ch13 pandas corr, scipy.stats pearsonr, spearmanr, kendalltau.ipynb

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  {
   "cell_type": "markdown",
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   "source": [
    "# 상관분석\n",
    "\n",
    "## 01 상관 분석 개요\n",
    "\n",
    "### 다양한 상관 분석\n",
    "\n",
    "- 두 변수의 선형관계를 확인하기 위해서 상관분석을 실시\n",
    "- 두 수치형 변수의 비교는 Pearson's Correlation coefficient를 확인하며 그 외 다양한 상관계수 존재\n",
    "- 상관계수가 0에 가까울수록 선형관계가 약하며 절대값이 1에 가까울수록 선형관계가 강함\n",
    "\n",
    "## 02 주요 함수 및 메서드 소개\n",
    "\n",
    "### pandas - corr()\n",
    "\n",
    "- pandas에서 상관계수를 실시하는 데이터프레임 전용 메서드\n",
    "- method에 \"pearson\", \"kendall\", \"spearman\"은 각각의 상관계수로 계산\n",
    "\n",
    "### scipy - pearsonr()\n",
    "\n",
    "- Pearson 상관분석을 실시하는 scipy의 함수\n",
    "- 입력은 두 일차원 벡터를 넣고 출력은 상관계수와 p-value가 차례대로 출력\n",
    "\n",
    "### scipy - sparmanr()\n",
    "\n",
    "- Spearman 상관분석을 실시하는 scipy의 함수\n",
    "- 입력은 두 일차원 벡터를 넣고 출력은 상관계수와 p-value가 차례대로 출력\n",
    "\n",
    "### scipy - kendalltau()\n",
    "\n",
    "- Kendall 상관분석을 실시하는 scipy의 함수\n",
    "- 입력은 두 일차원 벡터를 넣고 출력은 상관계수와 p-value가 차례대로 출력"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "8a9ccc64",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from scipy.stats import pearsonr\n",
    "from scipy.stats import spearmanr\n",
    "from scipy.stats import kendalltau"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "636f76f4",
   "metadata": {},
   "outputs": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>datetime</th>\n",
       "      <th>season</th>\n",
       "      <th>holiday</th>\n",
       "      <th>workingday</th>\n",
       "      <th>weather</th>\n",
       "      <th>temp</th>\n",
       "      <th>atemp</th>\n",
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       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10881</th>\n",
       "      <td>2012-12-19 19:00:00</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>15.58</td>\n",
       "      <td>19.695</td>\n",
       "      <td>50</td>\n",
       "      <td>26.0027</td>\n",
       "      <td>7</td>\n",
       "      <td>329</td>\n",
       "      <td>336</td>\n",
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       "      <th>10882</th>\n",
       "      <td>2012-12-19 20:00:00</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>14.76</td>\n",
       "      <td>17.425</td>\n",
       "      <td>57</td>\n",
       "      <td>15.0013</td>\n",
       "      <td>10</td>\n",
       "      <td>231</td>\n",
       "      <td>241</td>\n",
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       "    <tr>\n",
       "      <th>10883</th>\n",
       "      <td>2012-12-19 21:00:00</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>13.94</td>\n",
       "      <td>15.910</td>\n",
       "      <td>61</td>\n",
       "      <td>15.0013</td>\n",
       "      <td>4</td>\n",
       "      <td>164</td>\n",
       "      <td>168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10884</th>\n",
       "      <td>2012-12-19 22:00:00</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>13.94</td>\n",
       "      <td>17.425</td>\n",
       "      <td>61</td>\n",
       "      <td>6.0032</td>\n",
       "      <td>12</td>\n",
       "      <td>117</td>\n",
       "      <td>129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10885</th>\n",
       "      <td>2012-12-19 23:00:00</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>13.12</td>\n",
       "      <td>16.665</td>\n",
       "      <td>66</td>\n",
       "      <td>8.9981</td>\n",
       "      <td>4</td>\n",
       "      <td>84</td>\n",
       "      <td>88</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      "text/plain": [
       "                  datetime  season  holiday  workingday  weather   temp  \\\n",
       "10881  2012-12-19 19:00:00       4        0           1        1  15.58   \n",
       "10882  2012-12-19 20:00:00       4        0           1        1  14.76   \n",
       "10883  2012-12-19 21:00:00       4        0           1        1  13.94   \n",
       "10884  2012-12-19 22:00:00       4        0           1        1  13.94   \n",
       "10885  2012-12-19 23:00:00       4        0           1        1  13.12   \n",
       "\n",
       "        atemp  humidity  windspeed  casual  registered  count  \n",
       "10881  19.695        50    26.0027       7         329    336  \n",
       "10882  17.425        57    15.0013      10         231    241  \n",
       "10883  15.910        61    15.0013       4         164    168  \n",
       "10884  17.425        61     6.0032      12         117    129  \n",
       "10885  16.665        66     8.9981       4          84     88  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "df = pd.read_csv(\"강의자료/실습파일/bike.csv\")\n",
    "df.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c3d780d5",
   "metadata": {},
   "outputs": [
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       "      <th>season</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.029368</td>\n",
       "      <td>-0.008126</td>\n",
       "      <td>0.008879</td>\n",
       "      <td>0.258689</td>\n",
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       "      <th>holiday</th>\n",
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       "      <td>1.000000</td>\n",
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       "      <td>-0.007074</td>\n",
       "      <td>0.000295</td>\n",
       "      <td>-0.005215</td>\n",
       "      <td>0.001929</td>\n",
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       "      <td>0.043799</td>\n",
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       "      <th>workingday</th>\n",
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       "      <td>1.000000</td>\n",
       "      <td>0.033772</td>\n",
       "      <td>0.029966</td>\n",
       "      <td>0.024660</td>\n",
       "      <td>-0.010880</td>\n",
       "      <td>0.013373</td>\n",
       "      <td>-0.319111</td>\n",
       "      <td>0.119460</td>\n",
       "      <td>0.011594</td>\n",
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       "      <th>weather</th>\n",
       "      <td>0.008879</td>\n",
       "      <td>-0.007074</td>\n",
       "      <td>0.033772</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.055035</td>\n",
       "      <td>-0.055376</td>\n",
       "      <td>0.406244</td>\n",
       "      <td>0.007261</td>\n",
       "      <td>-0.135918</td>\n",
       "      <td>-0.109340</td>\n",
       "      <td>-0.128655</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>temp</th>\n",
       "      <td>0.258689</td>\n",
       "      <td>0.000295</td>\n",
       "      <td>0.029966</td>\n",
       "      <td>-0.055035</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.984948</td>\n",
       "      <td>-0.064949</td>\n",
       "      <td>-0.017852</td>\n",
       "      <td>0.467097</td>\n",
       "      <td>0.318571</td>\n",
       "      <td>0.394454</td>\n",
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       "    <tr>\n",
       "      <th>atemp</th>\n",
       "      <td>0.264744</td>\n",
       "      <td>-0.005215</td>\n",
       "      <td>0.024660</td>\n",
       "      <td>-0.055376</td>\n",
       "      <td>0.984948</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.043536</td>\n",
       "      <td>-0.057473</td>\n",
       "      <td>0.462067</td>\n",
       "      <td>0.314635</td>\n",
       "      <td>0.389784</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>humidity</th>\n",
       "      <td>0.190610</td>\n",
       "      <td>0.001929</td>\n",
       "      <td>-0.010880</td>\n",
       "      <td>0.406244</td>\n",
       "      <td>-0.064949</td>\n",
       "      <td>-0.043536</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.318607</td>\n",
       "      <td>-0.348187</td>\n",
       "      <td>-0.265458</td>\n",
       "      <td>-0.317371</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>windspeed</th>\n",
       "      <td>-0.147121</td>\n",
       "      <td>0.008409</td>\n",
       "      <td>0.013373</td>\n",
       "      <td>0.007261</td>\n",
       "      <td>-0.017852</td>\n",
       "      <td>-0.057473</td>\n",
       "      <td>-0.318607</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.092276</td>\n",
       "      <td>0.091052</td>\n",
       "      <td>0.101369</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>casual</th>\n",
       "      <td>0.096758</td>\n",
       "      <td>0.043799</td>\n",
       "      <td>-0.319111</td>\n",
       "      <td>-0.135918</td>\n",
       "      <td>0.467097</td>\n",
       "      <td>0.462067</td>\n",
       "      <td>-0.348187</td>\n",
       "      <td>0.092276</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.497250</td>\n",
       "      <td>0.690414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>registered</th>\n",
       "      <td>0.164011</td>\n",
       "      <td>-0.020956</td>\n",
       "      <td>0.119460</td>\n",
       "      <td>-0.109340</td>\n",
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       "      <td>-0.265458</td>\n",
       "      <td>0.091052</td>\n",
       "      <td>0.497250</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.970948</td>\n",
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       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>0.163439</td>\n",
       "      <td>-0.005393</td>\n",
       "      <td>0.011594</td>\n",
       "      <td>-0.128655</td>\n",
       "      <td>0.394454</td>\n",
       "      <td>0.389784</td>\n",
       "      <td>-0.317371</td>\n",
       "      <td>0.101369</td>\n",
       "      <td>0.690414</td>\n",
       "      <td>0.970948</td>\n",
       "      <td>1.000000</td>\n",
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       "              season   holiday  workingday   weather      temp     atemp  \\\n",
       "season      1.000000  0.029368   -0.008126  0.008879  0.258689  0.264744   \n",
       "holiday     0.029368  1.000000   -0.250491 -0.007074  0.000295 -0.005215   \n",
       "workingday -0.008126 -0.250491    1.000000  0.033772  0.029966  0.024660   \n",
       "weather     0.008879 -0.007074    0.033772  1.000000 -0.055035 -0.055376   \n",
       "temp        0.258689  0.000295    0.029966 -0.055035  1.000000  0.984948   \n",
       "atemp       0.264744 -0.005215    0.024660 -0.055376  0.984948  1.000000   \n",
       "humidity    0.190610  0.001929   -0.010880  0.406244 -0.064949 -0.043536   \n",
       "windspeed  -0.147121  0.008409    0.013373  0.007261 -0.017852 -0.057473   \n",
       "casual      0.096758  0.043799   -0.319111 -0.135918  0.467097  0.462067   \n",
       "registered  0.164011 -0.020956    0.119460 -0.109340  0.318571  0.314635   \n",
       "count       0.163439 -0.005393    0.011594 -0.128655  0.394454  0.389784   \n",
       "\n",
       "            humidity  windspeed    casual  registered     count  \n",
       "season      0.190610  -0.147121  0.096758    0.164011  0.163439  \n",
       "holiday     0.001929   0.008409  0.043799   -0.020956 -0.005393  \n",
       "workingday -0.010880   0.013373 -0.319111    0.119460  0.011594  \n",
       "weather     0.406244   0.007261 -0.135918   -0.109340 -0.128655  \n",
       "temp       -0.064949  -0.017852  0.467097    0.318571  0.394454  \n",
       "atemp      -0.043536  -0.057473  0.462067    0.314635  0.389784  \n",
       "humidity    1.000000  -0.318607 -0.348187   -0.265458 -0.317371  \n",
       "windspeed  -0.318607   1.000000  0.092276    0.091052  0.101369  \n",
       "casual     -0.348187   0.092276  1.000000    0.497250  0.690414  \n",
       "registered -0.265458   0.091052  0.497250    1.000000  0.970948  \n",
       "count      -0.317371   0.101369  0.690414    0.970948  1.000000  "
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     "execution_count": 5,
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   ],
   "source": [
    "df.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "7f31008c",
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   "outputs": [
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       "      <th>casual</th>\n",
       "      <td>1.00000</td>\n",
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       "      <th>registered</th>\n",
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       "             casual  registered\n",
       "casual      1.00000     0.49725\n",
       "registered  0.49725     1.00000"
      ]
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   "source": [
    "df[[\"casual\", \"registered\"]].corr()"
   ]
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  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "00407eb8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PearsonRResult(statistic=0.49724968508700795, pvalue=0.0)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pearsonr(df[\"casual\"], df[\"registered\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "0b2114fc",
   "metadata": {
    "scrolled": true
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   "outputs": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>casual</th>\n",
       "      <th>registered</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>casual</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.775785</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>registered</th>\n",
       "      <td>0.775785</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              casual  registered\n",
       "casual      1.000000    0.775785\n",
       "registered  0.775785    1.000000"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[[\"casual\", \"registered\"]].corr(method = \"spearman\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0a4a4ecf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "SpearmanrResult(correlation=0.775785305888168, pvalue=0.0)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "spearmanr(df[\"casual\"], df[\"registered\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "5cbbd1f0",
   "metadata": {
    "scrolled": true
   },
   "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>casual</th>\n",
       "      <th>registered</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>casual</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.582213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>registered</th>\n",
       "      <td>0.582213</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              casual  registered\n",
       "casual      1.000000    0.582213\n",
       "registered  0.582213    1.000000"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df[[\"casual\", \"registered\"]].corr(method = \"kendall\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "bfda0e8a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KendalltauResult(correlation=0.5822127999867908, pvalue=0.0)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "kendalltau(df[\"casual\"], df[\"registered\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f386b85b",
   "metadata": {},
   "source": [
    "## Q1 기온, 체감온도, 상대습도, 총 자전거 대여 숫자의 상관관계를 분석하였을 대 가장 낮은 상관계수는 얼마인가?\n",
    "1) 데이터 속성에 맞는 적절한 상관분석 기법 사용  \n",
    "2) 자전거 대여 숫자는 casual 변수를 사용"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "96b4d88c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
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       "        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>datetime</th>\n",
       "      <th>season</th>\n",
       "      <th>holiday</th>\n",
       "      <th>workingday</th>\n",
       "      <th>weather</th>\n",
       "      <th>temp</th>\n",
       "      <th>atemp</th>\n",
       "      <th>humidity</th>\n",
       "      <th>windspeed</th>\n",
       "      <th>casual</th>\n",
       "      <th>registered</th>\n",
       "      <th>count</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10881</th>\n",
       "      <td>2012-12-19 19:00:00</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>15.58</td>\n",
       "      <td>19.695</td>\n",
       "      <td>50</td>\n",
       "      <td>26.0027</td>\n",
       "      <td>7</td>\n",
       "      <td>329</td>\n",
       "      <td>336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10882</th>\n",
       "      <td>2012-12-19 20:00:00</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>14.76</td>\n",
       "      <td>17.425</td>\n",
       "      <td>57</td>\n",
       "      <td>15.0013</td>\n",
       "      <td>10</td>\n",
       "      <td>231</td>\n",
       "      <td>241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10883</th>\n",
       "      <td>2012-12-19 21:00:00</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>13.94</td>\n",
       "      <td>15.910</td>\n",
       "      <td>61</td>\n",
       "      <td>15.0013</td>\n",
       "      <td>4</td>\n",
       "      <td>164</td>\n",
       "      <td>168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10884</th>\n",
       "      <td>2012-12-19 22:00:00</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>13.94</td>\n",
       "      <td>17.425</td>\n",
       "      <td>61</td>\n",
       "      <td>6.0032</td>\n",
       "      <td>12</td>\n",
       "      <td>117</td>\n",
       "      <td>129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10885</th>\n",
       "      <td>2012-12-19 23:00:00</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>13.12</td>\n",
       "      <td>16.665</td>\n",
       "      <td>66</td>\n",
       "      <td>8.9981</td>\n",
       "      <td>4</td>\n",
       "      <td>84</td>\n",
       "      <td>88</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  datetime  season  holiday  workingday  weather   temp  \\\n",
       "10881  2012-12-19 19:00:00       4        0           1        1  15.58   \n",
       "10882  2012-12-19 20:00:00       4        0           1        1  14.76   \n",
       "10883  2012-12-19 21:00:00       4        0           1        1  13.94   \n",
       "10884  2012-12-19 22:00:00       4        0           1        1  13.94   \n",
       "10885  2012-12-19 23:00:00       4        0           1        1  13.12   \n",
       "\n",
       "        atemp  humidity  windspeed  casual  registered  count  \n",
       "10881  19.695        50    26.0027       7         329    336  \n",
       "10882  17.425        57    15.0013      10         231    241  \n",
       "10883  15.910        61    15.0013       4         164    168  \n",
       "10884  17.425        61     6.0032      12         117    129  \n",
       "10885  16.665        66     8.9981       4          84     88  "
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q1 = pd.read_csv(\"강의자료/실습파일/bike.csv\")\n",
    "Q1.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "f887d0f2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "        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>temp</th>\n",
       "      <th>atemp</th>\n",
       "      <th>humidity</th>\n",
       "      <th>casual</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>temp</th>\n",
       "      <td>1.000</td>\n",
       "      <td>0.985</td>\n",
       "      <td>-0.065</td>\n",
       "      <td>0.467</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>atemp</th>\n",
       "      <td>0.985</td>\n",
       "      <td>1.000</td>\n",
       "      <td>-0.044</td>\n",
       "      <td>0.462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>humidity</th>\n",
       "      <td>-0.065</td>\n",
       "      <td>-0.044</td>\n",
       "      <td>1.000</td>\n",
       "      <td>-0.348</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>casual</th>\n",
       "      <td>0.467</td>\n",
       "      <td>0.462</td>\n",
       "      <td>-0.348</td>\n",
       "      <td>1.000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           temp  atemp  humidity  casual\n",
       "temp      1.000  0.985    -0.065   0.467\n",
       "atemp     0.985  1.000    -0.044   0.462\n",
       "humidity -0.065 -0.044     1.000  -0.348\n",
       "casual    0.467  0.462    -0.348   1.000"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q1[[\"temp\", \"atemp\", \"humidity\", \"casual\"]].corr().round(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39f6f9cd",
   "metadata": {},
   "source": [
    "## Q2 계절별로 체감온도와 자전거 대여 숫자의 상관관계를 알아보고자 한다. 이 때 적절한 상관분석기법을 사용하였을 때 상관계수로 옳은 것은?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "5342473a",
   "metadata": {},
   "outputs": [],
   "source": [
    "Q2_Spring = Q1[Q1[\"season\"] == 1]\n",
    "Q2_Summer = Q1[Q1[\"season\"] == 2]\n",
    "Q2_Fall = Q1[Q1[\"season\"] == 3]\n",
    "Q2_Winter = Q1[Q1[\"season\"] == 4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "8f0f7890",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>atemp</th>\n",
       "      <th>casual</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>atemp</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.478312</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>casual</th>\n",
       "      <td>0.478312</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           atemp    casual\n",
       "atemp   1.000000  0.478312\n",
       "casual  0.478312  1.000000"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q2_Spring[[\"atemp\", \"casual\"]].corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "7eb3a852",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>atemp</th>\n",
       "      <th>casual</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>atemp</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.378122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>casual</th>\n",
       "      <td>0.378122</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           atemp    casual\n",
       "atemp   1.000000  0.378122\n",
       "casual  0.378122  1.000000"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q2_Summer[[\"atemp\", \"casual\"]].corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "d3f76e02",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
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       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>atemp</th>\n",
       "      <th>casual</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>atemp</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.381423</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>casual</th>\n",
       "      <td>0.381423</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           atemp    casual\n",
       "atemp   1.000000  0.381423\n",
       "casual  0.381423  1.000000"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q2_Fall[[\"atemp\", \"casual\"]].corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "1324154c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\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>atemp</th>\n",
       "      <th>casual</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>atemp</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.443751</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>casual</th>\n",
       "      <td>0.443751</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           atemp    casual\n",
       "atemp   1.000000  0.443751\n",
       "casual  0.443751  1.000000"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q2_Winter[[\"atemp\", \"casual\"]].corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "8fa35a49",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\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>season</th>\n",
       "      <th>level_1</th>\n",
       "      <th>atemp</th>\n",
       "      <th>casual</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>casual</td>\n",
       "      <td>0.478312</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>2</td>\n",
       "      <td>casual</td>\n",
       "      <td>0.378122</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>3</td>\n",
       "      <td>casual</td>\n",
       "      <td>0.381423</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>4</td>\n",
       "      <td>casual</td>\n",
       "      <td>0.443751</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   season level_1     atemp  casual\n",
       "1       1  casual  0.478312     1.0\n",
       "3       2  casual  0.378122     1.0\n",
       "5       3  casual  0.381423     1.0\n",
       "7       4  casual  0.443751     1.0"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## 답안\n",
    "Q2_corr = Q1[[\"season\", \"atemp\", \"casual\"]].groupby(\"season\").corr().reset_index()\n",
    "Q2_corr.loc[Q2_corr[\"atemp\"] < 1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc3c85c5",
   "metadata": {},
   "source": [
    "## Q3 날씨에 따른 기온과 자전거 대여의 상관계수 변화를 알아보고자 한다. 날씨가 맑은 날과 그렇지 않은 날의 상관계수 차이의 절대값은 얼마인가?\n",
    "1) weather 변수의 값이 1인 것이 맑은 날"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "a0c67a81",
   "metadata": {
    "scrolled": true
   },
   "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>datetime</th>\n",
       "      <th>season</th>\n",
       "      <th>holiday</th>\n",
       "      <th>workingday</th>\n",
       "      <th>weather</th>\n",
       "      <th>temp</th>\n",
       "      <th>atemp</th>\n",
       "      <th>humidity</th>\n",
       "      <th>windspeed</th>\n",
       "      <th>casual</th>\n",
       "      <th>registered</th>\n",
       "      <th>count</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10881</th>\n",
       "      <td>2012-12-19 19:00:00</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>15.58</td>\n",
       "      <td>19.695</td>\n",
       "      <td>50</td>\n",
       "      <td>26.0027</td>\n",
       "      <td>7</td>\n",
       "      <td>329</td>\n",
       "      <td>336</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10882</th>\n",
       "      <td>2012-12-19 20:00:00</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>14.76</td>\n",
       "      <td>17.425</td>\n",
       "      <td>57</td>\n",
       "      <td>15.0013</td>\n",
       "      <td>10</td>\n",
       "      <td>231</td>\n",
       "      <td>241</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10883</th>\n",
       "      <td>2012-12-19 21:00:00</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>13.94</td>\n",
       "      <td>15.910</td>\n",
       "      <td>61</td>\n",
       "      <td>15.0013</td>\n",
       "      <td>4</td>\n",
       "      <td>164</td>\n",
       "      <td>168</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10884</th>\n",
       "      <td>2012-12-19 22:00:00</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>13.94</td>\n",
       "      <td>17.425</td>\n",
       "      <td>61</td>\n",
       "      <td>6.0032</td>\n",
       "      <td>12</td>\n",
       "      <td>117</td>\n",
       "      <td>129</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10885</th>\n",
       "      <td>2012-12-19 23:00:00</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>13.12</td>\n",
       "      <td>16.665</td>\n",
       "      <td>66</td>\n",
       "      <td>8.9981</td>\n",
       "      <td>4</td>\n",
       "      <td>84</td>\n",
       "      <td>88</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  datetime  season  holiday  workingday  weather   temp  \\\n",
       "10881  2012-12-19 19:00:00       4        0           1        1  15.58   \n",
       "10882  2012-12-19 20:00:00       4        0           1        1  14.76   \n",
       "10883  2012-12-19 21:00:00       4        0           1        1  13.94   \n",
       "10884  2012-12-19 22:00:00       4        0           1        1  13.94   \n",
       "10885  2012-12-19 23:00:00       4        0           1        1  13.12   \n",
       "\n",
       "        atemp  humidity  windspeed  casual  registered  count  \n",
       "10881  19.695        50    26.0027       7         329    336  \n",
       "10882  17.425        57    15.0013      10         231    241  \n",
       "10883  15.910        61    15.0013       4         164    168  \n",
       "10884  17.425        61     6.0032      12         117    129  \n",
       "10885  16.665        66     8.9981       4          84     88  "
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q3 = pd.read_csv(\"강의자료/실습파일/bike.csv\")\n",
    "Q3.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "055e6964",
   "metadata": {},
   "outputs": [],
   "source": [
    "Q3_clean = Q3[Q3[\"weather\"] == 1]\n",
    "Q3_other = Q3[Q3[\"weather\"] != 1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "5210d24a",
   "metadata": {},
   "outputs": [],
   "source": [
    "stat1, p1 = pearsonr(Q3_clean[\"temp\"], Q3_clean[\"casual\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "54ec4103",
   "metadata": {},
   "outputs": [],
   "source": [
    "stat2, p2 = pearsonr(Q3_other[\"temp\"], Q3_other[\"casual\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "87a5cc2f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0246916461938268"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stat1 - stat2"
   ]
  }
 ],
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