ch15 patsy dmatrices, statsmodels.stats.outliers_influence variance_inflation_factor.ipynb

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   "id": "ab667db1",
   "metadata": {},
   "source": [
    "# 15차시 다중 회귀분석(Multiple Linear Regression)\n",
    "\n",
    "## 01 다중 회귀분석 개요\n",
    "\n",
    "### 다중 회귀분석 특징\n",
    "\n",
    "- 연속형 종속변수와 두 개 이상의 독립변수 간 선형관계 및 설명력을 확인하는 기법\n",
    "- 필요 시 모델 성능 향상을 위한 파생변수 생성 및 성능 비교 필요\n",
    "- 명목형 변수가 독립변수인 경우 가변수 변환 후 모델 적합\n",
    "\n",
    "### 다중 공선성 문제\n",
    "\n",
    "- 독립변수 간 강한 상관관계가 나타나는 문제\n",
    "- 상관계수를 확인하여 그 값이 높은 것을 사전에 제거\n",
    "- 회귀 모델 생성 이후 분산 팽창 계수(VIF) 확인(10 이상)하여 관련 변수 처리\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71c10793",
   "metadata": {},
   "source": [
    "## 02 주요 함수 및 메서드 소개\n",
    "\n",
    "### patsy - dmatrices()\n",
    "\n",
    "- 수식을 기반으로 데이터 행렬을 생성하는 pasty의 함수\n",
    "- 분산 팽창 계수 확인을 위해 입력 데이터를 전처리 할 때 필요한 함수\n",
    "- return_type 인자에 \"dataframe\" 으로 설정 시 후처리 용이\n",
    "\n",
    "### statsmodels - variance_inflation_factor()\n",
    "\n",
    "- 분산 팽창 계수를 연산하기 위한 statsmodels 함수\n",
    "- 분산 팽창 계수 연산을 위해 반복문 또는 list comprehension 사용"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0d405963",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from patsy import dmatrices\n",
    "from statsmodels.stats.outliers_influence import variance_inflation_factor as vif"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "cb5ca281",
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.read_csv(\"강의자료/실습파일/bike.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fe962bc1",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></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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       "      <th>10881</th>\n",
       "      <td>4</td>\n",
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       "      <td>15.58</td>\n",
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       "      <td>26.0027</td>\n",
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       "      <td>12</td>\n",
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       "    <tr>\n",
       "      <th>10885</th>\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",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      "text/plain": [
       "       season  holiday  workingday  weather   temp   atemp  humidity  \\\n",
       "10881       4        0           1        1  15.58  19.695        50   \n",
       "10882       4        0           1        1  14.76  17.425        57   \n",
       "10883       4        0           1        1  13.94  15.910        61   \n",
       "10884       4        0           1        1  13.94  17.425        61   \n",
       "10885       4        0           1        1  13.12  16.665        66   \n",
       "\n",
       "       windspeed  casual  \n",
       "10881    26.0027       7  \n",
       "10882    15.0013      10  \n",
       "10883    15.0013       4  \n",
       "10884     6.0032      12  \n",
       "10885     8.9981       4  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_sub = df.loc[:, \"season\":\"casual\"]\n",
    "df_sub.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4e6569db",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'casual ~ season + holiday + workingday + ... + windspeed'"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"casual ~ season + holiday + workingday + ... + windspeed\" #  종속변수 ~  독립변수1 + 독립변수2 ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "037638a2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'casual ~ season + holiday'"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"casual ~ \" + \"season + holiday\""
   ]
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  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b2a46e56",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'casual ~ season + holiday + workingday + weather + temp + atemp + humidity + windspeed'"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\"casual ~ \" + \" + \".join(df_sub.columns[:-1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "cb0c8256",
   "metadata": {},
   "outputs": [],
   "source": [
    "formula = \"casual ~ \" + \" + \".join(df_sub.columns[:-1])\n",
    "y, X = dmatrices(formula, data = df_sub, return_type = \"dataframe\")"
   ]
  },
  {
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   "execution_count": 11,
   "id": "939ff005",
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       "   casual\n",
       "0     3.0\n",
       "1     8.0\n",
       "2     5.0\n",
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       "4     0.0"
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   "execution_count": 12,
   "id": "50791a83",
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   "outputs": [
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       "      <th>holiday</th>\n",
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       "      <th>weather</th>\n",
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       "      <td>75.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>1.0</td>\n",
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      "text/plain": [
       "   Intercept  season  holiday  workingday  weather  temp   atemp  humidity  \\\n",
       "0        1.0     1.0      0.0         0.0      1.0  9.84  14.395      81.0   \n",
       "1        1.0     1.0      0.0         0.0      1.0  9.02  13.635      80.0   \n",
       "2        1.0     1.0      0.0         0.0      1.0  9.02  13.635      80.0   \n",
       "3        1.0     1.0      0.0         0.0      1.0  9.84  14.395      75.0   \n",
       "4        1.0     1.0      0.0         0.0      1.0  9.84  14.395      75.0   \n",
       "\n",
       "   windspeed  \n",
       "0        0.0  \n",
       "1        0.0  \n",
       "2        0.0  \n",
       "3        0.0  \n",
       "4        0.0  "
      ]
     },
     "execution_count": 12,
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    "X.head()"
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   "execution_count": 14,
   "id": "2cc73893",
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   "outputs": [
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       "      <td>1.137211</td>\n",
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       "      <td>holiday</td>\n",
       "      <td>1.069731</td>\n",
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       "      <th>3</th>\n",
       "      <td>workingday</td>\n",
       "      <td>1.071196</td>\n",
       "    </tr>\n",
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       "      <th>4</th>\n",
       "      <td>weather</td>\n",
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       "      <th>6</th>\n",
       "      <td>atemp</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>humidity</td>\n",
       "      <td>1.425034</td>\n",
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       "      <th>8</th>\n",
       "      <td>windspeed</td>\n",
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       "      colname        VIF\n",
       "0   Intercept  34.029472\n",
       "1      season   1.137211\n",
       "2     holiday   1.069731\n",
       "3  workingday   1.071196\n",
       "4     weather   1.236150\n",
       "5        temp  35.516012\n",
       "6       atemp  35.550831\n",
       "7    humidity   1.425034\n",
       "8   windspeed   1.195704"
      ]
     },
     "execution_count": 14,
     "metadata": {},
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   "source": [
    "df_vif = pd.DataFrame()\n",
    "df_vif[\"colname\"] = X.columns\n",
    "df_vif[\"VIF\"] = [vif(X.values, i) for i in range(X.shape[1])]\n",
    "df_vif"
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     "execution_count": 15,
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   "outputs": [
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       "       [ 1.    ,  1.    ,  0.    , ..., 13.635 , 80.    ,  0.    ],\n",
       "       [ 1.    ,  1.    ,  0.    , ..., 13.635 , 80.    ,  0.    ],\n",
       "       ...,\n",
       "       [ 1.    ,  4.    ,  0.    , ..., 15.91  , 61.    , 15.0013],\n",
       "       [ 1.    ,  4.    ,  0.    , ..., 17.425 , 61.    ,  6.0032],\n",
       "       [ 1.    ,  4.    ,  0.    , ..., 16.665 , 66.    ,  8.9981]])"
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>season</th>\n",
       "      <th>holiday</th>\n",
       "      <th>workingday</th>\n",
       "      <th>weather</th>\n",
       "      <th>temp</th>\n",
       "      <th>humidity</th>\n",
       "      <th>windspeed</th>\n",
       "      <th>casual</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>10881</th>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>15.58</td>\n",
       "      <td>50</td>\n",
       "      <td>26.0027</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10882</th>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>14.76</td>\n",
       "      <td>57</td>\n",
       "      <td>15.0013</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10883</th>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>13.94</td>\n",
       "      <td>61</td>\n",
       "      <td>15.0013</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10884</th>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>13.94</td>\n",
       "      <td>61</td>\n",
       "      <td>6.0032</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10885</th>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>13.12</td>\n",
       "      <td>66</td>\n",
       "      <td>8.9981</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       season  holiday  workingday  weather   temp  humidity  windspeed  \\\n",
       "10881       4        0           1        1  15.58        50    26.0027   \n",
       "10882       4        0           1        1  14.76        57    15.0013   \n",
       "10883       4        0           1        1  13.94        61    15.0013   \n",
       "10884       4        0           1        1  13.94        61     6.0032   \n",
       "10885       4        0           1        1  13.12        66     8.9981   \n",
       "\n",
       "       casual  \n",
       "10881       7  \n",
       "10882      10  \n",
       "10883       4  \n",
       "10884      12  \n",
       "10885       4  "
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_sub2 = pd.concat([df.loc[:, \"season\":\"temp\"],\n",
    "                     df.loc[:, \"humidity\":\"casual\"]],\n",
    "                     axis = 1)\n",
    "df_sub2.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "6926f7de",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>colname</th>\n",
       "      <th>VIF</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Intercept</td>\n",
       "      <td>31.375118</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>season</td>\n",
       "      <td>1.136866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>holiday</td>\n",
       "      <td>1.068094</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>workingday</td>\n",
       "      <td>1.070025</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>weather</td>\n",
       "      <td>1.235251</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>temp</td>\n",
       "      <td>1.089028</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>humidity</td>\n",
       "      <td>1.421256</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>windspeed</td>\n",
       "      <td>1.149650</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      colname        VIF\n",
       "0   Intercept  31.375118\n",
       "1      season   1.136866\n",
       "2     holiday   1.068094\n",
       "3  workingday   1.070025\n",
       "4     weather   1.235251\n",
       "5        temp   1.089028\n",
       "6    humidity   1.421256\n",
       "7   windspeed   1.149650"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "formula = \"casual ~ \" + \" + \".join(df_sub2.columns[:-1])\n",
    "y, X = dmatrices(formula, data = df_sub2, return_type = \"dataframe\")\n",
    "df_vif = pd.DataFrame()\n",
    "df_vif[\"colname\"] = X.columns\n",
    "df_vif[\"VIF\"] = [vif(X.values, i) for i in range(X.shape[1])]\n",
    "df_vif"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "dabfc069",
   "metadata": {},
   "outputs": [
    {
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       "      <th>season</th>\n",
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       "      <th>weather</th>\n",
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       "      <th>season</th>\n",
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       "      <td>0.12</td>\n",
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       "    <tr>\n",
       "      <th>weather</th>\n",
       "      <td>0.01</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.03</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.06</td>\n",
       "      <td>-0.06</td>\n",
       "      <td>0.41</td>\n",
       "      <td>0.01</td>\n",
       "      <td>-0.14</td>\n",
       "      <td>-0.11</td>\n",
       "      <td>-0.13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>temp</th>\n",
       "      <td>0.26</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.03</td>\n",
       "      <td>-0.06</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.98</td>\n",
       "      <td>-0.06</td>\n",
       "      <td>-0.02</td>\n",
       "      <td>0.47</td>\n",
       "      <td>0.32</td>\n",
       "      <td>0.39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>atemp</th>\n",
       "      <td>0.26</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.02</td>\n",
       "      <td>-0.06</td>\n",
       "      <td>0.98</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>-0.06</td>\n",
       "      <td>0.46</td>\n",
       "      <td>0.31</td>\n",
       "      <td>0.39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>humidity</th>\n",
       "      <td>0.19</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.41</td>\n",
       "      <td>-0.06</td>\n",
       "      <td>-0.04</td>\n",
       "      <td>1.00</td>\n",
       "      <td>-0.32</td>\n",
       "      <td>-0.35</td>\n",
       "      <td>-0.27</td>\n",
       "      <td>-0.32</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>windspeed</th>\n",
       "      <td>-0.15</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.01</td>\n",
       "      <td>0.01</td>\n",
       "      <td>-0.02</td>\n",
       "      <td>-0.06</td>\n",
       "      <td>-0.32</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>casual</th>\n",
       "      <td>0.10</td>\n",
       "      <td>0.04</td>\n",
       "      <td>-0.32</td>\n",
       "      <td>-0.14</td>\n",
       "      <td>0.47</td>\n",
       "      <td>0.46</td>\n",
       "      <td>-0.35</td>\n",
       "      <td>0.09</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.50</td>\n",
       "      <td>0.69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>registered</th>\n",
       "      <td>0.16</td>\n",
       "      <td>-0.02</td>\n",
       "      <td>0.12</td>\n",
       "      <td>-0.11</td>\n",
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       "      <td>1.00</td>\n",
       "      <td>0.97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>0.16</td>\n",
       "      <td>-0.01</td>\n",
       "      <td>0.01</td>\n",
       "      <td>-0.13</td>\n",
       "      <td>0.39</td>\n",
       "      <td>0.39</td>\n",
       "      <td>-0.32</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.69</td>\n",
       "      <td>0.97</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            season  holiday  workingday  weather  temp  atemp  humidity  \\\n",
       "season        1.00     0.03       -0.01     0.01  0.26   0.26      0.19   \n",
       "holiday       0.03     1.00       -0.25    -0.01  0.00  -0.01      0.00   \n",
       "workingday   -0.01    -0.25        1.00     0.03  0.03   0.02     -0.01   \n",
       "weather       0.01    -0.01        0.03     1.00 -0.06  -0.06      0.41   \n",
       "temp          0.26     0.00        0.03    -0.06  1.00   0.98     -0.06   \n",
       "atemp         0.26    -0.01        0.02    -0.06  0.98   1.00     -0.04   \n",
       "humidity      0.19     0.00       -0.01     0.41 -0.06  -0.04      1.00   \n",
       "windspeed    -0.15     0.01        0.01     0.01 -0.02  -0.06     -0.32   \n",
       "casual        0.10     0.04       -0.32    -0.14  0.47   0.46     -0.35   \n",
       "registered    0.16    -0.02        0.12    -0.11  0.32   0.31     -0.27   \n",
       "count         0.16    -0.01        0.01    -0.13  0.39   0.39     -0.32   \n",
       "\n",
       "            windspeed  casual  registered  count  \n",
       "season          -0.15    0.10        0.16   0.16  \n",
       "holiday          0.01    0.04       -0.02  -0.01  \n",
       "workingday       0.01   -0.32        0.12   0.01  \n",
       "weather          0.01   -0.14       -0.11  -0.13  \n",
       "temp            -0.02    0.47        0.32   0.39  \n",
       "atemp           -0.06    0.46        0.31   0.39  \n",
       "humidity        -0.32   -0.35       -0.27  -0.32  \n",
       "windspeed        1.00    0.09        0.09   0.10  \n",
       "casual           0.09    1.00        0.50   0.69  \n",
       "registered       0.09    0.50        1.00   0.97  \n",
       "count            0.10    0.69        0.97   1.00  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.corr().round(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "da9ab1c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>datetime</th>\n",
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       "      <th>0</th>\n",
       "      <td>2011-01-01 00:00:00</td>\n",
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       "      <td>75</td>\n",
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       "      <th>4</th>\n",
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      ],
      "text/plain": [
       "              datetime  holiday  workingday  weather  temp   atemp  humidity  \\\n",
       "0  2011-01-01 00:00:00        0           0        1  9.84  14.395        81   \n",
       "1  2011-01-01 01:00:00        0           0        1  9.02  13.635        80   \n",
       "2  2011-01-01 02:00:00        0           0        1  9.02  13.635        80   \n",
       "3  2011-01-01 03:00:00        0           0        1  9.84  14.395        75   \n",
       "4  2011-01-01 04:00:00        0           0        1  9.84  14.395        75   \n",
       "\n",
       "   windspeed  casual  registered  count  season_2  season_3  season_4  \n",
       "0        0.0       3          13     16         0         0         0  \n",
       "1        0.0       8          32     40         0         0         0  \n",
       "2        0.0       5          27     32         0         0         0  \n",
       "3        0.0       3          10     13         0         0         0  \n",
       "4        0.0       0           1      1         0         0         0  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_dum = pd.get_dummies(df, columns = [\"season\"], drop_first = True)\n",
    "df_dum.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "037406b9",
   "metadata": {},
   "source": [
    "## Q1 Price를 종속변수로 하고 나머지 수치형 변수를 독립변수로 했을 때 다중 공선성의 문제가 있다고 판단되는 변수의 개수는?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b53c4107",
   "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",
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       "    }\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>carat</th>\n",
       "      <th>depth</th>\n",
       "      <th>table</th>\n",
       "      <th>price</th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>z</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>carat</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.028224</td>\n",
       "      <td>0.181618</td>\n",
       "      <td>0.921591</td>\n",
       "      <td>0.975094</td>\n",
       "      <td>0.951722</td>\n",
       "      <td>0.953387</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>depth</th>\n",
       "      <td>0.028224</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>-0.295779</td>\n",
       "      <td>-0.010647</td>\n",
       "      <td>-0.025289</td>\n",
       "      <td>-0.029341</td>\n",
       "      <td>0.094924</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>table</th>\n",
       "      <td>0.181618</td>\n",
       "      <td>-0.295779</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.127134</td>\n",
       "      <td>0.195344</td>\n",
       "      <td>0.183760</td>\n",
       "      <td>0.150929</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>price</th>\n",
       "      <td>0.921591</td>\n",
       "      <td>-0.010647</td>\n",
       "      <td>0.127134</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.884435</td>\n",
       "      <td>0.865421</td>\n",
       "      <td>0.861249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>x</th>\n",
       "      <td>0.975094</td>\n",
       "      <td>-0.025289</td>\n",
       "      <td>0.195344</td>\n",
       "      <td>0.884435</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.974701</td>\n",
       "      <td>0.970772</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>y</th>\n",
       "      <td>0.951722</td>\n",
       "      <td>-0.029341</td>\n",
       "      <td>0.183760</td>\n",
       "      <td>0.865421</td>\n",
       "      <td>0.974701</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.952006</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>z</th>\n",
       "      <td>0.953387</td>\n",
       "      <td>0.094924</td>\n",
       "      <td>0.150929</td>\n",
       "      <td>0.861249</td>\n",
       "      <td>0.970772</td>\n",
       "      <td>0.952006</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          carat     depth     table     price         x         y         z\n",
       "carat  1.000000  0.028224  0.181618  0.921591  0.975094  0.951722  0.953387\n",
       "depth  0.028224  1.000000 -0.295779 -0.010647 -0.025289 -0.029341  0.094924\n",
       "table  0.181618 -0.295779  1.000000  0.127134  0.195344  0.183760  0.150929\n",
       "price  0.921591 -0.010647  0.127134  1.000000  0.884435  0.865421  0.861249\n",
       "x      0.975094 -0.025289  0.195344  0.884435  1.000000  0.974701  0.970772\n",
       "y      0.951722 -0.029341  0.183760  0.865421  0.974701  1.000000  0.952006\n",
       "z      0.953387  0.094924  0.150929  0.861249  0.970772  0.952006  1.000000"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q1 = pd.read_csv(\"강의자료/실습파일/diamonds.csv\")\n",
    "Q1.corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0643c608",
   "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>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>326.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>326.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>327.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>334.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>335.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   price\n",
       "0  326.0\n",
       "1  326.0\n",
       "2  327.0\n",
       "3  334.0\n",
       "4  335.0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "formula = \"price ~ carat + depth + table + x + y + z\"\n",
    "y, X = dmatrices(formula, data = Q1, return_type = \"dataframe\")\n",
    "y.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "0fc21e52",
   "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",
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       "    }\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>Intercept</th>\n",
       "      <th>carat</th>\n",
       "      <th>depth</th>\n",
       "      <th>table</th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>z</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.23</td>\n",
       "      <td>61.5</td>\n",
       "      <td>55.0</td>\n",
       "      <td>3.95</td>\n",
       "      <td>3.98</td>\n",
       "      <td>2.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.21</td>\n",
       "      <td>59.8</td>\n",
       "      <td>61.0</td>\n",
       "      <td>3.89</td>\n",
       "      <td>3.84</td>\n",
       "      <td>2.31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.23</td>\n",
       "      <td>56.9</td>\n",
       "      <td>65.0</td>\n",
       "      <td>4.05</td>\n",
       "      <td>4.07</td>\n",
       "      <td>2.31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.29</td>\n",
       "      <td>62.4</td>\n",
       "      <td>58.0</td>\n",
       "      <td>4.20</td>\n",
       "      <td>4.23</td>\n",
       "      <td>2.63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.0</td>\n",
       "      <td>0.31</td>\n",
       "      <td>63.3</td>\n",
       "      <td>58.0</td>\n",
       "      <td>4.34</td>\n",
       "      <td>4.35</td>\n",
       "      <td>2.75</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Intercept  carat  depth  table     x     y     z\n",
       "0        1.0   0.23   61.5   55.0  3.95  3.98  2.43\n",
       "1        1.0   0.21   59.8   61.0  3.89  3.84  2.31\n",
       "2        1.0   0.23   56.9   65.0  4.05  4.07  2.31\n",
       "3        1.0   0.29   62.4   58.0  4.20  4.23  2.63\n",
       "4        1.0   0.31   63.3   58.0  4.34  4.35  2.75"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "8de2cd88",
   "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>colname</th>\n",
       "      <th>VIF</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Intercept</td>\n",
       "      <td>4821.696350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>carat</td>\n",
       "      <td>21.602712</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>depth</td>\n",
       "      <td>1.496590</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>table</td>\n",
       "      <td>1.143225</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>x</td>\n",
       "      <td>56.187704</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>y</td>\n",
       "      <td>20.454295</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>z</td>\n",
       "      <td>23.530049</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     colname          VIF\n",
       "0  Intercept  4821.696350\n",
       "1      carat    21.602712\n",
       "2      depth     1.496590\n",
       "3      table     1.143225\n",
       "4          x    56.187704\n",
       "5          y    20.454295\n",
       "6          z    23.530049"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q1_vif = pd.DataFrame()\n",
    "Q1_vif[\"colname\"] = X.columns\n",
    "Q1_vif[\"VIF\"] = [vif(X.values, i) for i in range(X.shape[1])]\n",
    "Q1_vif"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a926fed3",
   "metadata": {},
   "source": [
    "## Q2 price를 종속변수로 하고 carat과 depth를 독립변수로 하여 생성한 선형 회귀 모델을 사용하여 알아본 carat이 1이고 depth가 60, table이 55인 다이아온드의 가격은 얼마인가?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "8169358e",
   "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>carat</th>\n",
       "      <th>cut</th>\n",
       "      <th>color</th>\n",
       "      <th>clarity</th>\n",
       "      <th>depth</th>\n",
       "      <th>table</th>\n",
       "      <th>price</th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>z</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.23</td>\n",
       "      <td>Ideal</td>\n",
       "      <td>E</td>\n",
       "      <td>SI2</td>\n",
       "      <td>61.5</td>\n",
       "      <td>55.0</td>\n",
       "      <td>326</td>\n",
       "      <td>3.95</td>\n",
       "      <td>3.98</td>\n",
       "      <td>2.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.21</td>\n",
       "      <td>Premium</td>\n",
       "      <td>E</td>\n",
       "      <td>SI1</td>\n",
       "      <td>59.8</td>\n",
       "      <td>61.0</td>\n",
       "      <td>326</td>\n",
       "      <td>3.89</td>\n",
       "      <td>3.84</td>\n",
       "      <td>2.31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.23</td>\n",
       "      <td>Good</td>\n",
       "      <td>E</td>\n",
       "      <td>VS1</td>\n",
       "      <td>56.9</td>\n",
       "      <td>65.0</td>\n",
       "      <td>327</td>\n",
       "      <td>4.05</td>\n",
       "      <td>4.07</td>\n",
       "      <td>2.31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.29</td>\n",
       "      <td>Premium</td>\n",
       "      <td>I</td>\n",
       "      <td>VS2</td>\n",
       "      <td>62.4</td>\n",
       "      <td>58.0</td>\n",
       "      <td>334</td>\n",
       "      <td>4.20</td>\n",
       "      <td>4.23</td>\n",
       "      <td>2.63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.31</td>\n",
       "      <td>Good</td>\n",
       "      <td>J</td>\n",
       "      <td>SI2</td>\n",
       "      <td>63.3</td>\n",
       "      <td>58.0</td>\n",
       "      <td>335</td>\n",
       "      <td>4.34</td>\n",
       "      <td>4.35</td>\n",
       "      <td>2.75</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   carat      cut color clarity  depth  table  price     x     y     z\n",
       "0   0.23    Ideal     E     SI2   61.5   55.0    326  3.95  3.98  2.43\n",
       "1   0.21  Premium     E     SI1   59.8   61.0    326  3.89  3.84  2.31\n",
       "2   0.23     Good     E     VS1   56.9   65.0    327  4.05  4.07  2.31\n",
       "3   0.29  Premium     I     VS2   62.4   58.0    334  4.20  4.23  2.63\n",
       "4   0.31     Good     J     SI2   63.3   58.0    335  4.34  4.35  2.75"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q2 = pd.read_csv(\"강의자료/실습파일/diamonds.csv\")\n",
    "Q2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "46998808",
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.formula.api import ols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "c97bf1d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>price</td>      <th>  R-squared:         </th>  <td>   0.851</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th>  <td>   0.851</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>  <td>1.536e+05</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 29 Dec 2023</td> <th>  Prob (F-statistic):</th>   <td>  0.00</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>02:06:29</td>     <th>  Log-Likelihood:    </th> <td>-4.7249e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td> 53940</td>      <th>  AIC:               </th>  <td>9.450e+05</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td> 53937</td>      <th>  BIC:               </th>  <td>9.450e+05</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>      <td> </td>     \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>      <td> </td>     \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td> 4045.3332</td> <td>  286.205</td> <td>   14.134</td> <td> 0.000</td> <td> 3484.368</td> <td> 4606.298</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>carat</th>     <td> 7765.1407</td> <td>   14.009</td> <td>  554.282</td> <td> 0.000</td> <td> 7737.682</td> <td> 7792.599</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>depth</th>     <td> -102.1653</td> <td>    4.635</td> <td>  -22.041</td> <td> 0.000</td> <td> -111.251</td> <td>  -93.080</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>14148.858</td> <th>  Durbin-Watson:     </th>  <td>   0.992</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>   <th>  Jarque-Bera (JB):  </th> <td>148236.675</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 0.962</td>   <th>  Prob(JB):          </th>  <td>    0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td>10.890</td>   <th>  Cond. No.          </th>  <td>2.66e+03</td> \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 2.66e+03. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  price   R-squared:                       0.851\n",
       "Model:                            OLS   Adj. R-squared:                  0.851\n",
       "Method:                 Least Squares   F-statistic:                 1.536e+05\n",
       "Date:                Fri, 29 Dec 2023   Prob (F-statistic):               0.00\n",
       "Time:                        02:06:29   Log-Likelihood:            -4.7249e+05\n",
       "No. Observations:               53940   AIC:                         9.450e+05\n",
       "Df Residuals:                   53937   BIC:                         9.450e+05\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept   4045.3332    286.205     14.134      0.000    3484.368    4606.298\n",
       "carat       7765.1407     14.009    554.282      0.000    7737.682    7792.599\n",
       "depth       -102.1653      4.635    -22.041      0.000    -111.251     -93.080\n",
       "==============================================================================\n",
       "Omnibus:                    14148.858   Durbin-Watson:                   0.992\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):           148236.675\n",
       "Skew:                           0.962   Prob(JB):                         0.00\n",
       "Kurtosis:                      10.890   Cond. No.                     2.66e+03\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 2.66e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = ols(formula = \"price ~ carat + depth\", data = Q2).fit()\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "40f0e5f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>carat</th>\n",
       "      <th>depth</th>\n",
       "      <th>table</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>60</td>\n",
       "      <td>55</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   carat  depth  table\n",
       "0      1     60     55"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q2_test = pd.DataFrame({\"carat\": [1],\n",
    "                       \"depth\": [60],\n",
    "                       \"table\": [55]})\n",
    "Q2_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "fd6dc705",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    5680.554517\n",
       "dtype: float64"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict(Q2_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "083768cb",
   "metadata": {},
   "source": [
    "## Q3 price를 종속변수로 하고 carat, color, depth를 독립변수로 하여 생성한 선형 회귀 모델을 사용하여 알아본 carat이 1이고 depth가 50, color가 E인 다이아몬드의 가격은 얼마인가?\n",
    "1) 가변수 생성 시 마지막 변수 하나를 제거"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "b1648ad2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
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       "        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>carat</th>\n",
       "      <th>cut</th>\n",
       "      <th>color</th>\n",
       "      <th>clarity</th>\n",
       "      <th>depth</th>\n",
       "      <th>table</th>\n",
       "      <th>price</th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>z</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.23</td>\n",
       "      <td>Ideal</td>\n",
       "      <td>E</td>\n",
       "      <td>SI2</td>\n",
       "      <td>61.5</td>\n",
       "      <td>55.0</td>\n",
       "      <td>326</td>\n",
       "      <td>3.95</td>\n",
       "      <td>3.98</td>\n",
       "      <td>2.43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.21</td>\n",
       "      <td>Premium</td>\n",
       "      <td>E</td>\n",
       "      <td>SI1</td>\n",
       "      <td>59.8</td>\n",
       "      <td>61.0</td>\n",
       "      <td>326</td>\n",
       "      <td>3.89</td>\n",
       "      <td>3.84</td>\n",
       "      <td>2.31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.23</td>\n",
       "      <td>Good</td>\n",
       "      <td>E</td>\n",
       "      <td>VS1</td>\n",
       "      <td>56.9</td>\n",
       "      <td>65.0</td>\n",
       "      <td>327</td>\n",
       "      <td>4.05</td>\n",
       "      <td>4.07</td>\n",
       "      <td>2.31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.29</td>\n",
       "      <td>Premium</td>\n",
       "      <td>I</td>\n",
       "      <td>VS2</td>\n",
       "      <td>62.4</td>\n",
       "      <td>58.0</td>\n",
       "      <td>334</td>\n",
       "      <td>4.20</td>\n",
       "      <td>4.23</td>\n",
       "      <td>2.63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.31</td>\n",
       "      <td>Good</td>\n",
       "      <td>J</td>\n",
       "      <td>SI2</td>\n",
       "      <td>63.3</td>\n",
       "      <td>58.0</td>\n",
       "      <td>335</td>\n",
       "      <td>4.34</td>\n",
       "      <td>4.35</td>\n",
       "      <td>2.75</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   carat      cut color clarity  depth  table  price     x     y     z\n",
       "0   0.23    Ideal     E     SI2   61.5   55.0    326  3.95  3.98  2.43\n",
       "1   0.21  Premium     E     SI1   59.8   61.0    326  3.89  3.84  2.31\n",
       "2   0.23     Good     E     VS1   56.9   65.0    327  4.05  4.07  2.31\n",
       "3   0.29  Premium     I     VS2   62.4   58.0    334  4.20  4.23  2.63\n",
       "4   0.31     Good     J     SI2   63.3   58.0    335  4.34  4.35  2.75"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q3 = pd.read_csv(\"강의자료/실습파일/diamonds.csv\")\n",
    "Q3.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "757eb8cc",
   "metadata": {},
   "outputs": [],
   "source": [
    "Q3_sub = Q3.loc[:, [\"price\", \"carat\", \"color\", \"depth\"]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "88849b34",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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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>price</th>\n",
       "      <th>carat</th>\n",
       "      <th>depth</th>\n",
       "      <th>color_E</th>\n",
       "      <th>color_F</th>\n",
       "      <th>color_G</th>\n",
       "      <th>color_H</th>\n",
       "      <th>color_I</th>\n",
       "      <th>color_J</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>326</td>\n",
       "      <td>0.23</td>\n",
       "      <td>61.5</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>326</td>\n",
       "      <td>0.21</td>\n",
       "      <td>59.8</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>327</td>\n",
       "      <td>0.23</td>\n",
       "      <td>56.9</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>334</td>\n",
       "      <td>0.29</td>\n",
       "      <td>62.4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>335</td>\n",
       "      <td>0.31</td>\n",
       "      <td>63.3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   price  carat  depth  color_E  color_F  color_G  color_H  color_I  color_J\n",
       "0    326   0.23   61.5        1        0        0        0        0        0\n",
       "1    326   0.21   59.8        1        0        0        0        0        0\n",
       "2    327   0.23   56.9        1        0        0        0        0        0\n",
       "3    334   0.29   62.4        0        0        0        0        1        0\n",
       "4    335   0.31   63.3        0        0        0        0        0        1"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Q3_dum = pd.get_dummies(Q3_sub, columns = [\"color\"], drop_first = True)\n",
    "Q3_dum.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "be0b211e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>price</td>      <th>  R-squared:         </th>  <td>   0.865</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th>  <td>   0.865</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th>  <td>4.319e+04</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Fri, 29 Dec 2023</td> <th>  Prob (F-statistic):</th>   <td>  0.00</td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>02:15:10</td>     <th>  Log-Likelihood:    </th> <td>-4.6977e+05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td> 53940</td>      <th>  AIC:               </th>  <td>9.396e+05</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td> 53931</td>      <th>  BIC:               </th>  <td>9.396e+05</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     8</td>      <th>                     </th>      <td> </td>     \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>      <td> </td>     \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td> 3399.1860</td> <td>  272.825</td> <td>   12.459</td> <td> 0.000</td> <td> 2864.447</td> <td> 3933.925</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>carat</th>     <td> 8070.6389</td> <td>   13.988</td> <td>  576.983</td> <td> 0.000</td> <td> 8043.223</td> <td> 8098.055</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>depth</th>     <td>  -89.7605</td> <td>    4.412</td> <td>  -20.344</td> <td> 0.000</td> <td>  -98.408</td> <td>  -81.113</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>color_E</th>   <td>  -97.0161</td> <td>   23.164</td> <td>   -4.188</td> <td> 0.000</td> <td> -142.417</td> <td>  -51.615</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>color_F</th>   <td>  -80.8972</td> <td>   23.316</td> <td>   -3.470</td> <td> 0.001</td> <td> -126.596</td> <td>  -35.199</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>color_G</th>   <td>  -80.6971</td> <td>   22.585</td> <td>   -3.573</td> <td> 0.000</td> <td> -124.963</td> <td>  -36.431</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>color_H</th>   <td> -720.8099</td> <td>   24.268</td> <td>  -29.703</td> <td> 0.000</td> <td> -768.374</td> <td> -673.245</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>color_I</th>   <td>-1043.9064</td> <td>   27.213</td> <td>  -38.361</td> <td> 0.000</td> <td>-1097.243</td> <td> -990.570</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>color_J</th>   <td>-1899.5248</td> <td>   33.657</td> <td>  -56.438</td> <td> 0.000</td> <td>-1965.493</td> <td>-1833.557</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>12411.519</td> <th>  Durbin-Watson:     </th>  <td>   0.953</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th>  <td> 0.000</td>   <th>  Jarque-Bera (JB):  </th> <td>159901.705</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>           <td> 0.746</td>   <th>  Prob(JB):          </th>  <td>    0.00</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>       <td>11.302</td>   <th>  Cond. No.          </th>  <td>2.67e+03</td> \n",
       "</tr>\n",
       "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 2.67e+03. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  price   R-squared:                       0.865\n",
       "Model:                            OLS   Adj. R-squared:                  0.865\n",
       "Method:                 Least Squares   F-statistic:                 4.319e+04\n",
       "Date:                Fri, 29 Dec 2023   Prob (F-statistic):               0.00\n",
       "Time:                        02:15:10   Log-Likelihood:            -4.6977e+05\n",
       "No. Observations:               53940   AIC:                         9.396e+05\n",
       "Df Residuals:                   53931   BIC:                         9.396e+05\n",
       "Df Model:                           8                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept   3399.1860    272.825     12.459      0.000    2864.447    3933.925\n",
       "carat       8070.6389     13.988    576.983      0.000    8043.223    8098.055\n",
       "depth        -89.7605      4.412    -20.344      0.000     -98.408     -81.113\n",
       "color_E      -97.0161     23.164     -4.188      0.000    -142.417     -51.615\n",
       "color_F      -80.8972     23.316     -3.470      0.001    -126.596     -35.199\n",
       "color_G      -80.6971     22.585     -3.573      0.000    -124.963     -36.431\n",
       "color_H     -720.8099     24.268    -29.703      0.000    -768.374    -673.245\n",
       "color_I    -1043.9064     27.213    -38.361      0.000   -1097.243    -990.570\n",
       "color_J    -1899.5248     33.657    -56.438      0.000   -1965.493   -1833.557\n",
       "==============================================================================\n",
       "Omnibus:                    12411.519   Durbin-Watson:                   0.953\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):           159901.705\n",
       "Skew:                           0.746   Prob(JB):                         0.00\n",
       "Kurtosis:                      11.302   Cond. No.                     2.67e+03\n",
       "==============================================================================\n",
       "\n",
       "Notes:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 2.67e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = ols(formula = \"price ~ \" + \"+\".join(Q3_dum.columns[1:]),\n",
    "           data = Q3_dum).fit()\n",
    "model.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "c3d304cd",
   "metadata": {},
   "outputs": [
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       "   price  carat  depth  color_E  color_F  color_G  color_H  color_I  color_J\n",
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     "execution_count": 28,
     "metadata": {},
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   ],
   "source": [
    "Q3_test = Q3_dum.iloc[[0],]\n",
    "Q3_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "56ccdebb",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\jtkim\\AppData\\Local\\Temp\\ipykernel_24744\\2829292061.py:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  Q3_test[\"carat\"] = 1\n",
      "C:\\Users\\jtkim\\AppData\\Local\\Temp\\ipykernel_24744\\2829292061.py:2: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  Q3_test[\"depth\"] = 50\n"
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    "Q3_test[\"carat\"] = 1\n",
    "Q3_test[\"depth\"] = 50\n",
    "Q3_test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "ae6f9759",
   "metadata": {},
   "outputs": [
    {
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   "source": [
    "model.predict(Q3_test)"
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