\n",
+       "      <td>3</td>\n",
+       "      <td>1876000.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>7</th>\n",
+       "      <td>107.0</td>\n",
+       "      <td>2</td>\n",
+       "      <td>1636000.0</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   BuildingArea  Rooms      Price\n",
+       "1          79.0      2  1035000.0\n",
+       "2         150.0      3  1465000.0\n",
+       "4         142.0      4  1600000.0\n",
+       "6         210.0      3  1876000.0\n",
+       "7         107.0      2  1636000.0"
+      ]
+     },
+     "execution_count": 2,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "melbourne_file_path = 'data/melb_data.csv'\n",
+    "melbourne_data = pd.read_csv(melbourne_file_path)\n",
+    "melbourne_data = melbourne_data.dropna(axis=0)  # entfernen von Daten mit fehlenden Werten\n",
+    "# wählen für unser Beispiel einen kleinen Ausschnitt aus den Daten (denselben, wie im ersten Beispiel)\n",
+    "max_area = 400\n",
+    "max_datapoints = 100\n",
+    "data = melbourne_data[melbourne_data['BuildingArea'] < max_area][:max_datapoints][['BuildingArea', 'Rooms', 'Price']]\n",
+    "data.head()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7b226e29",
+   "metadata": {},
+   "source": [
+    "Die scikit-learn API erwartet die Trainingsdaten (Inputs, Features) ähnlich zu unserer Feature-Matrix als 2D-Array, allerdings ohne der '1'."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "9e851d19",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([1, 2, 3])"
+      ]
+     },
+     "execution_count": 3,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "r = np.array([1,2,3])\n",
+    "r"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "a2903e63",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "array([[1],\n",
+       "       [2],\n",
+       "       [3]])"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "# ändern eines Vektors der Länge n in eine Matrix der Dimension n x 1:\n",
+    "r.reshape((-1,1))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "89d8210c",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x = data[['BuildingArea'] ].to_numpy(copy=True).reshape((-1, 1))\n",
+    "y = data['Price'].to_numpy(copy=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "b0d5c350",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(100, 1)"
+      ]
+     },
+     "execution_count": 6,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "x.shape"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "bd1d76e9",
+   "metadata": {
+    "scrolled": true
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "w0: 441524.4208318128\n",
+      "w1: [6024.22929588]\n"
+     ]
+    }
+   ],
+   "source": [
+    "model = LinearRegression().fit(x, y)\n",
+    "# print model parameters\n",
+    "print('w0: {}'.format(model.intercept_))\n",
+    "print('w1: {}'.format(model.coef_))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "12eacd13",
+   "metadata": {},
+   "source": [
+    "Vergleichen Sie die Werte mit der selbstprogrammierten Lösung!"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c5f6e509",
+   "metadata": {},
+   "source": [
+    "**Achtung:** Alle scikit-learn Modelle haben Parameter, die das Verhalten beeinflussen. Mehr in der scikit-learn Dokumentation, z.B. hier für LinearRegression: https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "055183fa",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "erklärte Varianz (R^2): 0.22971025499088593\n"
+     ]
+    }
+   ],
+   "source": [
+    "r_sq = model.score(x, y)\n",
+    "print('erklärte Varianz (R^2): {}'.format(r_sq))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5a66667c",
+   "metadata": {},
+   "source": [
+    "Vorhersage mit trainiertem scikit-learn Modell"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "b81f3f03",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Preis-Vorhersage für ein neues Haus mit Wohnfläche 287: [2170478.22874863]\n"
+     ]
+    }
+   ],
+   "source": [
+    "building_area_new_house = [[287]]\n",
+    "y_pred = model.predict(building_area_new_house)\n",
+    "print('Preis-Vorhersage für ein neues Haus mit Wohnfläche {}: {}'.format(building_area_new_house[0][0], y_pred))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "0d1da016",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Preis-Vorhersagen für Objekte mit den Wohnflächen [[287], [80], [110]]: [2170478.22874863  923462.76450201 1104189.64337833]\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Vorhersage für mehrere Objekte auf einmal\n",
+    "building_area_new_houses = [[287], [80], [110]]\n",
+    "y_preds = model.predict(building_area_new_houses)\n",
+    "print('Preis-Vorhersagen für Objekte mit den Wohnflächen {}: {}'.format(building_area_new_houses, y_preds))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5aac9e7a",
+   "metadata": {},
+   "source": [
+    "Alle scikit-learm Modelle haben bestimmte Funktionen, insbesondere `model.fit()` und `model.predict()`, sodass es sehr einfach ist, verschiedene ML-Modelle auszuprobieren."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f39ef84b",
+   "metadata": {},
+   "source": [
+    "**Aufgabe: Mehrere Input-Features ausprobieren!**"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.13.1"
+  },
+  "varInspector": {
+   "cols": {
+    "lenName": 16,
+    "lenType": 16,
+    "lenVar": 40
+   },
+   "kernels_config": {
+    "python": {
+     "delete_cmd_postfix": "",
+     "delete_cmd_prefix": "del ",
+     "library": "var_list.py",
+     "varRefreshCmd": "print(var_dic_list())"
+    },
+    "r": {
+     "delete_cmd_postfix": ") ",
+     "delete_cmd_prefix": "rm(",
+     "library": "var_list.r",
+     "varRefreshCmd": "cat(var_dic_list()) "
+    }
+   },
+   "types_to_exclude": [
+    "module",
+    "function",
+    "builtin_function_or_method",
+    "instance",
+    "_Feature"
+   ],
+   "window_display": false
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/requirements.txt b/requirements.txt
index cdc4384..b4696d1 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -31,6 +31,7 @@ ipywidgets==8.1.5
 isoduration==20.11.0
 jedi==0.19.2
 Jinja2==3.1.5
+joblib==1.4.2
 json5==0.10.0
 jsonpointer==3.0.0
 jsonschema==4.23.0
@@ -86,6 +87,8 @@ requests==2.32.3
 rfc3339-validator==0.1.4
 rfc3986-validator==0.1.1
 rpds-py==0.22.3
+scikit-learn==1.6.1
+scipy==1.15.1
 seaborn==0.13.2
 Send2Trash==1.8.3
 setuptools==75.8.0
@@ -94,6 +97,7 @@ sniffio==1.3.1
 soupsieve==2.6
 stack-data==0.6.3
 terminado==0.18.1
+threadpoolctl==3.5.0
 tinycss2==1.4.0
 tornado==6.4.2
 tqdm==4.67.1
diff --git a/tasks/03skykit-regularisierung.ipynb b/tasks/03skykit-regularisierung.ipynb
new file mode 100644
index 0000000..9dc473c
--- /dev/null
+++ b/tasks/03skykit-regularisierung.ipynb
@@ -0,0 +1,1079 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "id": "0c067959-88f2-4579-ba5f-b4fe8a3b81fe",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "# plotting settings\n",
+    "pd.plotting.register_matplotlib_converters()\n",
+    "import matplotlib.pyplot as plt\n",
+    "%matplotlib inline\n",
+    "import seaborn as sns\n",
+    "import sklearn\n",
+    "from sklearn.linear_model import LinearRegression,Ridge\n",
+    "from sklearn.pipeline import make_pipeline\n",
+    "from sklearn.preprocessing import StandardScaler, PolynomialFeatures"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "f068fcd9-6023-4f40-87fe-3323ef241ab1",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
+       "        vertical-align: middle;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
+       "    }\n",
+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>BuildingArea</th>\n",
+       "      <th>Rooms</th>\n",
+       "      <th>Price</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>79.0</td>\n",
+       "      <td>2</td>\n",
+       "      <td>1035000.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>150.0</td>\n",
+       "      <td>3</td>\n",
+       "      <td>1465000.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>142.0</td>\n",
+       "      <td>4</td>\n",
+       "      <td>1600000.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>6</th>\n",
+       "      <td>210.0</td>\n",
+       "      <td>3</td>\n",
+       "      <td>1876000.0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>7</th>\n",
+       "      <td>107.0</td>\n",
+       "      <td>2</td>\n",
+       "      <td>1636000.0</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "   BuildingArea  Rooms      Price\n",
+       "1          79.0      2  1035000.0\n",
+       "2         150.0      3  1465000.0\n",
+       "4         142.0      4  1600000.0\n",
+       "6         210.0      3  1876000.0\n",
+       "7         107.0      2  1636000.0"
+      ]
+     },
+     "execution_count": 4,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "melbourne_file_path = 'data/melb_data.csv'\n",
+    "melbourne_data = pd.read_csv(melbourne_file_path)\n",
+    "melbourne_data = melbourne_data.dropna(axis=0)  # entfernen von Daten mit fehlenden Werten\n",
+    "# wählen für unser Beispiel einen kleinen Ausschnitt aus den Daten (denselben, wie im ersten Beispiel)\n",
+    "max_area = 400\n",
+    "max_datapoints = 10\n",
+    "data = melbourne_data[melbourne_data['BuildingArea'] < max_area][:max_datapoints][['BuildingArea', 'Rooms', 'Price']]\n",
+    "data.head()\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "d09ea079-2ec7-4e6c-ba46-497874008564",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "x = data[['BuildingArea'] ].to_numpy(copy=True).reshape((-1, 1))\n",
+    "y = data['Price'].to_numpy(copy=True)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 24,
+   "id": "41a5faf5-33a0-4b71-bb3c-7255d09602a4",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<style>#sk-container-id-6 {\n",
+       "  /* Definition of color scheme common for light and dark mode */\n",
+       "  --sklearn-color-text: #000;\n",
+       "  --sklearn-color-text-muted: #666;\n",
+       "  --sklearn-color-line: gray;\n",
+       "  /* Definition of color scheme for unfitted estimators */\n",
+       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
+       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
+       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
+       "  --sklearn-color-unfitted-level-3: chocolate;\n",
+       "  /* Definition of color scheme for fitted estimators */\n",
+       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
+       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
+       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
+       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
+       "\n",
+       "  /* Specific color for light theme */\n",
+       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
+       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
+       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
+       "  --sklearn-color-icon: #696969;\n",
+       "\n",
+       "  @media (prefers-color-scheme: dark) {\n",
+       "    /* Redefinition of color scheme for dark theme */\n",
+       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
+       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
+       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
+       "    --sklearn-color-icon: #878787;\n",
+       "  }\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 {\n",
+       "  color: var(--sklearn-color-text);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 pre {\n",
+       "  padding: 0;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 input.sk-hidden--visually {\n",
+       "  border: 0;\n",
+       "  clip: rect(1px 1px 1px 1px);\n",
+       "  clip: rect(1px, 1px, 1px, 1px);\n",
+       "  height: 1px;\n",
+       "  margin: -1px;\n",
+       "  overflow: hidden;\n",
+       "  padding: 0;\n",
+       "  position: absolute;\n",
+       "  width: 1px;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 div.sk-dashed-wrapped {\n",
+       "  border: 1px dashed var(--sklearn-color-line);\n",
+       "  margin: 0 0.4em 0.5em 0.4em;\n",
+       "  box-sizing: border-box;\n",
+       "  padding-bottom: 0.4em;\n",
+       "  background-color: var(--sklearn-color-background);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 div.sk-container {\n",
+       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
+       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
+       "     so we also need the `!important` here to be able to override the\n",
+       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
+       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
+       "  display: inline-block !important;\n",
+       "  position: relative;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 div.sk-text-repr-fallback {\n",
+       "  display: none;\n",
+       "}\n",
+       "\n",
+       "div.sk-parallel-item,\n",
+       "div.sk-serial,\n",
+       "div.sk-item {\n",
+       "  /* draw centered vertical line to link estimators */\n",
+       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
+       "  background-size: 2px 100%;\n",
+       "  background-repeat: no-repeat;\n",
+       "  background-position: center center;\n",
+       "}\n",
+       "\n",
+       "/* Parallel-specific style estimator block */\n",
+       "\n",
+       "#sk-container-id-6 div.sk-parallel-item::after {\n",
+       "  content: \"\";\n",
+       "  width: 100%;\n",
+       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
+       "  flex-grow: 1;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 div.sk-parallel {\n",
+       "  display: flex;\n",
+       "  align-items: stretch;\n",
+       "  justify-content: center;\n",
+       "  background-color: var(--sklearn-color-background);\n",
+       "  position: relative;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 div.sk-parallel-item {\n",
+       "  display: flex;\n",
+       "  flex-direction: column;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 div.sk-parallel-item:first-child::after {\n",
+       "  align-self: flex-end;\n",
+       "  width: 50%;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 div.sk-parallel-item:last-child::after {\n",
+       "  align-self: flex-start;\n",
+       "  width: 50%;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 div.sk-parallel-item:only-child::after {\n",
+       "  width: 0;\n",
+       "}\n",
+       "\n",
+       "/* Serial-specific style estimator block */\n",
+       "\n",
+       "#sk-container-id-6 div.sk-serial {\n",
+       "  display: flex;\n",
+       "  flex-direction: column;\n",
+       "  align-items: center;\n",
+       "  background-color: var(--sklearn-color-background);\n",
+       "  padding-right: 1em;\n",
+       "  padding-left: 1em;\n",
+       "}\n",
+       "\n",
+       "\n",
+       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
+       "clickable and can be expanded/collapsed.\n",
+       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
+       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
+       "*/\n",
+       "\n",
+       "/* Pipeline and ColumnTransformer style (default) */\n",
+       "\n",
+       "#sk-container-id-6 div.sk-toggleable {\n",
+       "  /* Default theme specific background. It is overwritten whether we have a\n",
+       "  specific estimator or a Pipeline/ColumnTransformer */\n",
+       "  background-color: var(--sklearn-color-background);\n",
+       "}\n",
+       "\n",
+       "/* Toggleable label */\n",
+       "#sk-container-id-6 label.sk-toggleable__label {\n",
+       "  cursor: pointer;\n",
+       "  display: flex;\n",
+       "  width: 100%;\n",
+       "  margin-bottom: 0;\n",
+       "  padding: 0.5em;\n",
+       "  box-sizing: border-box;\n",
+       "  text-align: center;\n",
+       "  align-items: start;\n",
+       "  justify-content: space-between;\n",
+       "  gap: 0.5em;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 label.sk-toggleable__label .caption {\n",
+       "  font-size: 0.6rem;\n",
+       "  font-weight: lighter;\n",
+       "  color: var(--sklearn-color-text-muted);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 label.sk-toggleable__label-arrow:before {\n",
+       "  /* Arrow on the left of the label */\n",
+       "  content: \"▸\";\n",
+       "  float: left;\n",
+       "  margin-right: 0.25em;\n",
+       "  color: var(--sklearn-color-icon);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 label.sk-toggleable__label-arrow:hover:before {\n",
+       "  color: var(--sklearn-color-text);\n",
+       "}\n",
+       "\n",
+       "/* Toggleable content - dropdown */\n",
+       "\n",
+       "#sk-container-id-6 div.sk-toggleable__content {\n",
+       "  max-height: 0;\n",
+       "  max-width: 0;\n",
+       "  overflow: hidden;\n",
+       "  text-align: left;\n",
+       "  /* unfitted */\n",
+       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 div.sk-toggleable__content.fitted {\n",
+       "  /* fitted */\n",
+       "  background-color: var(--sklearn-color-fitted-level-0);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 div.sk-toggleable__content pre {\n",
+       "  margin: 0.2em;\n",
+       "  border-radius: 0.25em;\n",
+       "  color: var(--sklearn-color-text);\n",
+       "  /* unfitted */\n",
+       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 div.sk-toggleable__content.fitted pre {\n",
+       "  /* unfitted */\n",
+       "  background-color: var(--sklearn-color-fitted-level-0);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
+       "  /* Expand drop-down */\n",
+       "  max-height: 200px;\n",
+       "  max-width: 100%;\n",
+       "  overflow: auto;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
+       "  content: \"▾\";\n",
+       "}\n",
+       "\n",
+       "/* Pipeline/ColumnTransformer-specific style */\n",
+       "\n",
+       "#sk-container-id-6 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
+       "  color: var(--sklearn-color-text);\n",
+       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
+       "  background-color: var(--sklearn-color-fitted-level-2);\n",
+       "}\n",
+       "\n",
+       "/* Estimator-specific style */\n",
+       "\n",
+       "/* Colorize estimator box */\n",
+       "#sk-container-id-6 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
+       "  /* unfitted */\n",
+       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
+       "  /* fitted */\n",
+       "  background-color: var(--sklearn-color-fitted-level-2);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 div.sk-label label.sk-toggleable__label,\n",
+       "#sk-container-id-6 div.sk-label label {\n",
+       "  /* The background is the default theme color */\n",
+       "  color: var(--sklearn-color-text-on-default-background);\n",
+       "}\n",
+       "\n",
+       "/* On hover, darken the color of the background */\n",
+       "#sk-container-id-6 div.sk-label:hover label.sk-toggleable__label {\n",
+       "  color: var(--sklearn-color-text);\n",
+       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
+       "}\n",
+       "\n",
+       "/* Label box, darken color on hover, fitted */\n",
+       "#sk-container-id-6 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
+       "  color: var(--sklearn-color-text);\n",
+       "  background-color: var(--sklearn-color-fitted-level-2);\n",
+       "}\n",
+       "\n",
+       "/* Estimator label */\n",
+       "\n",
+       "#sk-container-id-6 div.sk-label label {\n",
+       "  font-family: monospace;\n",
+       "  font-weight: bold;\n",
+       "  display: inline-block;\n",
+       "  line-height: 1.2em;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 div.sk-label-container {\n",
+       "  text-align: center;\n",
+       "}\n",
+       "\n",
+       "/* Estimator-specific */\n",
+       "#sk-container-id-6 div.sk-estimator {\n",
+       "  font-family: monospace;\n",
+       "  border: 1px dotted var(--sklearn-color-border-box);\n",
+       "  border-radius: 0.25em;\n",
+       "  box-sizing: border-box;\n",
+       "  margin-bottom: 0.5em;\n",
+       "  /* unfitted */\n",
+       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 div.sk-estimator.fitted {\n",
+       "  /* fitted */\n",
+       "  background-color: var(--sklearn-color-fitted-level-0);\n",
+       "}\n",
+       "\n",
+       "/* on hover */\n",
+       "#sk-container-id-6 div.sk-estimator:hover {\n",
+       "  /* unfitted */\n",
+       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 div.sk-estimator.fitted:hover {\n",
+       "  /* fitted */\n",
+       "  background-color: var(--sklearn-color-fitted-level-2);\n",
+       "}\n",
+       "\n",
+       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
+       "\n",
+       "/* Common style for \"i\" and \"?\" */\n",
+       "\n",
+       ".sk-estimator-doc-link,\n",
+       "a:link.sk-estimator-doc-link,\n",
+       "a:visited.sk-estimator-doc-link {\n",
+       "  float: right;\n",
+       "  font-size: smaller;\n",
+       "  line-height: 1em;\n",
+       "  font-family: monospace;\n",
+       "  background-color: var(--sklearn-color-background);\n",
+       "  border-radius: 1em;\n",
+       "  height: 1em;\n",
+       "  width: 1em;\n",
+       "  text-decoration: none !important;\n",
+       "  margin-left: 0.5em;\n",
+       "  text-align: center;\n",
+       "  /* unfitted */\n",
+       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
+       "  color: var(--sklearn-color-unfitted-level-1);\n",
+       "}\n",
+       "\n",
+       ".sk-estimator-doc-link.fitted,\n",
+       "a:link.sk-estimator-doc-link.fitted,\n",
+       "a:visited.sk-estimator-doc-link.fitted {\n",
+       "  /* fitted */\n",
+       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
+       "  color: var(--sklearn-color-fitted-level-1);\n",
+       "}\n",
+       "\n",
+       "/* On hover */\n",
+       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
+       ".sk-estimator-doc-link:hover,\n",
+       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
+       ".sk-estimator-doc-link:hover {\n",
+       "  /* unfitted */\n",
+       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
+       "  color: var(--sklearn-color-background);\n",
+       "  text-decoration: none;\n",
+       "}\n",
+       "\n",
+       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
+       ".sk-estimator-doc-link.fitted:hover,\n",
+       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
+       ".sk-estimator-doc-link.fitted:hover {\n",
+       "  /* fitted */\n",
+       "  background-color: var(--sklearn-color-fitted-level-3);\n",
+       "  color: var(--sklearn-color-background);\n",
+       "  text-decoration: none;\n",
+       "}\n",
+       "\n",
+       "/* Span, style for the box shown on hovering the info icon */\n",
+       ".sk-estimator-doc-link span {\n",
+       "  display: none;\n",
+       "  z-index: 9999;\n",
+       "  position: relative;\n",
+       "  font-weight: normal;\n",
+       "  right: .2ex;\n",
+       "  padding: .5ex;\n",
+       "  margin: .5ex;\n",
+       "  width: min-content;\n",
+       "  min-width: 20ex;\n",
+       "  max-width: 50ex;\n",
+       "  color: var(--sklearn-color-text);\n",
+       "  box-shadow: 2pt 2pt 4pt #999;\n",
+       "  /* unfitted */\n",
+       "  background: var(--sklearn-color-unfitted-level-0);\n",
+       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
+       "}\n",
+       "\n",
+       ".sk-estimator-doc-link.fitted span {\n",
+       "  /* fitted */\n",
+       "  background: var(--sklearn-color-fitted-level-0);\n",
+       "  border: var(--sklearn-color-fitted-level-3);\n",
+       "}\n",
+       "\n",
+       ".sk-estimator-doc-link:hover span {\n",
+       "  display: block;\n",
+       "}\n",
+       "\n",
+       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
+       "\n",
+       "#sk-container-id-6 a.estimator_doc_link {\n",
+       "  float: right;\n",
+       "  font-size: 1rem;\n",
+       "  line-height: 1em;\n",
+       "  font-family: monospace;\n",
+       "  background-color: var(--sklearn-color-background);\n",
+       "  border-radius: 1rem;\n",
+       "  height: 1rem;\n",
+       "  width: 1rem;\n",
+       "  text-decoration: none;\n",
+       "  /* unfitted */\n",
+       "  color: var(--sklearn-color-unfitted-level-1);\n",
+       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 a.estimator_doc_link.fitted {\n",
+       "  /* fitted */\n",
+       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
+       "  color: var(--sklearn-color-fitted-level-1);\n",
+       "}\n",
+       "\n",
+       "/* On hover */\n",
+       "#sk-container-id-6 a.estimator_doc_link:hover {\n",
+       "  /* unfitted */\n",
+       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
+       "  color: var(--sklearn-color-background);\n",
+       "  text-decoration: none;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-6 a.estimator_doc_link.fitted:hover {\n",
+       "  /* fitted */\n",
+       "  background-color: var(--sklearn-color-fitted-level-3);\n",
+       "}\n",
+       "</style><div id=\"sk-container-id-6\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>PolynomialFeatures(degree=4)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator  sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-6\" type=\"checkbox\" checked><label for=\"sk-estimator-id-6\" class=\"sk-toggleable__label  sk-toggleable__label-arrow\"><div><div>PolynomialFeatures</div></div><div><a class=\"sk-estimator-doc-link \" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.6/modules/generated/sklearn.preprocessing.PolynomialFeatures.html\">?<span>Documentation for PolynomialFeatures</span></a><span class=\"sk-estimator-doc-link \">i<span>Not fitted</span></span></div></label><div class=\"sk-toggleable__content \"><pre>PolynomialFeatures(degree=4)</pre></div> </div></div></div></div>"
+      ],
+      "text/plain": [
+       "PolynomialFeatures(degree=4)"
+      ]
+     },
+     "execution_count": 24,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pfeats = PolynomialFeatures(4)\n",
+    "pfeats"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 27,
+   "id": "fbb2ddae-a717-41be-8eb5-c777f60344c9",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<style>#sk-container-id-7 {\n",
+       "  /* Definition of color scheme common for light and dark mode */\n",
+       "  --sklearn-color-text: #000;\n",
+       "  --sklearn-color-text-muted: #666;\n",
+       "  --sklearn-color-line: gray;\n",
+       "  /* Definition of color scheme for unfitted estimators */\n",
+       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
+       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
+       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
+       "  --sklearn-color-unfitted-level-3: chocolate;\n",
+       "  /* Definition of color scheme for fitted estimators */\n",
+       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
+       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
+       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
+       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
+       "\n",
+       "  /* Specific color for light theme */\n",
+       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
+       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
+       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
+       "  --sklearn-color-icon: #696969;\n",
+       "\n",
+       "  @media (prefers-color-scheme: dark) {\n",
+       "    /* Redefinition of color scheme for dark theme */\n",
+       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
+       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
+       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
+       "    --sklearn-color-icon: #878787;\n",
+       "  }\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 {\n",
+       "  color: var(--sklearn-color-text);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 pre {\n",
+       "  padding: 0;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 input.sk-hidden--visually {\n",
+       "  border: 0;\n",
+       "  clip: rect(1px 1px 1px 1px);\n",
+       "  clip: rect(1px, 1px, 1px, 1px);\n",
+       "  height: 1px;\n",
+       "  margin: -1px;\n",
+       "  overflow: hidden;\n",
+       "  padding: 0;\n",
+       "  position: absolute;\n",
+       "  width: 1px;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 div.sk-dashed-wrapped {\n",
+       "  border: 1px dashed var(--sklearn-color-line);\n",
+       "  margin: 0 0.4em 0.5em 0.4em;\n",
+       "  box-sizing: border-box;\n",
+       "  padding-bottom: 0.4em;\n",
+       "  background-color: var(--sklearn-color-background);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 div.sk-container {\n",
+       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
+       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
+       "     so we also need the `!important` here to be able to override the\n",
+       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
+       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
+       "  display: inline-block !important;\n",
+       "  position: relative;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 div.sk-text-repr-fallback {\n",
+       "  display: none;\n",
+       "}\n",
+       "\n",
+       "div.sk-parallel-item,\n",
+       "div.sk-serial,\n",
+       "div.sk-item {\n",
+       "  /* draw centered vertical line to link estimators */\n",
+       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
+       "  background-size: 2px 100%;\n",
+       "  background-repeat: no-repeat;\n",
+       "  background-position: center center;\n",
+       "}\n",
+       "\n",
+       "/* Parallel-specific style estimator block */\n",
+       "\n",
+       "#sk-container-id-7 div.sk-parallel-item::after {\n",
+       "  content: \"\";\n",
+       "  width: 100%;\n",
+       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
+       "  flex-grow: 1;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 div.sk-parallel {\n",
+       "  display: flex;\n",
+       "  align-items: stretch;\n",
+       "  justify-content: center;\n",
+       "  background-color: var(--sklearn-color-background);\n",
+       "  position: relative;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 div.sk-parallel-item {\n",
+       "  display: flex;\n",
+       "  flex-direction: column;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 div.sk-parallel-item:first-child::after {\n",
+       "  align-self: flex-end;\n",
+       "  width: 50%;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 div.sk-parallel-item:last-child::after {\n",
+       "  align-self: flex-start;\n",
+       "  width: 50%;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 div.sk-parallel-item:only-child::after {\n",
+       "  width: 0;\n",
+       "}\n",
+       "\n",
+       "/* Serial-specific style estimator block */\n",
+       "\n",
+       "#sk-container-id-7 div.sk-serial {\n",
+       "  display: flex;\n",
+       "  flex-direction: column;\n",
+       "  align-items: center;\n",
+       "  background-color: var(--sklearn-color-background);\n",
+       "  padding-right: 1em;\n",
+       "  padding-left: 1em;\n",
+       "}\n",
+       "\n",
+       "\n",
+       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
+       "clickable and can be expanded/collapsed.\n",
+       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
+       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
+       "*/\n",
+       "\n",
+       "/* Pipeline and ColumnTransformer style (default) */\n",
+       "\n",
+       "#sk-container-id-7 div.sk-toggleable {\n",
+       "  /* Default theme specific background. It is overwritten whether we have a\n",
+       "  specific estimator or a Pipeline/ColumnTransformer */\n",
+       "  background-color: var(--sklearn-color-background);\n",
+       "}\n",
+       "\n",
+       "/* Toggleable label */\n",
+       "#sk-container-id-7 label.sk-toggleable__label {\n",
+       "  cursor: pointer;\n",
+       "  display: flex;\n",
+       "  width: 100%;\n",
+       "  margin-bottom: 0;\n",
+       "  padding: 0.5em;\n",
+       "  box-sizing: border-box;\n",
+       "  text-align: center;\n",
+       "  align-items: start;\n",
+       "  justify-content: space-between;\n",
+       "  gap: 0.5em;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 label.sk-toggleable__label .caption {\n",
+       "  font-size: 0.6rem;\n",
+       "  font-weight: lighter;\n",
+       "  color: var(--sklearn-color-text-muted);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 label.sk-toggleable__label-arrow:before {\n",
+       "  /* Arrow on the left of the label */\n",
+       "  content: \"▸\";\n",
+       "  float: left;\n",
+       "  margin-right: 0.25em;\n",
+       "  color: var(--sklearn-color-icon);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 label.sk-toggleable__label-arrow:hover:before {\n",
+       "  color: var(--sklearn-color-text);\n",
+       "}\n",
+       "\n",
+       "/* Toggleable content - dropdown */\n",
+       "\n",
+       "#sk-container-id-7 div.sk-toggleable__content {\n",
+       "  max-height: 0;\n",
+       "  max-width: 0;\n",
+       "  overflow: hidden;\n",
+       "  text-align: left;\n",
+       "  /* unfitted */\n",
+       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 div.sk-toggleable__content.fitted {\n",
+       "  /* fitted */\n",
+       "  background-color: var(--sklearn-color-fitted-level-0);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 div.sk-toggleable__content pre {\n",
+       "  margin: 0.2em;\n",
+       "  border-radius: 0.25em;\n",
+       "  color: var(--sklearn-color-text);\n",
+       "  /* unfitted */\n",
+       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 div.sk-toggleable__content.fitted pre {\n",
+       "  /* unfitted */\n",
+       "  background-color: var(--sklearn-color-fitted-level-0);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
+       "  /* Expand drop-down */\n",
+       "  max-height: 200px;\n",
+       "  max-width: 100%;\n",
+       "  overflow: auto;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
+       "  content: \"▾\";\n",
+       "}\n",
+       "\n",
+       "/* Pipeline/ColumnTransformer-specific style */\n",
+       "\n",
+       "#sk-container-id-7 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
+       "  color: var(--sklearn-color-text);\n",
+       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
+       "  background-color: var(--sklearn-color-fitted-level-2);\n",
+       "}\n",
+       "\n",
+       "/* Estimator-specific style */\n",
+       "\n",
+       "/* Colorize estimator box */\n",
+       "#sk-container-id-7 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
+       "  /* unfitted */\n",
+       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
+       "  /* fitted */\n",
+       "  background-color: var(--sklearn-color-fitted-level-2);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 div.sk-label label.sk-toggleable__label,\n",
+       "#sk-container-id-7 div.sk-label label {\n",
+       "  /* The background is the default theme color */\n",
+       "  color: var(--sklearn-color-text-on-default-background);\n",
+       "}\n",
+       "\n",
+       "/* On hover, darken the color of the background */\n",
+       "#sk-container-id-7 div.sk-label:hover label.sk-toggleable__label {\n",
+       "  color: var(--sklearn-color-text);\n",
+       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
+       "}\n",
+       "\n",
+       "/* Label box, darken color on hover, fitted */\n",
+       "#sk-container-id-7 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
+       "  color: var(--sklearn-color-text);\n",
+       "  background-color: var(--sklearn-color-fitted-level-2);\n",
+       "}\n",
+       "\n",
+       "/* Estimator label */\n",
+       "\n",
+       "#sk-container-id-7 div.sk-label label {\n",
+       "  font-family: monospace;\n",
+       "  font-weight: bold;\n",
+       "  display: inline-block;\n",
+       "  line-height: 1.2em;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 div.sk-label-container {\n",
+       "  text-align: center;\n",
+       "}\n",
+       "\n",
+       "/* Estimator-specific */\n",
+       "#sk-container-id-7 div.sk-estimator {\n",
+       "  font-family: monospace;\n",
+       "  border: 1px dotted var(--sklearn-color-border-box);\n",
+       "  border-radius: 0.25em;\n",
+       "  box-sizing: border-box;\n",
+       "  margin-bottom: 0.5em;\n",
+       "  /* unfitted */\n",
+       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 div.sk-estimator.fitted {\n",
+       "  /* fitted */\n",
+       "  background-color: var(--sklearn-color-fitted-level-0);\n",
+       "}\n",
+       "\n",
+       "/* on hover */\n",
+       "#sk-container-id-7 div.sk-estimator:hover {\n",
+       "  /* unfitted */\n",
+       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 div.sk-estimator.fitted:hover {\n",
+       "  /* fitted */\n",
+       "  background-color: var(--sklearn-color-fitted-level-2);\n",
+       "}\n",
+       "\n",
+       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
+       "\n",
+       "/* Common style for \"i\" and \"?\" */\n",
+       "\n",
+       ".sk-estimator-doc-link,\n",
+       "a:link.sk-estimator-doc-link,\n",
+       "a:visited.sk-estimator-doc-link {\n",
+       "  float: right;\n",
+       "  font-size: smaller;\n",
+       "  line-height: 1em;\n",
+       "  font-family: monospace;\n",
+       "  background-color: var(--sklearn-color-background);\n",
+       "  border-radius: 1em;\n",
+       "  height: 1em;\n",
+       "  width: 1em;\n",
+       "  text-decoration: none !important;\n",
+       "  margin-left: 0.5em;\n",
+       "  text-align: center;\n",
+       "  /* unfitted */\n",
+       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
+       "  color: var(--sklearn-color-unfitted-level-1);\n",
+       "}\n",
+       "\n",
+       ".sk-estimator-doc-link.fitted,\n",
+       "a:link.sk-estimator-doc-link.fitted,\n",
+       "a:visited.sk-estimator-doc-link.fitted {\n",
+       "  /* fitted */\n",
+       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
+       "  color: var(--sklearn-color-fitted-level-1);\n",
+       "}\n",
+       "\n",
+       "/* On hover */\n",
+       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
+       ".sk-estimator-doc-link:hover,\n",
+       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
+       ".sk-estimator-doc-link:hover {\n",
+       "  /* unfitted */\n",
+       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
+       "  color: var(--sklearn-color-background);\n",
+       "  text-decoration: none;\n",
+       "}\n",
+       "\n",
+       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
+       ".sk-estimator-doc-link.fitted:hover,\n",
+       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
+       ".sk-estimator-doc-link.fitted:hover {\n",
+       "  /* fitted */\n",
+       "  background-color: var(--sklearn-color-fitted-level-3);\n",
+       "  color: var(--sklearn-color-background);\n",
+       "  text-decoration: none;\n",
+       "}\n",
+       "\n",
+       "/* Span, style for the box shown on hovering the info icon */\n",
+       ".sk-estimator-doc-link span {\n",
+       "  display: none;\n",
+       "  z-index: 9999;\n",
+       "  position: relative;\n",
+       "  font-weight: normal;\n",
+       "  right: .2ex;\n",
+       "  padding: .5ex;\n",
+       "  margin: .5ex;\n",
+       "  width: min-content;\n",
+       "  min-width: 20ex;\n",
+       "  max-width: 50ex;\n",
+       "  color: var(--sklearn-color-text);\n",
+       "  box-shadow: 2pt 2pt 4pt #999;\n",
+       "  /* unfitted */\n",
+       "  background: var(--sklearn-color-unfitted-level-0);\n",
+       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
+       "}\n",
+       "\n",
+       ".sk-estimator-doc-link.fitted span {\n",
+       "  /* fitted */\n",
+       "  background: var(--sklearn-color-fitted-level-0);\n",
+       "  border: var(--sklearn-color-fitted-level-3);\n",
+       "}\n",
+       "\n",
+       ".sk-estimator-doc-link:hover span {\n",
+       "  display: block;\n",
+       "}\n",
+       "\n",
+       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
+       "\n",
+       "#sk-container-id-7 a.estimator_doc_link {\n",
+       "  float: right;\n",
+       "  font-size: 1rem;\n",
+       "  line-height: 1em;\n",
+       "  font-family: monospace;\n",
+       "  background-color: var(--sklearn-color-background);\n",
+       "  border-radius: 1rem;\n",
+       "  height: 1rem;\n",
+       "  width: 1rem;\n",
+       "  text-decoration: none;\n",
+       "  /* unfitted */\n",
+       "  color: var(--sklearn-color-unfitted-level-1);\n",
+       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 a.estimator_doc_link.fitted {\n",
+       "  /* fitted */\n",
+       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
+       "  color: var(--sklearn-color-fitted-level-1);\n",
+       "}\n",
+       "\n",
+       "/* On hover */\n",
+       "#sk-container-id-7 a.estimator_doc_link:hover {\n",
+       "  /* unfitted */\n",
+       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
+       "  color: var(--sklearn-color-background);\n",
+       "  text-decoration: none;\n",
+       "}\n",
+       "\n",
+       "#sk-container-id-7 a.estimator_doc_link.fitted:hover {\n",
+       "  /* fitted */\n",
+       "  background-color: var(--sklearn-color-fitted-level-3);\n",
+       "}\n",
+       "</style><div id=\"sk-container-id-7\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>Pipeline(steps=[(&#x27;polynomialfeatures&#x27;,\n",
+       "                 PolynomialFeatures(degree=4, include_bias=False)),\n",
+       "                (&#x27;standardscaler&#x27;, StandardScaler()),\n",
+       "                (&#x27;linearregression&#x27;, LinearRegression())])</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item sk-dashed-wrapped\"><div class=\"sk-label-container\"><div class=\"sk-label  sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-7\" type=\"checkbox\" ><label for=\"sk-estimator-id-7\" class=\"sk-toggleable__label  sk-toggleable__label-arrow\"><div><div>Pipeline</div></div><div><a class=\"sk-estimator-doc-link \" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.6/modules/generated/sklearn.pipeline.Pipeline.html\">?<span>Documentation for Pipeline</span></a><span class=\"sk-estimator-doc-link \">i<span>Not fitted</span></span></div></label><div class=\"sk-toggleable__content \"><pre>Pipeline(steps=[(&#x27;polynomialfeatures&#x27;,\n",
+       "                 PolynomialFeatures(degree=4, include_bias=False)),\n",
+       "                (&#x27;standardscaler&#x27;, StandardScaler()),\n",
+       "                (&#x27;linearregression&#x27;, LinearRegression())])</pre></div> </div></div><div class=\"sk-serial\"><div class=\"sk-item\"><div class=\"sk-estimator  sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-8\" type=\"checkbox\" ><label for=\"sk-estimator-id-8\" class=\"sk-toggleable__label  sk-toggleable__label-arrow\"><div><div>PolynomialFeatures</div></div><div><a class=\"sk-estimator-doc-link \" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.6/modules/generated/sklearn.preprocessing.PolynomialFeatures.html\">?<span>Documentation for PolynomialFeatures</span></a></div></label><div class=\"sk-toggleable__content \"><pre>PolynomialFeatures(degree=4, include_bias=False)</pre></div> </div></div><div class=\"sk-item\"><div class=\"sk-estimator  sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-9\" type=\"checkbox\" ><label for=\"sk-estimator-id-9\" class=\"sk-toggleable__label  sk-toggleable__label-arrow\"><div><div>StandardScaler</div></div><div><a class=\"sk-estimator-doc-link \" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.6/modules/generated/sklearn.preprocessing.StandardScaler.html\">?<span>Documentation for StandardScaler</span></a></div></label><div class=\"sk-toggleable__content \"><pre>StandardScaler()</pre></div> </div></div><div class=\"sk-item\"><div class=\"sk-estimator  sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-10\" type=\"checkbox\" ><label for=\"sk-estimator-id-10\" class=\"sk-toggleable__label  sk-toggleable__label-arrow\"><div><div>LinearRegression</div></div><div><a class=\"sk-estimator-doc-link \" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.6/modules/generated/sklearn.linear_model.LinearRegression.html\">?<span>Documentation for LinearRegression</span></a></div></label><div class=\"sk-toggleable__content \"><pre>LinearRegression()</pre></div> </div></div></div></div></div></div>"
+      ],
+      "text/plain": [
+       "Pipeline(steps=[('polynomialfeatures',\n",
+       "                 PolynomialFeatures(degree=4, include_bias=False)),\n",
+       "                ('standardscaler', StandardScaler()),\n",
+       "                ('linearregression', LinearRegression())])"
+      ]
+     },
+     "execution_count": 27,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "pipeline = make_pipeline(PolynomialFeatures(4,include_bias=False), StandardScaler(), LinearRegression())\n",
+    "pipeline"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 31,
+   "id": "3daa0a07-5e9f-49b8-a3b2-ca33ae47bd79",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "w0: 708105.2074469186\n",
+      "w1: [4974.440132]\n"
+     ]
+    }
+   ],
+   "source": [
+    "pipeline.fit(x,y)\n",
+    "# print model parameters\n",
+    "print('w0: {}'.format(model.intercept_))\n",
+    "print('w1: {}'.format(model.coef_))\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 32,
+   "id": "ce945e46-d16a-47dd-ba9c-6bf3920cf8c5",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "erklärte Varianz (R^2): 0.4874972676252126\n"
+     ]
+    }
+   ],
+   "source": [
+    "r_sq = model.score(x, y)\n",
+    "print('erklärte Varianz (R^2): {}'.format(r_sq))\n"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python (ki)",
+   "language": "python",
+   "name": "myenv"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.13.1"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/tasks/Untitled.ipynb b/tasks/Untitled.ipynb
index c749d4c..cd097e5 100644
--- a/tasks/Untitled.ipynb
+++ b/tasks/Untitled.ipynb
@@ -10,7 +10,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 51,
+   "execution_count": 74,
    "id": "8b1ff6ff-f80e-4cc3-b266-0ad417911d1d",
    "metadata": {},
    "outputs": [],
@@ -27,7 +27,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 52,
+   "execution_count": 75,
    "id": "f698283d-7346-4618-9b87-60a3de061a98",
    "metadata": {},
    "outputs": [
@@ -41,7 +41,7 @@
        "      dtype='object')"
       ]
      },
-     "execution_count": 52,
+     "execution_count": 75,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -55,10 +55,18 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 53,
+   "execution_count": 83,
    "id": "dac65c52-f2ce-47b6-ba65-3c6bd915dfe8",
    "metadata": {},
    "outputs": [
+    {
+     "name": "stderr",
+     "output_type": "stream",
+     "text": [
+      "/home/plex/.pyenv/versions/ki/lib/python3.12/site-packages/pandas/core/nanops.py:1016: RuntimeWarning: invalid value encountered in subtract\n",
+      "  sqr = _ensure_numeric((avg - values) ** 2)\n"
+     ]
+    },
     {
      "data": {
       "text/html": [
@@ -94,7 +102,7 @@
        "      <td>79.0</td>\n",
        "      <td>-37.8079</td>\n",
        "      <td>1035000.0</td>\n",
-       "      <td>161460000.0</td>\n",
+       "      <td>6634.615385</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
@@ -102,7 +110,7 @@
        "      <td>150.0</td>\n",
        "      <td>-37.8093</td>\n",
        "      <td>1465000.0</td>\n",
-       "      <td>196310000.0</td>\n",
+       "      <td>10932.835821</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
@@ -110,7 +118,7 @@
        "      <td>142.0</td>\n",
        "      <td>-37.8072</td>\n",
        "      <td>1600000.0</td>\n",
-       "      <td>192000000.0</td>\n",
+       "      <td>13333.333333</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>6</th>\n",
@@ -118,7 +126,7 @@
        "      <td>210.0</td>\n",
        "      <td>-37.8024</td>\n",
        "      <td>1876000.0</td>\n",
-       "      <td>459620000.0</td>\n",
+       "      <td>7657.142857</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>7</th>\n",
@@ -126,7 +134,7 @@
        "      <td>107.0</td>\n",
        "      <td>-37.8060</td>\n",
        "      <td>1636000.0</td>\n",
-       "      <td>418816000.0</td>\n",
+       "      <td>6390.625000</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
@@ -134,14 +142,14 @@
       ],
       "text/plain": [
        "   Rooms  BuildingArea  Lattitude      Price  price_per_area\n",
-       "1      2          79.0   -37.8079  1035000.0     161460000.0\n",
-       "2      3         150.0   -37.8093  1465000.0     196310000.0\n",
-       "4      4         142.0   -37.8072  1600000.0     192000000.0\n",
-       "6      3         210.0   -37.8024  1876000.0     459620000.0\n",
-       "7      2         107.0   -37.8060  1636000.0     418816000.0"
+       "1      2          79.0   -37.8079  1035000.0     6634.615385\n",
+       "2      3         150.0   -37.8093  1465000.0    10932.835821\n",
+       "4      4         142.0   -37.8072  1600000.0    13333.333333\n",
+       "6      3         210.0   -37.8024  1876000.0     7657.142857\n",
+       "7      2         107.0   -37.8060  1636000.0     6390.625000"
       ]
      },
-     "execution_count": 53,
+     "execution_count": 83,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -150,14 +158,14 @@
     "#features = ['BuildingArea', Rooms', 'Bathroom', 'Landsize', 'Lattitude', 'Longtitude', 'YearBuilt', 'Distance']\n",
     "features = ['Rooms', 'BuildingArea', 'Lattitude']\n",
     "data = melbourne_data[features + ['Price']]\n",
-    "data = data.assign(price_per_area = melbourne_data['Price'] * melbourne_data[\"Landsize\"])\n",
+    "data = data.assign(price_per_area = melbourne_data['Price'] / melbourne_data[\"Landsize\"])\n",
     "data.describe()\n",
     "data.head()"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 54,
+   "execution_count": 77,
    "id": "afe5a08a-abec-4164-85c4-1d3ac8398a62",
    "metadata": {},
    "outputs": [],
@@ -173,7 +181,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 55,
+   "execution_count": 78,
    "id": "c2e256a3-3575-45c4-a99c-d41c3c56e1c3",
    "metadata": {},
    "outputs": [],
@@ -192,7 +200,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 56,
+   "execution_count": 79,
    "id": "b41b9c03-0c1d-4a6b-80e8-d7e8775b69c0",
    "metadata": {},
    "outputs": [],
@@ -204,7 +212,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 57,
+   "execution_count": 80,
    "id": "2c631e17-eb36-43d0-97b1-59add1c93dd9",
    "metadata": {},
    "outputs": [],
@@ -218,7 +226,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 58,
+   "execution_count": 81,
    "id": "8301eb74-9aae-446c-ad46-924811b99777",
    "metadata": {},
    "outputs": [
@@ -229,8 +237,8 @@
       "Die 4 Parameter der linearen Regression:\n",
       "[-6.97461781e+07  2.41559504e+05  2.31456611e+03 -1.84562537e+06]\n",
       "Kostenfunktion J(w_ana): 137899453867.5851\n",
-      "CPU times: user 475 μs, sys: 38 μs, total: 513 μs\n",
-      "Wall time: 500 μs\n"
+      "CPU times: user 495 μs, sys: 39 μs, total: 534 μs\n",
+      "Wall time: 553 μs\n"
      ]
     }
    ],
@@ -241,6 +249,80 @@
     "J_ana = J(w=w_ana, X=X, y=y)\n",
     "print('Kostenfunktion J(w_ana): {}'.format(J_ana))\n"
    ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 91,
+   "id": "a89c591c-4ebd-4a3d-958b-915738d7361a",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "1     6634.615385\n",
+      "2    10932.835821\n",
+      "4    13333.333333\n",
+      "6     7657.142857\n",
+      "7     6390.625000\n",
+      "Name: price_per_area, dtype: float64\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "<Axes: xlabel='BuildingArea', ylabel='Price'>"
+      ]
+     },
+     "execution_count": 91,
+     "metadata": {},
+     "output_type": "execute_result"
+    },
+    {
+     "data": {
+      "image/png": "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",
+      "text/plain": [
+       "<Figure size 640x480 with 1 Axes>"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "ax = sns.scatterplot(x=data['BuildingArea'], y=data['Price'])\n",
+    "\n",
+    "xplot = data['price_per_area']\n",
+    "yplot = data['price_per_area'][0:len(xplot)]\n",
+    "print(yplot.head())\n",
+    "sns.lineplot(x=xplot, y=yplot, ax=ax)\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 85,
+   "id": "e4fc1d51-3435-415d-875f-db85dfda39e2",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "1     6634.615385\n",
+       "2    10932.835821\n",
+       "4    13333.333333\n",
+       "6     7657.142857\n",
+       "7     6390.625000\n",
+       "Name: price_per_area, dtype: float64"
+      ]
+     },
+     "execution_count": 85,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "data['price_per_area'].head()"
+   ]
   }
  ],
  "metadata": {