regresja liniowa
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"## Przykład kodu na regresję liniową"
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]
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},
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{
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"cell_type": "markdown",
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"id": "1c1dd0af-74e4-4f7a-93bf-64a9d2be14c3",
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"metadata": {},
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"source": [
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"Zaczynamy od importu pewnych bibliotek, które ułatwiają pracę z danymi i uruchamianie algorytmów uczenia maszynowego:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "74d886ec-b819-48fa-aac2-e69c6160287b",
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"metadata": {},
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"outputs": [],
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"source": [
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"import pandas as pd\n",
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"import numpy as np\n",
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" \n",
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"from sklearn.linear_model import LinearRegression\n",
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"from sklearn.metrics import mean_squared_error"
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]
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},
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{
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"cell_type": "markdown",
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"id": "d9e1ee83-3b9d-439f-9aee-5ac095ded83a",
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"metadata": {},
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"source": [
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"Wczytajmy dane i podejrzyjmy nasz zbiór danych:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 11,
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"id": "f1111528-20ce-4ed5-9c5a-511f2c1041d2",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"<div>\n",
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"<style scoped>\n",
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" .dataframe tbody tr th:only-of-type {\n",
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" vertical-align: middle;\n",
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" }\n",
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"\n",
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" .dataframe tbody tr th {\n",
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" vertical-align: top;\n",
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" }\n",
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"\n",
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" .dataframe thead th {\n",
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" text-align: right;\n",
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" }\n",
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"</style>\n",
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"<table border=\"1\" class=\"dataframe\">\n",
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" <thead>\n",
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" <tr style=\"text-align: right;\">\n",
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" <th></th>\n",
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" <th>cwiczenia</th>\n",
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" <th>czas_min</th>\n",
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" <th>wejscia</th>\n",
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" <th>nieodwiedzone</th>\n",
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" <th>czas_do_testu_godziny</th>\n",
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" <th>test</th>\n",
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" </tr>\n",
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" </thead>\n",
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" <tbody>\n",
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" <tr>\n",
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" <th>0</th>\n",
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" <td>4</td>\n",
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" <td>12</td>\n",
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" <td>1</td>\n",
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" <td>1</td>\n",
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" <td>20</td>\n",
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" <td>20.00</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>1</th>\n",
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" <td>8</td>\n",
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" <td>25</td>\n",
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" <td>3</td>\n",
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" <td>3</td>\n",
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" <td>36</td>\n",
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" <td>60.00</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>2</th>\n",
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" <td>14</td>\n",
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" <td>48</td>\n",
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" <td>3</td>\n",
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" <td>1</td>\n",
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" <td>33</td>\n",
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" <td>92.86</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>3</th>\n",
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" <td>11</td>\n",
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" <td>37</td>\n",
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" <td>5</td>\n",
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" <td>0</td>\n",
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" <td>42</td>\n",
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" <td>65.34</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>4</th>\n",
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" <td>5</td>\n",
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" <td>29</td>\n",
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" <td>2</td>\n",
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" <td>0</td>\n",
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" <td>22</td>\n",
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" <td>42.35</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>5</th>\n",
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" <td>2</td>\n",
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" <td>5</td>\n",
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" <td>1</td>\n",
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" <td>4</td>\n",
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" <td>5</td>\n",
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" <td>13.14</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>6</th>\n",
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" <td>16</td>\n",
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" <td>36</td>\n",
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" <td>7</td>\n",
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" <td>1</td>\n",
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" <td>47</td>\n",
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" <td>85.13</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>7</th>\n",
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" <td>18</td>\n",
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" <td>55</td>\n",
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" <td>5</td>\n",
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" <td>0</td>\n",
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" <td>39</td>\n",
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" <td>98.33</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>8</th>\n",
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" <td>20</td>\n",
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" <td>48</td>\n",
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" <td>4</td>\n",
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" <td>0</td>\n",
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" <td>45</td>\n",
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" <td>100.00</td>\n",
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" </tr>\n",
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" <tr>\n",
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" <th>9</th>\n",
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" <td>10</td>\n",
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" <td>42</td>\n",
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" <td>7</td>\n",
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" <td>1</td>\n",
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" <td>37</td>\n",
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" <td>70.00</td>\n",
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" </tr>\n",
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" </tbody>\n",
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"</table>\n",
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"</div>"
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],
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"text/plain": [
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" cwiczenia czas_min wejscia nieodwiedzone czas_do_testu_godziny test\n",
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"0 4 12 1 1 20 20.00\n",
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"1 8 25 3 3 36 60.00\n",
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"2 14 48 3 1 33 92.86\n",
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"3 11 37 5 0 42 65.34\n",
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"4 5 29 2 0 22 42.35\n",
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"5 2 5 1 4 5 13.14\n",
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"6 16 36 7 1 47 85.13\n",
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"7 18 55 5 0 39 98.33\n",
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"8 20 48 4 0 45 100.00\n",
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"9 10 42 7 1 37 70.00"
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]
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},
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"execution_count": 11,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"data = pd.read_csv('data.csv', sep=';')\n",
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"data"
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]
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},
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{
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"cell_type": "markdown",
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"id": "2158a205-2c9e-41b9-9fe0-d56dd7b97213",
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"metadata": {},
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"source": [
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"Teraz obliczamy podstawowy model regresji liniowej i wyliczamy błąd (czyli jak bardzo obliczone wartości funkcji regresji różnią się od tych rzeczywistych) - weźmy miarę RMSE (omówimy ją na późniejszych zajęciach - na razie zapamiętajmy: im niższy błąd tym lepiej):"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 36,
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"id": "f7eade7c-def7-4944-8eea-7cba985e5bf5",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Współczynnik a: 4.8869552414605435\n",
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"Wyraz wolny: 11.935883392226131\n",
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"Błąd: Root Mean Squared Error (RMSE): 8.27\n"
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]
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}
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],
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"source": [
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"model = LinearRegression()\n",
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" \n",
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"X = data[['cwiczenia']]\n",
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"y = data['test']\n",
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" \n",
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"model.fit(X,y, sample_weight=None)\n",
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"y_pred = model.predict(X)\n",
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" \n",
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"print('Współczynnik a: ', model.coef_[0])\n",
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"print('Wyraz wolny: ', model.intercept_)\n",
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"print('Błąd: Root Mean Squared Error (RMSE): %.2f'% np.sqrt(mean_squared_error(y, y_pred)))\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "04bf6923-da81-40ca-96bd-33f1ad973ddc",
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"metadata": {},
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"source": [
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"A co by było jakbyśmy wzięli dodatkowo pod uwagę czas spędzony w kursie:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 48,
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"id": "2b232e81-9d0e-4817-ac0a-5f7b1d293666",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Współczynnik przy argumencie \"cwiczenia\": 2.793448759670846\n",
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"Współczynnik przy argumencie \"czas_min\": 0.9017691542564438\n",
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"Wyraz wolny: 4.156132897112705\n",
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"Błąd: Root Mean Squared Error (RMSE): 5.19\n"
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]
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}
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],
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"source": [
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"X = data[['cwiczenia', 'czas_min']]\n",
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"y = data['test']\n",
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" \n",
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"model.fit(X,y, sample_weight=None)\n",
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"y_pred = model.predict(X)\n",
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" \n",
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"print('Współczynnik przy argumencie \"cwiczenia\": ', model.coef_[0])\n",
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"print('Współczynnik przy argumencie \"czas_min\": ', model.coef_[1])\n",
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"print('Wyraz wolny: ', model.intercept_)\n",
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"print('Błąd: Root Mean Squared Error (RMSE): %.2f'% np.sqrt(mean_squared_error(y, y_pred)))\n"
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]
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},
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{
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"cell_type": "markdown",
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"id": "e49fa078-6216-4d83-bbbd-db0b58aa7c8e",
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"metadata": {},
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"source": [
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"Mamy lepszy wynik - błąd jest niższy :)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "d501bcc0-d3bf-4552-bf2b-c78753b4d5d6",
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"metadata": {},
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"source": [
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"A jak wyglądają nasze wyznaczone wartości funkcji regresji?"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 49,
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"id": "e539d645-86c6-42c0-9059-7a3c310cc2a3",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"array([ 26.15115779, 49.04795183, 86.54933494, 68.24952796,\n",
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" 44.27468217, 14.25187619, 81.31500261, 104.03551406,\n",
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" 103.31002749, 69.96492497])"
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]
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},
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"execution_count": 49,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"data_with_y_pred = data.copy()\n",
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"data_with_y_pred['y_pred'] = y_pred\n",
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"data_with_y_pred\n",
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"y_pred"
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]
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},
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{
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"cell_type": "markdown",
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"id": "7ea9c2cb-b654-4190-9e4f-972e4d3bf92f",
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"metadata": {},
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"source": [
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"## Zadanie 1.\n",
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"\n",
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"Dla całego zbioru danych oblicz sumę kwadratów róźnic pomiędzy kolumnami **test** i **y_pred**. Wynik zaokrąglij do dwóch miejsc po przecinku (pamiętaj, że od 5 zaokrąglamy w górę). Podpowiedź:"
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]
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},
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{
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"cell_type": "markdown",
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"id": "90d8f306-e823-4552-8f41-6aac1ee37611",
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"metadata": {},
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"source": [
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"- `data_with_y_pred['nazwa_kolumny'].size` - liczba elementów (wierszy) w danej kolumnie\n",
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"\n",
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"- `data_with_y_pred['nazwa_kolumny'][0]` - pierwszy (indeksujemy od zera) element (wiersz) kolumny"
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]
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},
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{
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"cell_type": "markdown",
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"id": "8d9c213b-5758-409b-a73d-1012a3709032",
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"metadata": {},
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"source": [
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"Konkretne zadanie: napisz funkcję o nazwie `fun1()`, która zwróci oczekiwany wynik. Kod tej funkcji wklej na Moodle'u w aktywności o nazwie **Regresja liniowa - zadanie 1**. Na Moodle'u poza powyższym zbiorem danych kod będzie sprawdzony na innym zbiorze danych, więc nie można napisać prostej funkcji, która zwróci wartość obliczoną np. na kartce - niestety trzeba napisać funkcję obliczającą poszukiwaną wartość ;)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "28e2ef8c-dbbf-4c3d-924e-f59318e4f383",
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"id": "7d1a8edd-0a16-4504-8383-1e9240504306",
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"metadata": {},
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"outputs": [],
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"source": []
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@ -215,10 +215,340 @@
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"## Przykład kodu na regresję liniową"
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]
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},
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{
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"cell_type": "markdown",
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"id": "1c1dd0af-74e4-4f7a-93bf-64a9d2be14c3",
|
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"metadata": {},
|
||||
"source": [
|
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"Zaczynamy od importu pewnych bibliotek, które ułatwiają pracę z danymi i uruchamianie algorytmów uczenia maszynowego:"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "74d886ec-b819-48fa-aac2-e69c6160287b",
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"metadata": {},
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"outputs": [],
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"source": [
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"import pandas as pd\n",
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"import numpy as np\n",
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" \n",
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"from sklearn.linear_model import LinearRegression\n",
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"from sklearn.metrics import mean_squared_error"
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]
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},
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{
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"cell_type": "markdown",
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"id": "d9e1ee83-3b9d-439f-9aee-5ac095ded83a",
|
||||
"metadata": {},
|
||||
"source": [
|
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"Wczytajmy dane i podejrzyjmy nasz zbiór danych:"
|
||||
]
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||||
},
|
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{
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"cell_type": "code",
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"execution_count": 11,
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"id": "f1111528-20ce-4ed5-9c5a-511f2c1041d2",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/html": [
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"<div>\n",
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"<style scoped>\n",
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" .dataframe tbody tr th:only-of-type {\n",
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" vertical-align: middle;\n",
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" }\n",
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"\n",
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" .dataframe tbody tr th {\n",
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" vertical-align: top;\n",
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" }\n",
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"\n",
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" .dataframe thead th {\n",
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" text-align: right;\n",
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" }\n",
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"</style>\n",
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"<table border=\"1\" class=\"dataframe\">\n",
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" <thead>\n",
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" <tr style=\"text-align: right;\">\n",
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" <th></th>\n",
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" <th>cwiczenia</th>\n",
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" <th>czas_min</th>\n",
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" <th>wejscia</th>\n",
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" <th>nieodwiedzone</th>\n",
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" <th>czas_do_testu_godziny</th>\n",
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" <th>test</th>\n",
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" </tr>\n",
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" </thead>\n",
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" <tbody>\n",
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" <tr>\n",
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" <th>0</th>\n",
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" <td>4</td>\n",
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" <td>12</td>\n",
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" <td>1</td>\n",
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" <td>1</td>\n",
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" <td>20</td>\n",
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" <td>20.00</td>\n",
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" </tr>\n",
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" <tr>\n",
|
||||
" <th>1</th>\n",
|
||||
" <td>8</td>\n",
|
||||
" <td>25</td>\n",
|
||||
" <td>3</td>\n",
|
||||
" <td>3</td>\n",
|
||||
" <td>36</td>\n",
|
||||
" <td>60.00</td>\n",
|
||||
" </tr>\n",
|
||||
" <tr>\n",
|
||||
" <th>2</th>\n",
|
||||
" <td>14</td>\n",
|
||||
" <td>48</td>\n",
|
||||
" <td>3</td>\n",
|
||||
" <td>1</td>\n",
|
||||
" <td>33</td>\n",
|
||||
" <td>92.86</td>\n",
|
||||
" </tr>\n",
|
||||
" <tr>\n",
|
||||
" <th>3</th>\n",
|
||||
" <td>11</td>\n",
|
||||
" <td>37</td>\n",
|
||||
" <td>5</td>\n",
|
||||
" <td>0</td>\n",
|
||||
" <td>42</td>\n",
|
||||
" <td>65.34</td>\n",
|
||||
" </tr>\n",
|
||||
" <tr>\n",
|
||||
" <th>4</th>\n",
|
||||
" <td>5</td>\n",
|
||||
" <td>29</td>\n",
|
||||
" <td>2</td>\n",
|
||||
" <td>0</td>\n",
|
||||
" <td>22</td>\n",
|
||||
" <td>42.35</td>\n",
|
||||
" </tr>\n",
|
||||
" <tr>\n",
|
||||
" <th>5</th>\n",
|
||||
" <td>2</td>\n",
|
||||
" <td>5</td>\n",
|
||||
" <td>1</td>\n",
|
||||
" <td>4</td>\n",
|
||||
" <td>5</td>\n",
|
||||
" <td>13.14</td>\n",
|
||||
" </tr>\n",
|
||||
" <tr>\n",
|
||||
" <th>6</th>\n",
|
||||
" <td>16</td>\n",
|
||||
" <td>36</td>\n",
|
||||
" <td>7</td>\n",
|
||||
" <td>1</td>\n",
|
||||
" <td>47</td>\n",
|
||||
" <td>85.13</td>\n",
|
||||
" </tr>\n",
|
||||
" <tr>\n",
|
||||
" <th>7</th>\n",
|
||||
" <td>18</td>\n",
|
||||
" <td>55</td>\n",
|
||||
" <td>5</td>\n",
|
||||
" <td>0</td>\n",
|
||||
" <td>39</td>\n",
|
||||
" <td>98.33</td>\n",
|
||||
" </tr>\n",
|
||||
" <tr>\n",
|
||||
" <th>8</th>\n",
|
||||
" <td>20</td>\n",
|
||||
" <td>48</td>\n",
|
||||
" <td>4</td>\n",
|
||||
" <td>0</td>\n",
|
||||
" <td>45</td>\n",
|
||||
" <td>100.00</td>\n",
|
||||
" </tr>\n",
|
||||
" <tr>\n",
|
||||
" <th>9</th>\n",
|
||||
" <td>10</td>\n",
|
||||
" <td>42</td>\n",
|
||||
" <td>7</td>\n",
|
||||
" <td>1</td>\n",
|
||||
" <td>37</td>\n",
|
||||
" <td>70.00</td>\n",
|
||||
" </tr>\n",
|
||||
" </tbody>\n",
|
||||
"</table>\n",
|
||||
"</div>"
|
||||
],
|
||||
"text/plain": [
|
||||
" cwiczenia czas_min wejscia nieodwiedzone czas_do_testu_godziny test\n",
|
||||
"0 4 12 1 1 20 20.00\n",
|
||||
"1 8 25 3 3 36 60.00\n",
|
||||
"2 14 48 3 1 33 92.86\n",
|
||||
"3 11 37 5 0 42 65.34\n",
|
||||
"4 5 29 2 0 22 42.35\n",
|
||||
"5 2 5 1 4 5 13.14\n",
|
||||
"6 16 36 7 1 47 85.13\n",
|
||||
"7 18 55 5 0 39 98.33\n",
|
||||
"8 20 48 4 0 45 100.00\n",
|
||||
"9 10 42 7 1 37 70.00"
|
||||
]
|
||||
},
|
||||
"execution_count": 11,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"data = pd.read_csv('data.csv', sep=';')\n",
|
||||
"data"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "2158a205-2c9e-41b9-9fe0-d56dd7b97213",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Teraz obliczamy podstawowy model regresji liniowej i wyliczamy błąd (czyli jak bardzo obliczone wartości funkcji regresji różnią się od tych rzeczywistych) - weźmy miarę RMSE (omówimy ją na późniejszych zajęciach - na razie zapamiętajmy: im niższy błąd tym lepiej):"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 36,
|
||||
"id": "f7eade7c-def7-4944-8eea-7cba985e5bf5",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Współczynnik a: 4.8869552414605435\n",
|
||||
"Wyraz wolny: 11.935883392226131\n",
|
||||
"Błąd: Root Mean Squared Error (RMSE): 8.27\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"model = LinearRegression()\n",
|
||||
" \n",
|
||||
"X = data[['cwiczenia']]\n",
|
||||
"y = data['test']\n",
|
||||
" \n",
|
||||
"model.fit(X,y, sample_weight=None)\n",
|
||||
"y_pred = model.predict(X)\n",
|
||||
" \n",
|
||||
"print('Współczynnik a: ', model.coef_[0])\n",
|
||||
"print('Wyraz wolny: ', model.intercept_)\n",
|
||||
"print('Błąd: Root Mean Squared Error (RMSE): %.2f'% np.sqrt(mean_squared_error(y, y_pred)))\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "04bf6923-da81-40ca-96bd-33f1ad973ddc",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"A co by było jakbyśmy wzięli dodatkowo pod uwagę czas spędzony w kursie:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 48,
|
||||
"id": "2b232e81-9d0e-4817-ac0a-5f7b1d293666",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"name": "stdout",
|
||||
"output_type": "stream",
|
||||
"text": [
|
||||
"Współczynnik przy argumencie \"cwiczenia\": 2.793448759670846\n",
|
||||
"Współczynnik przy argumencie \"czas_min\": 0.9017691542564438\n",
|
||||
"Wyraz wolny: 4.156132897112705\n",
|
||||
"Błąd: Root Mean Squared Error (RMSE): 5.19\n"
|
||||
]
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"X = data[['cwiczenia', 'czas_min']]\n",
|
||||
"y = data['test']\n",
|
||||
" \n",
|
||||
"model.fit(X,y, sample_weight=None)\n",
|
||||
"y_pred = model.predict(X)\n",
|
||||
" \n",
|
||||
"print('Współczynnik przy argumencie \"cwiczenia\": ', model.coef_[0])\n",
|
||||
"print('Współczynnik przy argumencie \"czas_min\": ', model.coef_[1])\n",
|
||||
"print('Wyraz wolny: ', model.intercept_)\n",
|
||||
"print('Błąd: Root Mean Squared Error (RMSE): %.2f'% np.sqrt(mean_squared_error(y, y_pred)))\n"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "e49fa078-6216-4d83-bbbd-db0b58aa7c8e",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Mamy lepszy wynik - błąd jest niższy :)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "d501bcc0-d3bf-4552-bf2b-c78753b4d5d6",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"A jak wyglądają nasze wyznaczone wartości funkcji regresji?"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 49,
|
||||
"id": "e539d645-86c6-42c0-9059-7a3c310cc2a3",
|
||||
"metadata": {},
|
||||
"outputs": [
|
||||
{
|
||||
"data": {
|
||||
"text/plain": [
|
||||
"array([ 26.15115779, 49.04795183, 86.54933494, 68.24952796,\n",
|
||||
" 44.27468217, 14.25187619, 81.31500261, 104.03551406,\n",
|
||||
" 103.31002749, 69.96492497])"
|
||||
]
|
||||
},
|
||||
"execution_count": 49,
|
||||
"metadata": {},
|
||||
"output_type": "execute_result"
|
||||
}
|
||||
],
|
||||
"source": [
|
||||
"data_with_y_pred = data.copy()\n",
|
||||
"data_with_y_pred['y_pred'] = y_pred\n",
|
||||
"data_with_y_pred\n",
|
||||
"y_pred"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "7ea9c2cb-b654-4190-9e4f-972e4d3bf92f",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Zadanie 1.\n",
|
||||
"\n",
|
||||
"Dla całego zbioru danych oblicz sumę kwadratów róźnic pomiędzy kolumnami **test** i **y_pred**. Wynik zaokrąglij do dwóch miejsc po przecinku (pamiętaj, że od 5 zaokrąglamy w górę). Podpowiedź:"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "90d8f306-e823-4552-8f41-6aac1ee37611",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"- `data_with_y_pred['nazwa_kolumny'].size` - liczba elementów (wierszy) w danej kolumnie\n",
|
||||
"\n",
|
||||
"- `data_with_y_pred['nazwa_kolumny'][0]` - pierwszy (indeksujemy od zera) element (wiersz) kolumny"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"id": "8d9c213b-5758-409b-a73d-1012a3709032",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"Konkretne zadanie: napisz funkcję o nazwie `fun1()`, która zwróci oczekiwany wynik. Kod tej funkcji wklej na Moodle'u w aktywności o nazwie **Regresja liniowa - zadanie 1**. Na Moodle'u poza powyższym zbiorem danych kod będzie sprawdzony na innym zbiorze danych, więc nie można napisać prostej funkcji, która zwróci wartość obliczoną np. na kartce - niestety trzeba napisać funkcję obliczającą poszukiwaną wartość ;)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": null,
|
||||
"id": "28e2ef8c-dbbf-4c3d-924e-f59318e4f383",
|
||||
"id": "7d1a8edd-0a16-4504-8383-1e9240504306",
|
||||
"metadata": {},
|
||||
"outputs": [],
|
||||
"source": []
|
||||
|
||||
Loading…
Reference in New Issue
Block a user