house_price_pred with Linear Regression and pca.ipynb

{"nbformat":4,"nbformat_minor":0,"metadata":{"colab":{"provenance":[{"file_id":"1EwYOp_h1sjqtPaQgSauO4diaM2eHyGSK","timestamp":1682772877638}]},"kernelspec":{"name":"python3","display_name":"Python 3"},"language_info":{"name":"python"},"gpuClass":"standard"},"cells":[{"cell_type":"code","execution_count":null,"metadata":{"id":"EkFmYRW7TfxB"},"outputs":[],"source":["import pandas as pd\n","import numpy as np\n","import matplotlib.pyplot as plt"]},{"cell_type":"markdown","source":["numpy <- matrix algebra and calculation  \n","uses numpy array which is a row major data structure\n","\n","pandas <- stats and data analysis  \n","uses pandas dataframe which is a column major data structure\n","\n","step 1. super or unsuper (type of learning)         \n","step 2. regression or classification or clustering or association (type of task)\n","\n","\n","---\n","\n"],"metadata":{"id":"5j4uoLczVNoF"}},{"cell_type":"code","source":["df = pd.read_csv(\"/content/sample_data/california_housing_train.csv\")\n","df[df.columns[2]]"],"metadata":{"id":"lSbJEW6kV4rM","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1681400606378,"user_tz":-330,"elapsed":130,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"c0f18d17-f2da-410a-f69a-4bebf2fc2bce"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["0        15.0\n","1        19.0\n","2        17.0\n","3        14.0\n","4        20.0\n","         ... \n","16995    52.0\n","16996    36.0\n","16997    17.0\n","16998    19.0\n","16999    52.0\n","Name: housing_median_age, Length: 17000, dtype: float64"]},"metadata":{},"execution_count":2}]},{"cell_type":"markdown","source":["**df.isna().sum()** is used for checking that our data does not contain a missing value or a NaN value\n","\n","Two types of calculation performed in python:- \n","*   lazy : uses yield in a fun like-range fun \n","*   eager : uses return in a fun like-pandas i.e., we don't use it for big data\\\n","\n","we use pyspark for big data\n","\n","**big data** = *when the size of training and testing data > ram size*"],"metadata":{"id":"PPIUBqCbjg7f"}},{"cell_type":"code","source":["df.isna().sum()"],"metadata":{"id":"eVfMMqLaa1ib","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1681400606379,"user_tz":-330,"elapsed":86,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"a7e48a16-6215-4d30-8aa8-88de93914485"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["longitude             0\n","latitude              0\n","housing_median_age    0\n","total_rooms           0\n","total_bedrooms        0\n","population            0\n","households            0\n","median_income         0\n","median_house_value    0\n","dtype: int64"]},"metadata":{},"execution_count":3}]},{"cell_type":"markdown","source":["input <- input features or independent variables  \n","output <- target features or dependent variables\n","\n","covariance is the variance for the case when two random variables co-exist together."],"metadata":{"id":"Os4V9JTdnVRO"}},{"cell_type":"markdown","source":["four compulsory observations/properties about the covariance matrix   \n","1.square matrix [where n*n]   \n","2.symmetric matrix [where upper triangle == lower triangle]  \n","3.cov(x,y) == cov(y,x)       \n","4.the dig is the var of each variable. "],"metadata":{"id":"0RbgHphh41Oe"}},{"cell_type":"markdown","source":["-♾ <= cov <= ♾  \n","cov has 2 parts : 1.sign (+ or -)  2.magnitude(number part)  \n","Here, sign determine the relationship that can be \n","A. direct (where x will increase then y will also increase and vice versa.)  \n","B. indirect (if x increase then y will decrease and vice versa.)   \n","Here, mag defines that the relation between the random variables is stong(in graph we can identitfy the line) or weak(we can not identify the line in the scatter plot)\n","\n","person corelation coefficient : r of x,y  \n","cov(x,y) / (sd of x * sd of y)  \n","it lies between -1 <= r of x,y <= 1  \n"],"metadata":{"id":"sZCc3YVEXlxw"}},{"cell_type":"markdown","source":["**Fake data**"],"metadata":{"id":"iV94ekFm3oPr"}},{"cell_type":"code","source":["x = np.random.normal(loc=0,scale=1,size=50)\n","y = (2*x) + 5 + np.random.normal(loc=0,scale=3,size=50)\n","fake = pd.DataFrame(data={\"X\":x,\"Y\":y})\n","plt.scatter(x,y)\n","fake.cov()\n","fake.corr()"],"metadata":{"id":"_wCIb455e2Dy","colab":{"base_uri":"https://localhost:8080/","height":525},"executionInfo":{"status":"ok","timestamp":1681400606380,"user_tz":-330,"elapsed":81,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"38cfe3cb-3d68-441e-a134-7f407cc59ebd"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["          X         Y\n","X  1.000000  0.669395\n","Y  0.669395  1.000000"],"text/html":["\n","  <div id=\"df-cd312d6e-d6f4-41a4-bf44-31c5ef28af02\">\n","    <div class=\"colab-df-container\">\n","      <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>X</th>\n","      <th>Y</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>X</th>\n","      <td>1.000000</td>\n","      <td>0.669395</td>\n","    </tr>\n","    <tr>\n","      <th>Y</th>\n","      <td>0.669395</td>\n","      <td>1.000000</td>\n","    </tr>\n","  </tbody>\n","</table>\n","</div>\n","      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-cd312d6e-d6f4-41a4-bf44-31c5ef28af02')\"\n","              title=\"Convert this dataframe to an interactive table.\"\n","              style=\"display:none;\">\n","        \n","  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n","       width=\"24px\">\n","    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n","    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n","  </svg>\n","      </button>\n","      \n","  <style>\n","    .colab-df-container {\n","      display:flex;\n","      flex-wrap:wrap;\n","      gap: 12px;\n","    }\n","\n","    .colab-df-convert {\n","      background-color: #E8F0FE;\n","      border: none;\n","      border-radius: 50%;\n","      cursor: pointer;\n","      display: none;\n","      fill: #1967D2;\n","      height: 32px;\n","      padding: 0 0 0 0;\n","      width: 32px;\n","    }\n","\n","    .colab-df-convert:hover {\n","      background-color: #E2EBFA;\n","      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n","      fill: #174EA6;\n","    }\n","\n","    [theme=dark] .colab-df-convert {\n","      background-color: #3B4455;\n","      fill: #D2E3FC;\n","    }\n","\n","    [theme=dark] .colab-df-convert:hover {\n","      background-color: #434B5C;\n","      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n","      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n","      fill: #FFFFFF;\n","    }\n","  </style>\n","\n","      <script>\n","        const buttonEl =\n","          document.querySelector('#df-cd312d6e-d6f4-41a4-bf44-31c5ef28af02 button.colab-df-convert');\n","        buttonEl.style.display =\n","          google.colab.kernel.accessAllowed ? 'block' : 'none';\n","\n","        async function convertToInteractive(key) {\n","          const element = document.querySelector('#df-cd312d6e-d6f4-41a4-bf44-31c5ef28af02');\n","          const dataTable =\n","            await google.colab.kernel.invokeFunction('convertToInteractive',\n","                                                     [key], {});\n","          if (!dataTable) return;\n","\n","          const docLinkHtml = 'Like what you see? Visit the ' +\n","            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n","            + ' to learn more about interactive tables.';\n","          element.innerHTML = '';\n","          dataTable['output_type'] = 'display_data';\n","          await google.colab.output.renderOutput(dataTable, element);\n","          const docLink = document.createElement('div');\n","          docLink.innerHTML = docLinkHtml;\n","          element.appendChild(docLink);\n","        }\n","      </script>\n","    </div>\n","  </div>\n","  "]},"metadata":{},"execution_count":4},{"output_type":"display_data","data":{"text/plain":["<Figure size 640x480 with 1 Axes>"],"image/png":"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\n"},"metadata":{}}]},{"cell_type":"markdown","source":["prediction of quality related data is classification  \n","prediction of quantity(related to any form of units : cm,euro,kg,mass,speed,etc.) related data is regression  \n","ground truth label = output column = y lable = target feature"],"metadata":{"id":"W-y1CLXBzRLx"}},{"cell_type":"markdown","source":["dividing data into 2 parts input features an questions and output feature as answer"],"metadata":{"id":"5LBt1sUS4DIO"}},{"cell_type":"code","source":["question  = df.iloc[:,:-1]\n","answer = df.iloc[:,-1]"],"metadata":{"id":"s6lDqaaLz-B9"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["from sklearn.linear_model import LinearRegression\n","algo = LinearRegression()\n","algo.fit(question,answer)\n","predictions = algo.predict(question)\n","mse = np.mean((predictions - answer)**2)\n","rmse = np.sqrt(mse)"],"metadata":{"id":"A8Ut_-WN3JgE"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["df.corr()"],"metadata":{"id":"fWLw5GvoBPCH","colab":{"base_uri":"https://localhost:8080/","height":395},"executionInfo":{"status":"ok","timestamp":1681400606385,"user_tz":-330,"elapsed":80,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"f4780e1e-469f-404c-d5e8-47db4bd21b97"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["                    longitude  latitude  housing_median_age  total_rooms  \\\n","longitude            1.000000 -0.925208           -0.114250     0.047010   \n","latitude            -0.925208  1.000000            0.016454    -0.038773   \n","housing_median_age  -0.114250  0.016454            1.000000    -0.360984   \n","total_rooms          0.047010 -0.038773           -0.360984     1.000000   \n","total_bedrooms       0.071802 -0.069373           -0.320434     0.928403   \n","population           0.101674 -0.111261           -0.295890     0.860170   \n","households           0.059628 -0.074902           -0.302754     0.919018   \n","median_income       -0.015485 -0.080303           -0.115932     0.195383   \n","median_house_value  -0.044982 -0.144917            0.106758     0.130991   \n","\n","                    total_bedrooms  population  households  median_income  \\\n","longitude                 0.071802    0.101674    0.059628      -0.015485   \n","latitude                 -0.069373   -0.111261   -0.074902      -0.080303   \n","housing_median_age       -0.320434   -0.295890   -0.302754      -0.115932   \n","total_rooms               0.928403    0.860170    0.919018       0.195383   \n","total_bedrooms            1.000000    0.881169    0.980920      -0.013495   \n","population                0.881169    1.000000    0.909247      -0.000638   \n","households                0.980920    0.909247    1.000000       0.007644   \n","median_income            -0.013495   -0.000638    0.007644       1.000000   \n","median_house_value        0.045783   -0.027850    0.061031       0.691871   \n","\n","                    median_house_value  \n","longitude                    -0.044982  \n","latitude                     -0.144917  \n","housing_median_age            0.106758  \n","total_rooms                   0.130991  \n","total_bedrooms                0.045783  \n","population                   -0.027850  \n","households                    0.061031  \n","median_income                 0.691871  \n","median_house_value            1.000000  "],"text/html":["\n","  <div id=\"df-046c2f3c-8871-4df6-a4a0-a19248f73921\">\n","    <div class=\"colab-df-container\">\n","      <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>longitude</th>\n","      <th>latitude</th>\n","      <th>housing_median_age</th>\n","      <th>total_rooms</th>\n","      <th>total_bedrooms</th>\n","      <th>population</th>\n","      <th>households</th>\n","      <th>median_income</th>\n","      <th>median_house_value</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>longitude</th>\n","      <td>1.000000</td>\n","      <td>-0.925208</td>\n","      <td>-0.114250</td>\n","      <td>0.047010</td>\n","      <td>0.071802</td>\n","      <td>0.101674</td>\n","      <td>0.059628</td>\n","      <td>-0.015485</td>\n","      <td>-0.044982</td>\n","    </tr>\n","    <tr>\n","      <th>latitude</th>\n","      <td>-0.925208</td>\n","      <td>1.000000</td>\n","      <td>0.016454</td>\n","      <td>-0.038773</td>\n","      <td>-0.069373</td>\n","      <td>-0.111261</td>\n","      <td>-0.074902</td>\n","      <td>-0.080303</td>\n","      <td>-0.144917</td>\n","    </tr>\n","    <tr>\n","      <th>housing_median_age</th>\n","      <td>-0.114250</td>\n","      <td>0.016454</td>\n","      <td>1.000000</td>\n","      <td>-0.360984</td>\n","      <td>-0.320434</td>\n","      <td>-0.295890</td>\n","      <td>-0.302754</td>\n","      <td>-0.115932</td>\n","      <td>0.106758</td>\n","    </tr>\n","    <tr>\n","      <th>total_rooms</th>\n","      <td>0.047010</td>\n","      <td>-0.038773</td>\n","      <td>-0.360984</td>\n","      <td>1.000000</td>\n","      <td>0.928403</td>\n","      <td>0.860170</td>\n","      <td>0.919018</td>\n","      <td>0.195383</td>\n","      <td>0.130991</td>\n","    </tr>\n","    <tr>\n","      <th>total_bedrooms</th>\n","      <td>0.071802</td>\n","      <td>-0.069373</td>\n","      <td>-0.320434</td>\n","      <td>0.928403</td>\n","      <td>1.000000</td>\n","      <td>0.881169</td>\n","      <td>0.980920</td>\n","      <td>-0.013495</td>\n","      <td>0.045783</td>\n","    </tr>\n","    <tr>\n","      <th>population</th>\n","      <td>0.101674</td>\n","      <td>-0.111261</td>\n","      <td>-0.295890</td>\n","      <td>0.860170</td>\n","      <td>0.881169</td>\n","      <td>1.000000</td>\n","      <td>0.909247</td>\n","      <td>-0.000638</td>\n","      <td>-0.027850</td>\n","    </tr>\n","    <tr>\n","      <th>households</th>\n","      <td>0.059628</td>\n","      <td>-0.074902</td>\n","      <td>-0.302754</td>\n","      <td>0.919018</td>\n","      <td>0.980920</td>\n","      <td>0.909247</td>\n","      <td>1.000000</td>\n","      <td>0.007644</td>\n","      <td>0.061031</td>\n","    </tr>\n","    <tr>\n","      <th>median_income</th>\n","      <td>-0.015485</td>\n","      <td>-0.080303</td>\n","      <td>-0.115932</td>\n","      <td>0.195383</td>\n","      <td>-0.013495</td>\n","      <td>-0.000638</td>\n","      <td>0.007644</td>\n","      <td>1.000000</td>\n","      <td>0.691871</td>\n","    </tr>\n","    <tr>\n","      <th>median_house_value</th>\n","      <td>-0.044982</td>\n","      <td>-0.144917</td>\n","      <td>0.106758</td>\n","      <td>0.130991</td>\n","      <td>0.045783</td>\n","      <td>-0.027850</td>\n","      <td>0.061031</td>\n","      <td>0.691871</td>\n","      <td>1.000000</td>\n","    </tr>\n","  </tbody>\n","</table>\n","</div>\n","      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-046c2f3c-8871-4df6-a4a0-a19248f73921')\"\n","              title=\"Convert this dataframe to an interactive table.\"\n","              style=\"display:none;\">\n","        \n","  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n","       width=\"24px\">\n","    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n","    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n","  </svg>\n","      </button>\n","      \n","  <style>\n","    .colab-df-container {\n","      display:flex;\n","      flex-wrap:wrap;\n","      gap: 12px;\n","    }\n","\n","    .colab-df-convert {\n","      background-color: #E8F0FE;\n","      border: none;\n","      border-radius: 50%;\n","      cursor: pointer;\n","      display: none;\n","      fill: #1967D2;\n","      height: 32px;\n","      padding: 0 0 0 0;\n","      width: 32px;\n","    }\n","\n","    .colab-df-convert:hover {\n","      background-color: #E2EBFA;\n","      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n","      fill: #174EA6;\n","    }\n","\n","    [theme=dark] .colab-df-convert {\n","      background-color: #3B4455;\n","      fill: #D2E3FC;\n","    }\n","\n","    [theme=dark] .colab-df-convert:hover {\n","      background-color: #434B5C;\n","      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n","      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n","      fill: #FFFFFF;\n","    }\n","  </style>\n","\n","      <script>\n","        const buttonEl =\n","          document.querySelector('#df-046c2f3c-8871-4df6-a4a0-a19248f73921 button.colab-df-convert');\n","        buttonEl.style.display =\n","          google.colab.kernel.accessAllowed ? 'block' : 'none';\n","\n","        async function convertToInteractive(key) {\n","          const element = document.querySelector('#df-046c2f3c-8871-4df6-a4a0-a19248f73921');\n","          const dataTable =\n","            await google.colab.kernel.invokeFunction('convertToInteractive',\n","                                                     [key], {});\n","          if (!dataTable) return;\n","\n","          const docLinkHtml = 'Like what you see? Visit the ' +\n","            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n","            + ' to learn more about interactive tables.';\n","          element.innerHTML = '';\n","          dataTable['output_type'] = 'display_data';\n","          await google.colab.output.renderOutput(dataTable, element);\n","          const docLink = document.createElement('div');\n","          docLink.innerHTML = docLinkHtml;\n","          element.appendChild(docLink);\n","        }\n","      </script>\n","    </div>\n","  </div>\n","  "]},"metadata":{},"execution_count":7}]},{"cell_type":"code","source":["matrix = df.corr()"],"metadata":{"id":"HxyItMusPMch"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["a = abs(matrix['median_house_value'])>=0.1"],"metadata":{"id":"7j3o56GlUNYD"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["a = a[a==1]"],"metadata":{"id":"tqqMeXbnUg0S"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["b = df[a.index]"],"metadata":{"id":"NrnPPdHmWhIj"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["b"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":423},"id":"OOyVkg-xXp2E","executionInfo":{"status":"ok","timestamp":1681400606389,"user_tz":-330,"elapsed":81,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"8adccea4-94f5-4918-da59-2104539f68bf"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["       latitude  housing_median_age  total_rooms  median_income  \\\n","0         34.19                15.0       5612.0         1.4936   \n","1         34.40                19.0       7650.0         1.8200   \n","2         33.69                17.0        720.0         1.6509   \n","3         33.64                14.0       1501.0         3.1917   \n","4         33.57                20.0       1454.0         1.9250   \n","...         ...                 ...          ...            ...   \n","16995     40.58                52.0       2217.0         2.3571   \n","16996     40.69                36.0       2349.0         2.5179   \n","16997     41.84                17.0       2677.0         3.0313   \n","16998     41.80                19.0       2672.0         1.9797   \n","16999     40.54                52.0       1820.0         3.0147   \n","\n","       median_house_value  \n","0                 66900.0  \n","1                 80100.0  \n","2                 85700.0  \n","3                 73400.0  \n","4                 65500.0  \n","...                   ...  \n","16995            111400.0  \n","16996             79000.0  \n","16997            103600.0  \n","16998             85800.0  \n","16999             94600.0  \n","\n","[17000 rows x 5 columns]"],"text/html":["\n","  <div id=\"df-2c43e6cd-81ff-4c09-86d8-0b364e35a9f5\">\n","    <div class=\"colab-df-container\">\n","      <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>latitude</th>\n","      <th>housing_median_age</th>\n","      <th>total_rooms</th>\n","      <th>median_income</th>\n","      <th>median_house_value</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>0</th>\n","      <td>34.19</td>\n","      <td>15.0</td>\n","      <td>5612.0</td>\n","      <td>1.4936</td>\n","      <td>66900.0</td>\n","    </tr>\n","    <tr>\n","      <th>1</th>\n","      <td>34.40</td>\n","      <td>19.0</td>\n","      <td>7650.0</td>\n","      <td>1.8200</td>\n","      <td>80100.0</td>\n","    </tr>\n","    <tr>\n","      <th>2</th>\n","      <td>33.69</td>\n","      <td>17.0</td>\n","      <td>720.0</td>\n","      <td>1.6509</td>\n","      <td>85700.0</td>\n","    </tr>\n","    <tr>\n","      <th>3</th>\n","      <td>33.64</td>\n","      <td>14.0</td>\n","      <td>1501.0</td>\n","      <td>3.1917</td>\n","      <td>73400.0</td>\n","    </tr>\n","    <tr>\n","      <th>4</th>\n","      <td>33.57</td>\n","      <td>20.0</td>\n","      <td>1454.0</td>\n","      <td>1.9250</td>\n","      <td>65500.0</td>\n","    </tr>\n","    <tr>\n","      <th>...</th>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","    </tr>\n","    <tr>\n","      <th>16995</th>\n","      <td>40.58</td>\n","      <td>52.0</td>\n","      <td>2217.0</td>\n","      <td>2.3571</td>\n","      <td>111400.0</td>\n","    </tr>\n","    <tr>\n","      <th>16996</th>\n","      <td>40.69</td>\n","      <td>36.0</td>\n","      <td>2349.0</td>\n","      <td>2.5179</td>\n","      <td>79000.0</td>\n","    </tr>\n","    <tr>\n","      <th>16997</th>\n","      <td>41.84</td>\n","      <td>17.0</td>\n","      <td>2677.0</td>\n","      <td>3.0313</td>\n","      <td>103600.0</td>\n","    </tr>\n","    <tr>\n","      <th>16998</th>\n","      <td>41.80</td>\n","      <td>19.0</td>\n","      <td>2672.0</td>\n","      <td>1.9797</td>\n","      <td>85800.0</td>\n","    </tr>\n","    <tr>\n","      <th>16999</th>\n","      <td>40.54</td>\n","      <td>52.0</td>\n","      <td>1820.0</td>\n","      <td>3.0147</td>\n","      <td>94600.0</td>\n","    </tr>\n","  </tbody>\n","</table>\n","<p>17000 rows × 5 columns</p>\n","</div>\n","      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-2c43e6cd-81ff-4c09-86d8-0b364e35a9f5')\"\n","              title=\"Convert this dataframe to an interactive table.\"\n","              style=\"display:none;\">\n","        \n","  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n","       width=\"24px\">\n","    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n","    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n","  </svg>\n","      </button>\n","      \n","  <style>\n","    .colab-df-container {\n","      display:flex;\n","      flex-wrap:wrap;\n","      gap: 12px;\n","    }\n","\n","    .colab-df-convert {\n","      background-color: #E8F0FE;\n","      border: none;\n","      border-radius: 50%;\n","      cursor: pointer;\n","      display: none;\n","      fill: #1967D2;\n","      height: 32px;\n","      padding: 0 0 0 0;\n","      width: 32px;\n","    }\n","\n","    .colab-df-convert:hover {\n","      background-color: #E2EBFA;\n","      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n","      fill: #174EA6;\n","    }\n","\n","    [theme=dark] .colab-df-convert {\n","      background-color: #3B4455;\n","      fill: #D2E3FC;\n","    }\n","\n","    [theme=dark] .colab-df-convert:hover {\n","      background-color: #434B5C;\n","      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n","      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n","      fill: #FFFFFF;\n","    }\n","  </style>\n","\n","      <script>\n","        const buttonEl =\n","          document.querySelector('#df-2c43e6cd-81ff-4c09-86d8-0b364e35a9f5 button.colab-df-convert');\n","        buttonEl.style.display =\n","          google.colab.kernel.accessAllowed ? 'block' : 'none';\n","\n","        async function convertToInteractive(key) {\n","          const element = document.querySelector('#df-2c43e6cd-81ff-4c09-86d8-0b364e35a9f5');\n","          const dataTable =\n","            await google.colab.kernel.invokeFunction('convertToInteractive',\n","                                                     [key], {});\n","          if (!dataTable) return;\n","\n","          const docLinkHtml = 'Like what you see? Visit the ' +\n","            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n","            + ' to learn more about interactive tables.';\n","          element.innerHTML = '';\n","          dataTable['output_type'] = 'display_data';\n","          await google.colab.output.renderOutput(dataTable, element);\n","          const docLink = document.createElement('div');\n","          docLink.innerHTML = docLinkHtml;\n","          element.appendChild(docLink);\n","        }\n","      </script>\n","    </div>\n","  </div>\n","  "]},"metadata":{},"execution_count":12}]},{"cell_type":"code","source":["new_question = b.iloc[:,0:4] "],"metadata":{"id":"yvz-DSc_ZIJs"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["new_question"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":423},"id":"ySn3PS9LbAE1","executionInfo":{"status":"ok","timestamp":1681400606391,"user_tz":-330,"elapsed":81,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"2a084a88-24d7-4226-bdb7-087e4a47e837"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["       latitude  housing_median_age  total_rooms  median_income\n","0         34.19                15.0       5612.0         1.4936\n","1         34.40                19.0       7650.0         1.8200\n","2         33.69                17.0        720.0         1.6509\n","3         33.64                14.0       1501.0         3.1917\n","4         33.57                20.0       1454.0         1.9250\n","...         ...                 ...          ...            ...\n","16995     40.58                52.0       2217.0         2.3571\n","16996     40.69                36.0       2349.0         2.5179\n","16997     41.84                17.0       2677.0         3.0313\n","16998     41.80                19.0       2672.0         1.9797\n","16999     40.54                52.0       1820.0         3.0147\n","\n","[17000 rows x 4 columns]"],"text/html":["\n","  <div id=\"df-009e96ea-b61d-48b6-8b68-4946f75c60e3\">\n","    <div class=\"colab-df-container\">\n","      <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>latitude</th>\n","      <th>housing_median_age</th>\n","      <th>total_rooms</th>\n","      <th>median_income</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>0</th>\n","      <td>34.19</td>\n","      <td>15.0</td>\n","      <td>5612.0</td>\n","      <td>1.4936</td>\n","    </tr>\n","    <tr>\n","      <th>1</th>\n","      <td>34.40</td>\n","      <td>19.0</td>\n","      <td>7650.0</td>\n","      <td>1.8200</td>\n","    </tr>\n","    <tr>\n","      <th>2</th>\n","      <td>33.69</td>\n","      <td>17.0</td>\n","      <td>720.0</td>\n","      <td>1.6509</td>\n","    </tr>\n","    <tr>\n","      <th>3</th>\n","      <td>33.64</td>\n","      <td>14.0</td>\n","      <td>1501.0</td>\n","      <td>3.1917</td>\n","    </tr>\n","    <tr>\n","      <th>4</th>\n","      <td>33.57</td>\n","      <td>20.0</td>\n","      <td>1454.0</td>\n","      <td>1.9250</td>\n","    </tr>\n","    <tr>\n","      <th>...</th>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","    </tr>\n","    <tr>\n","      <th>16995</th>\n","      <td>40.58</td>\n","      <td>52.0</td>\n","      <td>2217.0</td>\n","      <td>2.3571</td>\n","    </tr>\n","    <tr>\n","      <th>16996</th>\n","      <td>40.69</td>\n","      <td>36.0</td>\n","      <td>2349.0</td>\n","      <td>2.5179</td>\n","    </tr>\n","    <tr>\n","      <th>16997</th>\n","      <td>41.84</td>\n","      <td>17.0</td>\n","      <td>2677.0</td>\n","      <td>3.0313</td>\n","    </tr>\n","    <tr>\n","      <th>16998</th>\n","      <td>41.80</td>\n","      <td>19.0</td>\n","      <td>2672.0</td>\n","      <td>1.9797</td>\n","    </tr>\n","    <tr>\n","      <th>16999</th>\n","      <td>40.54</td>\n","      <td>52.0</td>\n","      <td>1820.0</td>\n","      <td>3.0147</td>\n","    </tr>\n","  </tbody>\n","</table>\n","<p>17000 rows × 4 columns</p>\n","</div>\n","      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-009e96ea-b61d-48b6-8b68-4946f75c60e3')\"\n","              title=\"Convert this dataframe to an interactive table.\"\n","              style=\"display:none;\">\n","        \n","  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n","       width=\"24px\">\n","    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n","    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n","  </svg>\n","      </button>\n","      \n","  <style>\n","    .colab-df-container {\n","      display:flex;\n","      flex-wrap:wrap;\n","      gap: 12px;\n","    }\n","\n","    .colab-df-convert {\n","      background-color: #E8F0FE;\n","      border: none;\n","      border-radius: 50%;\n","      cursor: pointer;\n","      display: none;\n","      fill: #1967D2;\n","      height: 32px;\n","      padding: 0 0 0 0;\n","      width: 32px;\n","    }\n","\n","    .colab-df-convert:hover {\n","      background-color: #E2EBFA;\n","      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n","      fill: #174EA6;\n","    }\n","\n","    [theme=dark] .colab-df-convert {\n","      background-color: #3B4455;\n","      fill: #D2E3FC;\n","    }\n","\n","    [theme=dark] .colab-df-convert:hover {\n","      background-color: #434B5C;\n","      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n","      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n","      fill: #FFFFFF;\n","    }\n","  </style>\n","\n","      <script>\n","        const buttonEl =\n","          document.querySelector('#df-009e96ea-b61d-48b6-8b68-4946f75c60e3 button.colab-df-convert');\n","        buttonEl.style.display =\n","          google.colab.kernel.accessAllowed ? 'block' : 'none';\n","\n","        async function convertToInteractive(key) {\n","          const element = document.querySelector('#df-009e96ea-b61d-48b6-8b68-4946f75c60e3');\n","          const dataTable =\n","            await google.colab.kernel.invokeFunction('convertToInteractive',\n","                                                     [key], {});\n","          if (!dataTable) return;\n","\n","          const docLinkHtml = 'Like what you see? Visit the ' +\n","            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n","            + ' to learn more about interactive tables.';\n","          element.innerHTML = '';\n","          dataTable['output_type'] = 'display_data';\n","          await google.colab.output.renderOutput(dataTable, element);\n","          const docLink = document.createElement('div');\n","          docLink.innerHTML = docLinkHtml;\n","          element.appendChild(docLink);\n","        }\n","      </script>\n","    </div>\n","  </div>\n","  "]},"metadata":{},"execution_count":14}]},{"cell_type":"code","source":["algo.fit(new_question,answer)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":75},"id":"qafyJoyebCal","executionInfo":{"status":"ok","timestamp":1681400606391,"user_tz":-330,"elapsed":79,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"86984c9c-0593-40b1-9925-0eb671bbe51f"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["LinearRegression()"],"text/html":["<style>#sk-container-id-1 {color: black;background-color: white;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LinearRegression</label><div class=\"sk-toggleable__content\"><pre>LinearRegression()</pre></div></div></div></div></div>"]},"metadata":{},"execution_count":15}]},{"cell_type":"code","source":["predictions = algo.predict(new_question)\n","predictions"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"FAoPzo1Ibrwd","executionInfo":{"status":"ok","timestamp":1681400606392,"user_tz":-330,"elapsed":79,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"9446f5ff-0122-4904-cf22-55280e4cc6a0"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([ 97273.71981984, 125380.69015186,  92433.73222587, ...,\n","       118232.12115153,  77858.65668167, 189664.51046922])"]},"metadata":{},"execution_count":16}]},{"cell_type":"code","source":["mse = np.mean((predictions - answer)**2)"],"metadata":{"id":"Oza_RciBeUdD"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["rmse = np.sqrt(mse)"],"metadata":{"id":"xcg1KHsaeUdD"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["rmse"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"gl6qWSJAeV5-","executionInfo":{"status":"ok","timestamp":1681400606400,"user_tz":-330,"elapsed":82,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"6da34cab-feae-4f43-9116-666c8c45c6f0"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["79817.22603819976"]},"metadata":{},"execution_count":19}]},{"cell_type":"markdown","source":["1.data filtering (by selecting the input features those who has high correlation with target feature) \n","\n","---\n","\n","\n","2.data normalization  \n","types of normalization :  \n","min normalization(each column will be divided by min of data) ,  \n","max normalization(each column will be divided by min of data) ,  \n","standard normalization(mostly used)(converting the data into the z score)  \n","\n","---\n","\n","\n","3.data filtering (by selecting those input features which do not have high correlation with each other but have a high correlation with the target,reason ,because we will not be able to create a good vector space to be learnt in linear algebra) this can be solved by pca or feature selection\n","pca - uses dimension reduction by transforming data  \n","feature selection - uses direction inspection over the persorn correlation matrix\n","\n","---\n","\n","\n","4."],"metadata":{"id":"OU5qVfJIfhwQ"}},{"cell_type":"code","source":["new_question = (new_question-new_question.mean())/new_question.std()\n","answer = (answer-answer.mean())/answer.std()"],"metadata":{"id":"hPq3B86Bn-l0"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["new_question"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":423},"id":"JEyvjwSGocCM","executionInfo":{"status":"ok","timestamp":1681400606402,"user_tz":-330,"elapsed":80,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"d00e9ea8-3f59-453a-ff89-5abe727cd030"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["       latitude  housing_median_age  total_rooms  median_income\n","0     -0.671500           -1.079639     1.361655      -1.252506\n","1     -0.573248           -0.761850     2.296540      -1.081451\n","2     -0.905436           -0.920744    -0.882436      -1.170071\n","3     -0.928830           -1.159087    -0.524171      -0.362590\n","4     -0.961581           -0.682402    -0.545731      -1.026424\n","...         ...                 ...          ...            ...\n","16995  2.318197            1.859916    -0.195722      -0.799975\n","16996  2.369663            0.588757    -0.135170      -0.715705\n","16997  2.907715           -0.920744     0.015292      -0.446650\n","16998  2.889000           -0.761850     0.012998      -0.997758\n","16999  2.299482            1.859916    -0.377837      -0.455349\n","\n","[17000 rows x 4 columns]"],"text/html":["\n","  <div id=\"df-fed3c8ae-e920-4100-a62d-8f2f4ed4a3b5\">\n","    <div class=\"colab-df-container\">\n","      <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>latitude</th>\n","      <th>housing_median_age</th>\n","      <th>total_rooms</th>\n","      <th>median_income</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>0</th>\n","      <td>-0.671500</td>\n","      <td>-1.079639</td>\n","      <td>1.361655</td>\n","      <td>-1.252506</td>\n","    </tr>\n","    <tr>\n","      <th>1</th>\n","      <td>-0.573248</td>\n","      <td>-0.761850</td>\n","      <td>2.296540</td>\n","      <td>-1.081451</td>\n","    </tr>\n","    <tr>\n","      <th>2</th>\n","      <td>-0.905436</td>\n","      <td>-0.920744</td>\n","      <td>-0.882436</td>\n","      <td>-1.170071</td>\n","    </tr>\n","    <tr>\n","      <th>3</th>\n","      <td>-0.928830</td>\n","      <td>-1.159087</td>\n","      <td>-0.524171</td>\n","      <td>-0.362590</td>\n","    </tr>\n","    <tr>\n","      <th>4</th>\n","      <td>-0.961581</td>\n","      <td>-0.682402</td>\n","      <td>-0.545731</td>\n","      <td>-1.026424</td>\n","    </tr>\n","    <tr>\n","      <th>...</th>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","    </tr>\n","    <tr>\n","      <th>16995</th>\n","      <td>2.318197</td>\n","      <td>1.859916</td>\n","      <td>-0.195722</td>\n","      <td>-0.799975</td>\n","    </tr>\n","    <tr>\n","      <th>16996</th>\n","      <td>2.369663</td>\n","      <td>0.588757</td>\n","      <td>-0.135170</td>\n","      <td>-0.715705</td>\n","    </tr>\n","    <tr>\n","      <th>16997</th>\n","      <td>2.907715</td>\n","      <td>-0.920744</td>\n","      <td>0.015292</td>\n","      <td>-0.446650</td>\n","    </tr>\n","    <tr>\n","      <th>16998</th>\n","      <td>2.889000</td>\n","      <td>-0.761850</td>\n","      <td>0.012998</td>\n","      <td>-0.997758</td>\n","    </tr>\n","    <tr>\n","      <th>16999</th>\n","      <td>2.299482</td>\n","      <td>1.859916</td>\n","      <td>-0.377837</td>\n","      <td>-0.455349</td>\n","    </tr>\n","  </tbody>\n","</table>\n","<p>17000 rows × 4 columns</p>\n","</div>\n","      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-fed3c8ae-e920-4100-a62d-8f2f4ed4a3b5')\"\n","              title=\"Convert this dataframe to an interactive table.\"\n","              style=\"display:none;\">\n","        \n","  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n","       width=\"24px\">\n","    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n","    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n","  </svg>\n","      </button>\n","      \n","  <style>\n","    .colab-df-container {\n","      display:flex;\n","      flex-wrap:wrap;\n","      gap: 12px;\n","    }\n","\n","    .colab-df-convert {\n","      background-color: #E8F0FE;\n","      border: none;\n","      border-radius: 50%;\n","      cursor: pointer;\n","      display: none;\n","      fill: #1967D2;\n","      height: 32px;\n","      padding: 0 0 0 0;\n","      width: 32px;\n","    }\n","\n","    .colab-df-convert:hover {\n","      background-color: #E2EBFA;\n","      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n","      fill: #174EA6;\n","    }\n","\n","    [theme=dark] .colab-df-convert {\n","      background-color: #3B4455;\n","      fill: #D2E3FC;\n","    }\n","\n","    [theme=dark] .colab-df-convert:hover {\n","      background-color: #434B5C;\n","      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n","      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n","      fill: #FFFFFF;\n","    }\n","  </style>\n","\n","      <script>\n","        const buttonEl =\n","          document.querySelector('#df-fed3c8ae-e920-4100-a62d-8f2f4ed4a3b5 button.colab-df-convert');\n","        buttonEl.style.display =\n","          google.colab.kernel.accessAllowed ? 'block' : 'none';\n","\n","        async function convertToInteractive(key) {\n","          const element = document.querySelector('#df-fed3c8ae-e920-4100-a62d-8f2f4ed4a3b5');\n","          const dataTable =\n","            await google.colab.kernel.invokeFunction('convertToInteractive',\n","                                                     [key], {});\n","          if (!dataTable) return;\n","\n","          const docLinkHtml = 'Like what you see? Visit the ' +\n","            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n","            + ' to learn more about interactive tables.';\n","          element.innerHTML = '';\n","          dataTable['output_type'] = 'display_data';\n","          await google.colab.output.renderOutput(dataTable, element);\n","          const docLink = document.createElement('div');\n","          docLink.innerHTML = docLinkHtml;\n","          element.appendChild(docLink);\n","        }\n","      </script>\n","    </div>\n","  </div>\n","  "]},"metadata":{},"execution_count":21}]},{"cell_type":"code","source":["algo.fit(new_question,answer)\n","predictions = algo.predict(new_question)\n","predictions"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1681400932263,"user_tz":-330,"elapsed":577,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"a12bcb5f-513b-4934-eafc-fc3153ab00d6","id":"56ZEXhp_rJiB"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([-0.94864305, -0.70630767, -0.99037293, ..., -0.76794189,\n","       -1.11603772, -0.15205923])"]},"metadata":{},"execution_count":62}]},{"cell_type":"code","source":["mse = np.mean((predictions - answer)/answer**2)"],"metadata":{"id":"ywL2zinnrJiD"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["rmse = np.sqrt(mse)"],"metadata":{"id":"uRz8qcHXrJiD"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["rmse"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1681400932809,"user_tz":-330,"elapsed":11,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"3cf5bd2e-449a-426f-cf59-c57ad47efb33","id":"x7JlWVG3rJiD"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["1011.0710443767184"]},"metadata":{},"execution_count":65}]},{"cell_type":"code","source":["answer"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"lHwFmMxOrM9k","executionInfo":{"status":"ok","timestamp":1681400933385,"user_tz":-330,"elapsed":4,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"e256db8e-54c7-43a5-b370-dfedc1df0189"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["0       -1.210522\n","1       -1.096713\n","2       -1.048430\n","3       -1.154480\n","4       -1.222593\n","           ...   \n","16995   -0.826848\n","16996   -1.106197\n","16997   -0.894099\n","16998   -1.047568\n","16999   -0.971696\n","Name: median_house_value, Length: 17000, dtype: float64"]},"metadata":{},"execution_count":66}]},{"cell_type":"code","source":["from sklearn.metrics import r2_score\n","percentage = r2_score(y_true = answer,y_pred=predictions)\n","percentage"],"metadata":{"id":"sLZvAU1vr4_z","executionInfo":{"status":"ok","timestamp":1681400934372,"user_tz":-330,"elapsed":3,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"colab":{"base_uri":"https://localhost:8080/"},"outputId":"a0b7551e-bb45-4629-9672-1fa952a918cb"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["0.5263861351522849"]},"metadata":{},"execution_count":67}]},{"cell_type":"markdown","source":["different dimension reduction algos':-  \n","pca - principal components analysis  \n","lda - linear discriminant analysis  \n","lsa - latent semantic analysis (used in chatgpt :)"],"metadata":{"id":"ettuIDfS8UVt"}},{"cell_type":"code","source":["question = (question-question.mean())/question.std()"],"metadata":{"id":"TpcLf0QX6szk"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["question"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":423},"id":"CgeB1xQH9vc2","executionInfo":{"status":"ok","timestamp":1681400940142,"user_tz":-330,"elapsed":21,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"2b080c87-7bd0-4b01-f91e-9b2b458c3437"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["       longitude  latitude  housing_median_age  total_rooms  total_bedrooms  \\\n","0       2.619288 -0.671500           -1.079639     1.361655        1.764152   \n","1       2.539494 -0.573248           -0.761850     2.296540        3.230346   \n","2       2.494610 -0.905436           -0.920744    -0.882436       -0.866931   \n","3       2.489623 -0.928830           -1.159087    -0.524171       -0.480216   \n","4       2.489623 -0.961581           -0.682402    -0.545731       -0.506313   \n","...          ...       ...                 ...          ...             ...   \n","16995  -2.342894  2.318197            1.859916    -0.195722       -0.344985   \n","16996  -2.347881  2.369663            0.588757    -0.135170       -0.027072   \n","16997  -2.362842  2.907715           -0.920744     0.015292       -0.019955   \n","16998  -2.362842  2.889000           -0.761850     0.012998        0.029868   \n","16999  -2.387778  2.299482            1.859916    -0.377837       -0.567998   \n","\n","       population  households  median_income  \n","0       -0.361173   -0.075996      -1.252506  \n","1       -0.261858   -0.099401      -1.081451  \n","2       -0.955326   -0.999223      -1.170071  \n","3       -0.796769   -0.715753      -0.362590  \n","4       -0.701809   -0.622130      -1.026424  \n","...           ...         ...            ...  \n","16995   -0.455262   -0.343862      -0.799975  \n","16996   -0.205230   -0.094200      -0.715705  \n","16997   -0.161670   -0.117606      -0.446650  \n","16998   -0.114626   -0.060392      -0.997758  \n","16999   -0.543252   -0.601325      -0.455349  \n","\n","[17000 rows x 8 columns]"],"text/html":["\n","  <div id=\"df-368cab9f-b8ee-4f65-a395-7d5e6a8c0f7a\">\n","    <div class=\"colab-df-container\">\n","      <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>longitude</th>\n","      <th>latitude</th>\n","      <th>housing_median_age</th>\n","      <th>total_rooms</th>\n","      <th>total_bedrooms</th>\n","      <th>population</th>\n","      <th>households</th>\n","      <th>median_income</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>0</th>\n","      <td>2.619288</td>\n","      <td>-0.671500</td>\n","      <td>-1.079639</td>\n","      <td>1.361655</td>\n","      <td>1.764152</td>\n","      <td>-0.361173</td>\n","      <td>-0.075996</td>\n","      <td>-1.252506</td>\n","    </tr>\n","    <tr>\n","      <th>1</th>\n","      <td>2.539494</td>\n","      <td>-0.573248</td>\n","      <td>-0.761850</td>\n","      <td>2.296540</td>\n","      <td>3.230346</td>\n","      <td>-0.261858</td>\n","      <td>-0.099401</td>\n","      <td>-1.081451</td>\n","    </tr>\n","    <tr>\n","      <th>2</th>\n","      <td>2.494610</td>\n","      <td>-0.905436</td>\n","      <td>-0.920744</td>\n","      <td>-0.882436</td>\n","      <td>-0.866931</td>\n","      <td>-0.955326</td>\n","      <td>-0.999223</td>\n","      <td>-1.170071</td>\n","    </tr>\n","    <tr>\n","      <th>3</th>\n","      <td>2.489623</td>\n","      <td>-0.928830</td>\n","      <td>-1.159087</td>\n","      <td>-0.524171</td>\n","      <td>-0.480216</td>\n","      <td>-0.796769</td>\n","      <td>-0.715753</td>\n","      <td>-0.362590</td>\n","    </tr>\n","    <tr>\n","      <th>4</th>\n","      <td>2.489623</td>\n","      <td>-0.961581</td>\n","      <td>-0.682402</td>\n","      <td>-0.545731</td>\n","      <td>-0.506313</td>\n","      <td>-0.701809</td>\n","      <td>-0.622130</td>\n","      <td>-1.026424</td>\n","    </tr>\n","    <tr>\n","      <th>...</th>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","    </tr>\n","    <tr>\n","      <th>16995</th>\n","      <td>-2.342894</td>\n","      <td>2.318197</td>\n","      <td>1.859916</td>\n","      <td>-0.195722</td>\n","      <td>-0.344985</td>\n","      <td>-0.455262</td>\n","      <td>-0.343862</td>\n","      <td>-0.799975</td>\n","    </tr>\n","    <tr>\n","      <th>16996</th>\n","      <td>-2.347881</td>\n","      <td>2.369663</td>\n","      <td>0.588757</td>\n","      <td>-0.135170</td>\n","      <td>-0.027072</td>\n","      <td>-0.205230</td>\n","      <td>-0.094200</td>\n","      <td>-0.715705</td>\n","    </tr>\n","    <tr>\n","      <th>16997</th>\n","      <td>-2.362842</td>\n","      <td>2.907715</td>\n","      <td>-0.920744</td>\n","      <td>0.015292</td>\n","      <td>-0.019955</td>\n","      <td>-0.161670</td>\n","      <td>-0.117606</td>\n","      <td>-0.446650</td>\n","    </tr>\n","    <tr>\n","      <th>16998</th>\n","      <td>-2.362842</td>\n","      <td>2.889000</td>\n","      <td>-0.761850</td>\n","      <td>0.012998</td>\n","      <td>0.029868</td>\n","      <td>-0.114626</td>\n","      <td>-0.060392</td>\n","      <td>-0.997758</td>\n","    </tr>\n","    <tr>\n","      <th>16999</th>\n","      <td>-2.387778</td>\n","      <td>2.299482</td>\n","      <td>1.859916</td>\n","      <td>-0.377837</td>\n","      <td>-0.567998</td>\n","      <td>-0.543252</td>\n","      <td>-0.601325</td>\n","      <td>-0.455349</td>\n","    </tr>\n","  </tbody>\n","</table>\n","<p>17000 rows × 8 columns</p>\n","</div>\n","      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-368cab9f-b8ee-4f65-a395-7d5e6a8c0f7a')\"\n","              title=\"Convert this dataframe to an interactive table.\"\n","              style=\"display:none;\">\n","        \n","  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n","       width=\"24px\">\n","    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n","    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n","  </svg>\n","      </button>\n","      \n","  <style>\n","    .colab-df-container {\n","      display:flex;\n","      flex-wrap:wrap;\n","      gap: 12px;\n","    }\n","\n","    .colab-df-convert {\n","      background-color: #E8F0FE;\n","      border: none;\n","      border-radius: 50%;\n","      cursor: pointer;\n","      display: none;\n","      fill: #1967D2;\n","      height: 32px;\n","      padding: 0 0 0 0;\n","      width: 32px;\n","    }\n","\n","    .colab-df-convert:hover {\n","      background-color: #E2EBFA;\n","      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n","      fill: #174EA6;\n","    }\n","\n","    [theme=dark] .colab-df-convert {\n","      background-color: #3B4455;\n","      fill: #D2E3FC;\n","    }\n","\n","    [theme=dark] .colab-df-convert:hover {\n","      background-color: #434B5C;\n","      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n","      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n","      fill: #FFFFFF;\n","    }\n","  </style>\n","\n","      <script>\n","        const buttonEl =\n","          document.querySelector('#df-368cab9f-b8ee-4f65-a395-7d5e6a8c0f7a button.colab-df-convert');\n","        buttonEl.style.display =\n","          google.colab.kernel.accessAllowed ? 'block' : 'none';\n","\n","        async function convertToInteractive(key) {\n","          const element = document.querySelector('#df-368cab9f-b8ee-4f65-a395-7d5e6a8c0f7a');\n","          const dataTable =\n","            await google.colab.kernel.invokeFunction('convertToInteractive',\n","                                                     [key], {});\n","          if (!dataTable) return;\n","\n","          const docLinkHtml = 'Like what you see? Visit the ' +\n","            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n","            + ' to learn more about interactive tables.';\n","          element.innerHTML = '';\n","          dataTable['output_type'] = 'display_data';\n","          await google.colab.output.renderOutput(dataTable, element);\n","          const docLink = document.createElement('div');\n","          docLink.innerHTML = docLinkHtml;\n","          element.appendChild(docLink);\n","        }\n","      </script>\n","    </div>\n","  </div>\n","  "]},"metadata":{},"execution_count":69}]},{"cell_type":"code","source":["from sklearn.decomposition import PCA "],"metadata":{"id":"SwSs4SnxmklT"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["for i in range(8,0,-1):\n","  pca = PCA(n_components=i)\n","  x = pca.fit_transform(question)\n","  obj = LinearRegression()\n","  obj.fit(x,answer)\n","  p = obj.predict(x)\n","  print(r2_score(y_true = answer,y_pred = p))"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"8rEB6T4B9_gl","executionInfo":{"status":"ok","timestamp":1681400946753,"user_tz":-330,"elapsed":11,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"2132aa22-ec74-4425-ff7c-aa78e6e2682d"},"execution_count":null,"outputs":[{"output_type":"stream","name":"stdout","text":["0.6413378529502689\n","0.6403406940196337\n","0.6302927692582099\n","0.5417640911270948\n","0.528361210858408\n","0.32096848270613765\n","0.0065215311612544236\n","0.003419012049628689\n"]}]},{"cell_type":"markdown","source":["using in built pca as well as user built pca"],"metadata":{"id":"mwDb45SKoydh"}},{"cell_type":"code","source":["question = df.drop(labels=df.columns[-1],axis = 1)\n","question"],"metadata":{"id":"v1HOrNNjFWy2","colab":{"base_uri":"https://localhost:8080/","height":423},"executionInfo":{"status":"ok","timestamp":1681400609602,"user_tz":-330,"elapsed":75,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"2728c872-d2fc-44c6-8f46-d1d8cec3110d"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["       longitude  latitude  housing_median_age  total_rooms  total_bedrooms  \\\n","0        -114.31     34.19                15.0       5612.0          1283.0   \n","1        -114.47     34.40                19.0       7650.0          1901.0   \n","2        -114.56     33.69                17.0        720.0           174.0   \n","3        -114.57     33.64                14.0       1501.0           337.0   \n","4        -114.57     33.57                20.0       1454.0           326.0   \n","...          ...       ...                 ...          ...             ...   \n","16995    -124.26     40.58                52.0       2217.0           394.0   \n","16996    -124.27     40.69                36.0       2349.0           528.0   \n","16997    -124.30     41.84                17.0       2677.0           531.0   \n","16998    -124.30     41.80                19.0       2672.0           552.0   \n","16999    -124.35     40.54                52.0       1820.0           300.0   \n","\n","       population  households  median_income  \n","0          1015.0       472.0         1.4936  \n","1          1129.0       463.0         1.8200  \n","2           333.0       117.0         1.6509  \n","3           515.0       226.0         3.1917  \n","4           624.0       262.0         1.9250  \n","...           ...         ...            ...  \n","16995       907.0       369.0         2.3571  \n","16996      1194.0       465.0         2.5179  \n","16997      1244.0       456.0         3.0313  \n","16998      1298.0       478.0         1.9797  \n","16999       806.0       270.0         3.0147  \n","\n","[17000 rows x 8 columns]"],"text/html":["\n","  <div id=\"df-e02fe053-b5e3-4ccf-b9de-41e45e35ac7d\">\n","    <div class=\"colab-df-container\">\n","      <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>longitude</th>\n","      <th>latitude</th>\n","      <th>housing_median_age</th>\n","      <th>total_rooms</th>\n","      <th>total_bedrooms</th>\n","      <th>population</th>\n","      <th>households</th>\n","      <th>median_income</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>0</th>\n","      <td>-114.31</td>\n","      <td>34.19</td>\n","      <td>15.0</td>\n","      <td>5612.0</td>\n","      <td>1283.0</td>\n","      <td>1015.0</td>\n","      <td>472.0</td>\n","      <td>1.4936</td>\n","    </tr>\n","    <tr>\n","      <th>1</th>\n","      <td>-114.47</td>\n","      <td>34.40</td>\n","      <td>19.0</td>\n","      <td>7650.0</td>\n","      <td>1901.0</td>\n","      <td>1129.0</td>\n","      <td>463.0</td>\n","      <td>1.8200</td>\n","    </tr>\n","    <tr>\n","      <th>2</th>\n","      <td>-114.56</td>\n","      <td>33.69</td>\n","      <td>17.0</td>\n","      <td>720.0</td>\n","      <td>174.0</td>\n","      <td>333.0</td>\n","      <td>117.0</td>\n","      <td>1.6509</td>\n","    </tr>\n","    <tr>\n","      <th>3</th>\n","      <td>-114.57</td>\n","      <td>33.64</td>\n","      <td>14.0</td>\n","      <td>1501.0</td>\n","      <td>337.0</td>\n","      <td>515.0</td>\n","      <td>226.0</td>\n","      <td>3.1917</td>\n","    </tr>\n","    <tr>\n","      <th>4</th>\n","      <td>-114.57</td>\n","      <td>33.57</td>\n","      <td>20.0</td>\n","      <td>1454.0</td>\n","      <td>326.0</td>\n","      <td>624.0</td>\n","      <td>262.0</td>\n","      <td>1.9250</td>\n","    </tr>\n","    <tr>\n","      <th>...</th>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","    </tr>\n","    <tr>\n","      <th>16995</th>\n","      <td>-124.26</td>\n","      <td>40.58</td>\n","      <td>52.0</td>\n","      <td>2217.0</td>\n","      <td>394.0</td>\n","      <td>907.0</td>\n","      <td>369.0</td>\n","      <td>2.3571</td>\n","    </tr>\n","    <tr>\n","      <th>16996</th>\n","      <td>-124.27</td>\n","      <td>40.69</td>\n","      <td>36.0</td>\n","      <td>2349.0</td>\n","      <td>528.0</td>\n","      <td>1194.0</td>\n","      <td>465.0</td>\n","      <td>2.5179</td>\n","    </tr>\n","    <tr>\n","      <th>16997</th>\n","      <td>-124.30</td>\n","      <td>41.84</td>\n","      <td>17.0</td>\n","      <td>2677.0</td>\n","      <td>531.0</td>\n","      <td>1244.0</td>\n","      <td>456.0</td>\n","      <td>3.0313</td>\n","    </tr>\n","    <tr>\n","      <th>16998</th>\n","      <td>-124.30</td>\n","      <td>41.80</td>\n","      <td>19.0</td>\n","      <td>2672.0</td>\n","      <td>552.0</td>\n","      <td>1298.0</td>\n","      <td>478.0</td>\n","      <td>1.9797</td>\n","    </tr>\n","    <tr>\n","      <th>16999</th>\n","      <td>-124.35</td>\n","      <td>40.54</td>\n","      <td>52.0</td>\n","      <td>1820.0</td>\n","      <td>300.0</td>\n","      <td>806.0</td>\n","      <td>270.0</td>\n","      <td>3.0147</td>\n","    </tr>\n","  </tbody>\n","</table>\n","<p>17000 rows × 8 columns</p>\n","</div>\n","      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-e02fe053-b5e3-4ccf-b9de-41e45e35ac7d')\"\n","              title=\"Convert this dataframe to an interactive table.\"\n","              style=\"display:none;\">\n","        \n","  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n","       width=\"24px\">\n","    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n","    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n","  </svg>\n","      </button>\n","      \n","  <style>\n","    .colab-df-container {\n","      display:flex;\n","      flex-wrap:wrap;\n","      gap: 12px;\n","    }\n","\n","    .colab-df-convert {\n","      background-color: #E8F0FE;\n","      border: none;\n","      border-radius: 50%;\n","      cursor: pointer;\n","      display: none;\n","      fill: #1967D2;\n","      height: 32px;\n","      padding: 0 0 0 0;\n","      width: 32px;\n","    }\n","\n","    .colab-df-convert:hover {\n","      background-color: #E2EBFA;\n","      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n","      fill: #174EA6;\n","    }\n","\n","    [theme=dark] .colab-df-convert {\n","      background-color: #3B4455;\n","      fill: #D2E3FC;\n","    }\n","\n","    [theme=dark] .colab-df-convert:hover {\n","      background-color: #434B5C;\n","      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n","      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n","      fill: #FFFFFF;\n","    }\n","  </style>\n","\n","      <script>\n","        const buttonEl =\n","          document.querySelector('#df-e02fe053-b5e3-4ccf-b9de-41e45e35ac7d button.colab-df-convert');\n","        buttonEl.style.display =\n","          google.colab.kernel.accessAllowed ? 'block' : 'none';\n","\n","        async function convertToInteractive(key) {\n","          const element = document.querySelector('#df-e02fe053-b5e3-4ccf-b9de-41e45e35ac7d');\n","          const dataTable =\n","            await google.colab.kernel.invokeFunction('convertToInteractive',\n","                                                     [key], {});\n","          if (!dataTable) return;\n","\n","          const docLinkHtml = 'Like what you see? Visit the ' +\n","            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n","            + ' to learn more about interactive tables.';\n","          element.innerHTML = '';\n","          dataTable['output_type'] = 'display_data';\n","          await google.colab.output.renderOutput(dataTable, element);\n","          const docLink = document.createElement('div');\n","          docLink.innerHTML = docLinkHtml;\n","          element.appendChild(docLink);\n","        }\n","      </script>\n","    </div>\n","  </div>\n","  "]},"metadata":{},"execution_count":35}]},{"cell_type":"code","source":["pca = PCA()"],"metadata":{"id":"1CV3v3ROosxp"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["projected_X = pca.fit_transform(X=question)"],"metadata":{"id":"C9uqU2Cyp5Gx"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["projected_X = pd.DataFrame(columns=[\"feature_\"+str(x) for x in range(1,9)],data=projected_X)"],"metadata":{"id":"RKS4OpHDqj35"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["projected_X"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":423},"id":"OU6Fs03mrpOy","executionInfo":{"status":"ok","timestamp":1681400609607,"user_tz":-330,"elapsed":73,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"d450b5bc-0338-4d30-d659-94f1ca170136"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["         feature_1    feature_2   feature_3   feature_4  feature_5  feature_6  \\\n","0      2548.462950 -1675.368431 -176.694599  451.797385   1.794425  -3.878558   \n","1      4486.293020 -2466.352693 -308.054162  839.231263  17.610251  -3.024562   \n","2     -2271.258841  -155.221708   14.677030   33.190517 -14.830972  -4.562708   \n","3     -1465.339874  -328.773036  -23.775044   54.142843 -15.831044  -4.701464   \n","4     -1456.886292  -208.071528  -23.881561   24.562863 -10.580953  -4.731190   \n","...            ...          ...         ...         ...        ...        ...   \n","16995  -639.653398  -289.531050   26.383700  -10.491428  22.731611   6.372973   \n","16996  -366.069656   -78.789431  -58.095235   13.515137   7.018859   6.862207   \n","16997   -57.434978  -184.177704    3.508883   21.144013 -10.865868   7.924719   \n","16998   -32.288309  -130.812676  -16.130231   20.183012  -8.996086   7.988086   \n","16999 -1061.136529  -213.830213   79.679991    4.595604  22.332635   6.426407   \n","\n","       feature_7  feature_8  \n","0      -1.179346   1.492993  \n","1       1.696091   1.033831  \n","2      -2.722381   1.760112  \n","3      -1.191306   1.843502  \n","4      -2.508884   1.770503  \n","...          ...        ...  \n","16995  -1.339104  -0.009410  \n","16996  -0.440339  -0.038868  \n","16997  -0.375002   0.481535  \n","16998  -1.266766   0.368891  \n","16999  -0.618891  -0.052695  \n","\n","[17000 rows x 8 columns]"],"text/html":["\n","  <div id=\"df-849e460d-66a0-45ed-899a-44775748a26f\">\n","    <div class=\"colab-df-container\">\n","      <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>feature_1</th>\n","      <th>feature_2</th>\n","      <th>feature_3</th>\n","      <th>feature_4</th>\n","      <th>feature_5</th>\n","      <th>feature_6</th>\n","      <th>feature_7</th>\n","      <th>feature_8</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>0</th>\n","      <td>2548.462950</td>\n","      <td>-1675.368431</td>\n","      <td>-176.694599</td>\n","      <td>451.797385</td>\n","      <td>1.794425</td>\n","      <td>-3.878558</td>\n","      <td>-1.179346</td>\n","      <td>1.492993</td>\n","    </tr>\n","    <tr>\n","      <th>1</th>\n","      <td>4486.293020</td>\n","      <td>-2466.352693</td>\n","      <td>-308.054162</td>\n","      <td>839.231263</td>\n","      <td>17.610251</td>\n","      <td>-3.024562</td>\n","      <td>1.696091</td>\n","      <td>1.033831</td>\n","    </tr>\n","    <tr>\n","      <th>2</th>\n","      <td>-2271.258841</td>\n","      <td>-155.221708</td>\n","      <td>14.677030</td>\n","      <td>33.190517</td>\n","      <td>-14.830972</td>\n","      <td>-4.562708</td>\n","      <td>-2.722381</td>\n","      <td>1.760112</td>\n","    </tr>\n","    <tr>\n","      <th>3</th>\n","      <td>-1465.339874</td>\n","      <td>-328.773036</td>\n","      <td>-23.775044</td>\n","      <td>54.142843</td>\n","      <td>-15.831044</td>\n","      <td>-4.701464</td>\n","      <td>-1.191306</td>\n","      <td>1.843502</td>\n","    </tr>\n","    <tr>\n","      <th>4</th>\n","      <td>-1456.886292</td>\n","      <td>-208.071528</td>\n","      <td>-23.881561</td>\n","      <td>24.562863</td>\n","      <td>-10.580953</td>\n","      <td>-4.731190</td>\n","      <td>-2.508884</td>\n","      <td>1.770503</td>\n","    </tr>\n","    <tr>\n","      <th>...</th>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","    </tr>\n","    <tr>\n","      <th>16995</th>\n","      <td>-639.653398</td>\n","      <td>-289.531050</td>\n","      <td>26.383700</td>\n","      <td>-10.491428</td>\n","      <td>22.731611</td>\n","      <td>6.372973</td>\n","      <td>-1.339104</td>\n","      <td>-0.009410</td>\n","    </tr>\n","    <tr>\n","      <th>16996</th>\n","      <td>-366.069656</td>\n","      <td>-78.789431</td>\n","      <td>-58.095235</td>\n","      <td>13.515137</td>\n","      <td>7.018859</td>\n","      <td>6.862207</td>\n","      <td>-0.440339</td>\n","      <td>-0.038868</td>\n","    </tr>\n","    <tr>\n","      <th>16997</th>\n","      <td>-57.434978</td>\n","      <td>-184.177704</td>\n","      <td>3.508883</td>\n","      <td>21.144013</td>\n","      <td>-10.865868</td>\n","      <td>7.924719</td>\n","      <td>-0.375002</td>\n","      <td>0.481535</td>\n","    </tr>\n","    <tr>\n","      <th>16998</th>\n","      <td>-32.288309</td>\n","      <td>-130.812676</td>\n","      <td>-16.130231</td>\n","      <td>20.183012</td>\n","      <td>-8.996086</td>\n","      <td>7.988086</td>\n","      <td>-1.266766</td>\n","      <td>0.368891</td>\n","    </tr>\n","    <tr>\n","      <th>16999</th>\n","      <td>-1061.136529</td>\n","      <td>-213.830213</td>\n","      <td>79.679991</td>\n","      <td>4.595604</td>\n","      <td>22.332635</td>\n","      <td>6.426407</td>\n","      <td>-0.618891</td>\n","      <td>-0.052695</td>\n","    </tr>\n","  </tbody>\n","</table>\n","<p>17000 rows × 8 columns</p>\n","</div>\n","      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-849e460d-66a0-45ed-899a-44775748a26f')\"\n","              title=\"Convert this dataframe to an interactive table.\"\n","              style=\"display:none;\">\n","        \n","  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n","       width=\"24px\">\n","    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n","    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n","  </svg>\n","      </button>\n","      \n","  <style>\n","    .colab-df-container {\n","      display:flex;\n","      flex-wrap:wrap;\n","      gap: 12px;\n","    }\n","\n","    .colab-df-convert {\n","      background-color: #E8F0FE;\n","      border: none;\n","      border-radius: 50%;\n","      cursor: pointer;\n","      display: none;\n","      fill: #1967D2;\n","      height: 32px;\n","      padding: 0 0 0 0;\n","      width: 32px;\n","    }\n","\n","    .colab-df-convert:hover {\n","      background-color: #E2EBFA;\n","      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n","      fill: #174EA6;\n","    }\n","\n","    [theme=dark] .colab-df-convert {\n","      background-color: #3B4455;\n","      fill: #D2E3FC;\n","    }\n","\n","    [theme=dark] .colab-df-convert:hover {\n","      background-color: #434B5C;\n","      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n","      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n","      fill: #FFFFFF;\n","    }\n","  </style>\n","\n","      <script>\n","        const buttonEl =\n","          document.querySelector('#df-849e460d-66a0-45ed-899a-44775748a26f button.colab-df-convert');\n","        buttonEl.style.display =\n","          google.colab.kernel.accessAllowed ? 'block' : 'none';\n","\n","        async function convertToInteractive(key) {\n","          const element = document.querySelector('#df-849e460d-66a0-45ed-899a-44775748a26f');\n","          const dataTable =\n","            await google.colab.kernel.invokeFunction('convertToInteractive',\n","                                                     [key], {});\n","          if (!dataTable) return;\n","\n","          const docLinkHtml = 'Like what you see? Visit the ' +\n","            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n","            + ' to learn more about interactive tables.';\n","          element.innerHTML = '';\n","          dataTable['output_type'] = 'display_data';\n","          await google.colab.output.renderOutput(dataTable, element);\n","          const docLink = document.createElement('div');\n","          docLink.innerHTML = docLinkHtml;\n","          element.appendChild(docLink);\n","        }\n","      </script>\n","    </div>\n","  </div>\n","  "]},"metadata":{},"execution_count":39}]},{"cell_type":"code","source":["projected_X.cov()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":300},"id":"nljVh1--rwtA","executionInfo":{"status":"ok","timestamp":1681400609608,"user_tz":-330,"elapsed":72,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"57485c64-9894-4615-a751-3abdfef1d515"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["              feature_1     feature_2     feature_3     feature_4  \\\n","feature_1  6.077377e+06  1.862755e-11  3.102308e-11 -1.177918e-12   \n","feature_2  1.862755e-11  2.849272e+05 -4.718522e-12  3.711813e-12   \n","feature_3  3.102308e-11 -4.718522e-12  3.035111e+04 -3.707532e-12   \n","feature_4 -1.177918e-12  3.711813e-12 -3.707532e-12  2.621575e+03   \n","feature_5 -8.015153e-12  1.262453e-12 -1.639862e-13 -2.568136e-14   \n","feature_6 -3.424181e-14 -4.160380e-13 -4.301628e-14 -3.948509e-14   \n","feature_7  1.284068e-13 -2.172215e-14  8.052177e-15  9.443250e-15   \n","feature_8 -8.553766e-14 -1.107509e-14 -1.205820e-14 -6.834987e-15   \n","\n","              feature_5     feature_6     feature_7     feature_8  \n","feature_1 -8.015153e-12 -3.424181e-14  1.284068e-13 -8.553766e-14  \n","feature_2  1.262453e-12 -4.160380e-13 -2.172215e-14 -1.107509e-14  \n","feature_3 -1.639862e-13 -4.301628e-14  8.052177e-15 -1.205820e-14  \n","feature_4 -2.568136e-14 -3.948509e-14  9.443250e-15 -6.834987e-15  \n","feature_5  1.363932e+02  3.878956e-15 -1.072565e-15  1.205486e-15  \n","feature_6  3.878956e-15  8.073986e+00  1.177062e-15 -4.961552e-16  \n","feature_7 -1.072565e-15  1.177062e-15  2.397131e+00  4.296946e-16  \n","feature_8  1.205486e-15 -4.961552e-16  4.296946e-16  2.444247e-01  "],"text/html":["\n","  <div id=\"df-277c5e8f-0f17-4dfc-89a2-dbbbf59e92bd\">\n","    <div class=\"colab-df-container\">\n","      <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>feature_1</th>\n","      <th>feature_2</th>\n","      <th>feature_3</th>\n","      <th>feature_4</th>\n","      <th>feature_5</th>\n","      <th>feature_6</th>\n","      <th>feature_7</th>\n","      <th>feature_8</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>feature_1</th>\n","      <td>6.077377e+06</td>\n","      <td>1.862755e-11</td>\n","      <td>3.102308e-11</td>\n","      <td>-1.177918e-12</td>\n","      <td>-8.015153e-12</td>\n","      <td>-3.424181e-14</td>\n","      <td>1.284068e-13</td>\n","      <td>-8.553766e-14</td>\n","    </tr>\n","    <tr>\n","      <th>feature_2</th>\n","      <td>1.862755e-11</td>\n","      <td>2.849272e+05</td>\n","      <td>-4.718522e-12</td>\n","      <td>3.711813e-12</td>\n","      <td>1.262453e-12</td>\n","      <td>-4.160380e-13</td>\n","      <td>-2.172215e-14</td>\n","      <td>-1.107509e-14</td>\n","    </tr>\n","    <tr>\n","      <th>feature_3</th>\n","      <td>3.102308e-11</td>\n","      <td>-4.718522e-12</td>\n","      <td>3.035111e+04</td>\n","      <td>-3.707532e-12</td>\n","      <td>-1.639862e-13</td>\n","      <td>-4.301628e-14</td>\n","      <td>8.052177e-15</td>\n","      <td>-1.205820e-14</td>\n","    </tr>\n","    <tr>\n","      <th>feature_4</th>\n","      <td>-1.177918e-12</td>\n","      <td>3.711813e-12</td>\n","      <td>-3.707532e-12</td>\n","      <td>2.621575e+03</td>\n","      <td>-2.568136e-14</td>\n","      <td>-3.948509e-14</td>\n","      <td>9.443250e-15</td>\n","      <td>-6.834987e-15</td>\n","    </tr>\n","    <tr>\n","      <th>feature_5</th>\n","      <td>-8.015153e-12</td>\n","      <td>1.262453e-12</td>\n","      <td>-1.639862e-13</td>\n","      <td>-2.568136e-14</td>\n","      <td>1.363932e+02</td>\n","      <td>3.878956e-15</td>\n","      <td>-1.072565e-15</td>\n","      <td>1.205486e-15</td>\n","    </tr>\n","    <tr>\n","      <th>feature_6</th>\n","      <td>-3.424181e-14</td>\n","      <td>-4.160380e-13</td>\n","      <td>-4.301628e-14</td>\n","      <td>-3.948509e-14</td>\n","      <td>3.878956e-15</td>\n","      <td>8.073986e+00</td>\n","      <td>1.177062e-15</td>\n","      <td>-4.961552e-16</td>\n","    </tr>\n","    <tr>\n","      <th>feature_7</th>\n","      <td>1.284068e-13</td>\n","      <td>-2.172215e-14</td>\n","      <td>8.052177e-15</td>\n","      <td>9.443250e-15</td>\n","      <td>-1.072565e-15</td>\n","      <td>1.177062e-15</td>\n","      <td>2.397131e+00</td>\n","      <td>4.296946e-16</td>\n","    </tr>\n","    <tr>\n","      <th>feature_8</th>\n","      <td>-8.553766e-14</td>\n","      <td>-1.107509e-14</td>\n","      <td>-1.205820e-14</td>\n","      <td>-6.834987e-15</td>\n","      <td>1.205486e-15</td>\n","      <td>-4.961552e-16</td>\n","      <td>4.296946e-16</td>\n","      <td>2.444247e-01</td>\n","    </tr>\n","  </tbody>\n","</table>\n","</div>\n","      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-277c5e8f-0f17-4dfc-89a2-dbbbf59e92bd')\"\n","              title=\"Convert this dataframe to an interactive table.\"\n","              style=\"display:none;\">\n","        \n","  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n","       width=\"24px\">\n","    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n","    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n","  </svg>\n","      </button>\n","      \n","  <style>\n","    .colab-df-container {\n","      display:flex;\n","      flex-wrap:wrap;\n","      gap: 12px;\n","    }\n","\n","    .colab-df-convert {\n","      background-color: #E8F0FE;\n","      border: none;\n","      border-radius: 50%;\n","      cursor: pointer;\n","      display: none;\n","      fill: #1967D2;\n","      height: 32px;\n","      padding: 0 0 0 0;\n","      width: 32px;\n","    }\n","\n","    .colab-df-convert:hover {\n","      background-color: #E2EBFA;\n","      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n","      fill: #174EA6;\n","    }\n","\n","    [theme=dark] .colab-df-convert {\n","      background-color: #3B4455;\n","      fill: #D2E3FC;\n","    }\n","\n","    [theme=dark] .colab-df-convert:hover {\n","      background-color: #434B5C;\n","      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n","      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n","      fill: #FFFFFF;\n","    }\n","  </style>\n","\n","      <script>\n","        const buttonEl =\n","          document.querySelector('#df-277c5e8f-0f17-4dfc-89a2-dbbbf59e92bd button.colab-df-convert');\n","        buttonEl.style.display =\n","          google.colab.kernel.accessAllowed ? 'block' : 'none';\n","\n","        async function convertToInteractive(key) {\n","          const element = document.querySelector('#df-277c5e8f-0f17-4dfc-89a2-dbbbf59e92bd');\n","          const dataTable =\n","            await google.colab.kernel.invokeFunction('convertToInteractive',\n","                                                     [key], {});\n","          if (!dataTable) return;\n","\n","          const docLinkHtml = 'Like what you see? Visit the ' +\n","            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n","            + ' to learn more about interactive tables.';\n","          element.innerHTML = '';\n","          dataTable['output_type'] = 'display_data';\n","          await google.colab.output.renderOutput(dataTable, element);\n","          const docLink = document.createElement('div');\n","          docLink.innerHTML = docLinkHtml;\n","          element.appendChild(docLink);\n","        }\n","      </script>\n","    </div>\n","  </div>\n","  "]},"metadata":{},"execution_count":40}]},{"cell_type":"code","source":["pca.get_covariance()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"LN8kZwwLxquY","executionInfo":{"status":"ok","timestamp":1681400609609,"user_tz":-330,"elapsed":71,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"04da4392-f85f-4728-8486-c05e5dc51c3c"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([[ 4.02069233e+00, -3.96518544e+00, -2.88355242e+00,\n","         2.05489998e+02,  6.06853288e+01,  2.34017167e+02,\n","         4.59746458e+01, -5.92481156e-02],\n","       [-3.96518544e+00,  4.56822140e+00,  4.42652137e-01,\n","        -1.80652575e+02, -6.24971957e+01, -2.72963262e+02,\n","        -6.15585795e+01, -3.27506114e-01],\n","       [-2.88355242e+00,  4.42652137e-01,  1.58430983e+02,\n","        -9.90499269e+03, -1.70002683e+03, -4.27500196e+03,\n","        -1.46531200e+03, -2.78442789e+00],\n","       [ 2.05489998e+02, -1.80652575e+02, -9.90499269e+03,\n","         4.75216923e+06,  8.53059831e+05,  2.15236872e+06,\n","         7.70353377e+05,  8.12729998e+02],\n","       [ 6.06853288e+01, -6.24971957e+01, -1.70002683e+03,\n","         8.53059831e+05,  1.77661788e+05,  4.26326445e+05,\n","         1.58982941e+05, -1.08535966e+01],\n","       [ 2.34017167e+02, -2.72963262e+02, -4.27500196e+03,\n","         2.15236872e+06,  4.26326445e+05,  1.31756642e+06,\n","         4.01317219e+05, -1.39658833e+00],\n","       [ 4.59746458e+01, -6.15585795e+01, -1.46531200e+03,\n","         7.70353377e+05,  1.58982941e+05,  4.01317219e+05,\n","         1.47856277e+05,  5.60839292e+00],\n","       [-5.92481156e-02, -3.27506114e-01, -2.78442789e+00,\n","         8.12729998e+02, -1.08535966e+01, -1.39658833e+00,\n","         5.60839292e+00,  3.64106130e+00]])"]},"metadata":{},"execution_count":41}]},{"cell_type":"code","source":["pca.singular_values_"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"HH7qG3zrtYTJ","executionInfo":{"status":"ok","timestamp":1681400609610,"user_tz":-330,"elapsed":65,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"58187254-bd65-4dab-9398-3d3d81076880"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["array([3.21417700e+05, 6.95950997e+04, 2.27142804e+04, 6.67563904e+03,\n","       1.52267805e+03, 3.70472239e+02, 2.01863382e+02, 6.44590968e+01])"]},"metadata":{},"execution_count":42}]},{"cell_type":"code","source":["np.mean(df,axis=0)"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"dTgn2bUfuiJq","executionInfo":{"status":"ok","timestamp":1681400609611,"user_tz":-330,"elapsed":62,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"220643c3-5a3e-4d92-acec-1e2cf4e01e49"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["longitude               -119.562108\n","latitude                  35.625225\n","housing_median_age        28.589353\n","total_rooms             2643.664412\n","total_bedrooms           539.410824\n","population              1429.573941\n","households               501.221941\n","median_income              3.883578\n","median_house_value    207300.912353\n","dtype: float64"]},"metadata":{},"execution_count":43}]},{"cell_type":"code","source":["zero = question - question.mean()\n","n=17000"],"metadata":{"id":"kFDXnj5I4KAu"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["covarian = 1/n * np.matmul(np.array(zero).T,np.array(zero))\n","covarian == question.cov()"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":300},"id":"PTlDnM4WCZJ0","executionInfo":{"status":"ok","timestamp":1681400609612,"user_tz":-330,"elapsed":58,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"9c51bb35-a909-481a-f12c-3f6527dcd5a5"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["                    longitude  latitude  housing_median_age  total_rooms  \\\n","longitude               False     False               False        False   \n","latitude                False     False               False        False   \n","housing_median_age      False     False               False        False   \n","total_rooms             False     False               False        False   \n","total_bedrooms          False     False               False        False   \n","population              False     False               False        False   \n","households              False     False               False        False   \n","median_income           False     False               False        False   \n","\n","                    total_bedrooms  population  households  median_income  \n","longitude                    False       False       False          False  \n","latitude                     False       False       False          False  \n","housing_median_age           False       False       False          False  \n","total_rooms                  False       False       False          False  \n","total_bedrooms               False       False       False          False  \n","population                   False       False       False          False  \n","households                   False       False       False          False  \n","median_income                False       False       False          False  "],"text/html":["\n","  <div id=\"df-8a0f2653-a526-4aed-ab2b-f33196bd0e0c\">\n","    <div class=\"colab-df-container\">\n","      <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>longitude</th>\n","      <th>latitude</th>\n","      <th>housing_median_age</th>\n","      <th>total_rooms</th>\n","      <th>total_bedrooms</th>\n","      <th>population</th>\n","      <th>households</th>\n","      <th>median_income</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>longitude</th>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","    </tr>\n","    <tr>\n","      <th>latitude</th>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","    </tr>\n","    <tr>\n","      <th>housing_median_age</th>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","    </tr>\n","    <tr>\n","      <th>total_rooms</th>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","    </tr>\n","    <tr>\n","      <th>total_bedrooms</th>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","    </tr>\n","    <tr>\n","      <th>population</th>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","    </tr>\n","    <tr>\n","      <th>households</th>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","    </tr>\n","    <tr>\n","      <th>median_income</th>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","    </tr>\n","  </tbody>\n","</table>\n","</div>\n","      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-8a0f2653-a526-4aed-ab2b-f33196bd0e0c')\"\n","              title=\"Convert this dataframe to an interactive table.\"\n","              style=\"display:none;\">\n","        \n","  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n","       width=\"24px\">\n","    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n","    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n","  </svg>\n","      </button>\n","      \n","  <style>\n","    .colab-df-container {\n","      display:flex;\n","      flex-wrap:wrap;\n","      gap: 12px;\n","    }\n","\n","    .colab-df-convert {\n","      background-color: #E8F0FE;\n","      border: none;\n","      border-radius: 50%;\n","      cursor: pointer;\n","      display: none;\n","      fill: #1967D2;\n","      height: 32px;\n","      padding: 0 0 0 0;\n","      width: 32px;\n","    }\n","\n","    .colab-df-convert:hover {\n","      background-color: #E2EBFA;\n","      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n","      fill: #174EA6;\n","    }\n","\n","    [theme=dark] .colab-df-convert {\n","      background-color: #3B4455;\n","      fill: #D2E3FC;\n","    }\n","\n","    [theme=dark] .colab-df-convert:hover {\n","      background-color: #434B5C;\n","      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n","      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n","      fill: #FFFFFF;\n","    }\n","  </style>\n","\n","      <script>\n","        const buttonEl =\n","          document.querySelector('#df-8a0f2653-a526-4aed-ab2b-f33196bd0e0c button.colab-df-convert');\n","        buttonEl.style.display =\n","          google.colab.kernel.accessAllowed ? 'block' : 'none';\n","\n","        async function convertToInteractive(key) {\n","          const element = document.querySelector('#df-8a0f2653-a526-4aed-ab2b-f33196bd0e0c');\n","          const dataTable =\n","            await google.colab.kernel.invokeFunction('convertToInteractive',\n","                                                     [key], {});\n","          if (!dataTable) return;\n","\n","          const docLinkHtml = 'Like what you see? Visit the ' +\n","            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n","            + ' to learn more about interactive tables.';\n","          element.innerHTML = '';\n","          dataTable['output_type'] = 'display_data';\n","          await google.colab.output.renderOutput(dataTable, element);\n","          const docLink = document.createElement('div');\n","          docLink.innerHTML = docLinkHtml;\n","          element.appendChild(docLink);\n","        }\n","      </script>\n","    </div>\n","  </div>\n","  "]},"metadata":{},"execution_count":45}]},{"cell_type":"code","source":["factors = np.linalg.svd(covarian)\n","factors"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"AZeOmaIzC0yj","executionInfo":{"status":"ok","timestamp":1681400609613,"user_tz":-330,"elapsed":57,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"be1bb0f5-f38e-4a87-9084-da7e99e54de2"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["(array([[-4.87779818e-05,  4.26597318e-04,  5.96219142e-05,\n","          4.44385427e-03,  1.75541809e-02,  6.74717920e-01,\n","          1.55069103e-01,  7.21374533e-01],\n","        [ 4.83304787e-05, -5.92830386e-04,  1.77408305e-04,\n","         -1.06187208e-03, -1.74489015e-03, -7.32744210e-01,\n","          2.49217466e-02,  6.80044316e-01],\n","        [ 1.81139134e-03,  1.66615756e-03, -3.76947307e-03,\n","         -1.92770694e-02, -9.99629800e-01,  1.37056902e-02,\n","         -3.08899604e-03,  1.22883216e-02],\n","        [-8.78741371e-01, -4.53645869e-01,  1.47944433e-01,\n","         -1.10543662e-02, -2.69649914e-03,  2.38305870e-04,\n","          1.38217673e-03, -1.89670088e-04],\n","        [-1.61685692e-01,  5.45364032e-02, -7.45061966e-01,\n","          6.44666720e-01, -9.82541906e-03, -1.70970188e-03,\n","         -8.45312761e-03, -2.97587618e-04],\n","        [-4.24259252e-01,  8.83742060e-01,  1.93001366e-01,\n","          4.18662496e-02, -8.38430316e-04, -7.41671896e-04,\n","         -7.02897990e-04,  4.00401040e-05],\n","        [-1.47214563e-01,  1.01124591e-01, -6.21059166e-01,\n","         -7.62939997e-01,  1.69922297e-02,  2.22759232e-03,\n","          3.76480287e-03,  1.37517588e-03],\n","        [-1.17264926e-04, -1.29843611e-03,  4.10522619e-03,\n","         -7.74073892e-03,  5.98494151e-03,  8.74374759e-02,\n","         -9.87539824e-01,  1.30405108e-01]]),\n"," array([6.07701986e+06, 2.84910464e+05, 3.03493254e+04, 2.62142098e+03,\n","        1.36385203e+02, 8.07351058e+00, 2.39698970e+00, 2.44410304e-01]),\n"," array([[-4.87779818e-05,  4.83304787e-05,  1.81139134e-03,\n","         -8.78741371e-01, -1.61685692e-01, -4.24259252e-01,\n","         -1.47214563e-01, -1.17264926e-04],\n","        [ 4.26597318e-04, -5.92830386e-04,  1.66615756e-03,\n","         -4.53645869e-01,  5.45364032e-02,  8.83742060e-01,\n","          1.01124591e-01, -1.29843611e-03],\n","        [ 5.96219142e-05,  1.77408305e-04, -3.76947307e-03,\n","          1.47944433e-01, -7.45061966e-01,  1.93001366e-01,\n","         -6.21059166e-01,  4.10522619e-03],\n","        [ 4.44385427e-03, -1.06187208e-03, -1.92770694e-02,\n","         -1.10543662e-02,  6.44666720e-01,  4.18662496e-02,\n","         -7.62939997e-01, -7.74073892e-03],\n","        [ 1.75541809e-02, -1.74489015e-03, -9.99629800e-01,\n","         -2.69649914e-03, -9.82541906e-03, -8.38430316e-04,\n","          1.69922297e-02,  5.98494151e-03],\n","        [ 6.74717920e-01, -7.32744210e-01,  1.37056902e-02,\n","          2.38305870e-04, -1.70970188e-03, -7.41671895e-04,\n","          2.22759232e-03,  8.74374759e-02],\n","        [ 1.55069103e-01,  2.49217466e-02, -3.08899604e-03,\n","          1.38217673e-03, -8.45312761e-03, -7.02897990e-04,\n","          3.76480287e-03, -9.87539824e-01],\n","        [ 7.21374533e-01,  6.80044316e-01,  1.22883216e-02,\n","         -1.89670088e-04, -2.97587618e-04,  4.00401040e-05,\n","          1.37517588e-03,  1.30405108e-01]]))"]},"metadata":{},"execution_count":46}]},{"cell_type":"code","source":["pro_x = np.matmul(np.array(zero),factors[0])\n","pro_x.shape"],"metadata":{"colab":{"base_uri":"https://localhost:8080/"},"id":"QK1OvwTSDJnc","executionInfo":{"status":"ok","timestamp":1681400609615,"user_tz":-330,"elapsed":55,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"c4b9643b-33ac-4862-c333-8507398cfbce"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["(17000, 8)"]},"metadata":{},"execution_count":47}]},{"cell_type":"code","source":["pro_x = pd.DataFrame(columns=[\"feature_\"+str(x) for x in range(1,9)],data=pro_x)"],"metadata":{"id":"6CplUTLEF6y9"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["pro_x == projected_X"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":423},"id":"cHF2ANvUDYN8","executionInfo":{"status":"ok","timestamp":1681400609617,"user_tz":-330,"elapsed":51,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"f3777489-32a1-4c5f-ccbf-84482e34d87c"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["       feature_1  feature_2  feature_3  feature_4  feature_5  feature_6  \\\n","0          False      False      False      False      False      False   \n","1          False      False      False      False      False      False   \n","2          False      False      False      False      False      False   \n","3          False      False      False      False      False      False   \n","4          False      False      False      False      False      False   \n","...          ...        ...        ...        ...        ...        ...   \n","16995      False      False      False      False      False      False   \n","16996      False      False      False      False      False      False   \n","16997      False      False      False      False      False      False   \n","16998      False      False      False      False      False      False   \n","16999      False      False      False      False      False      False   \n","\n","       feature_7  feature_8  \n","0          False      False  \n","1          False      False  \n","2          False      False  \n","3          False      False  \n","4          False      False  \n","...          ...        ...  \n","16995      False      False  \n","16996      False      False  \n","16997      False      False  \n","16998      False      False  \n","16999      False      False  \n","\n","[17000 rows x 8 columns]"],"text/html":["\n","  <div id=\"df-34c8001b-bed2-4448-b7f7-fdb06d5157a2\">\n","    <div class=\"colab-df-container\">\n","      <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>feature_1</th>\n","      <th>feature_2</th>\n","      <th>feature_3</th>\n","      <th>feature_4</th>\n","      <th>feature_5</th>\n","      <th>feature_6</th>\n","      <th>feature_7</th>\n","      <th>feature_8</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>0</th>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","    </tr>\n","    <tr>\n","      <th>1</th>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","    </tr>\n","    <tr>\n","      <th>2</th>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","    </tr>\n","    <tr>\n","      <th>3</th>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","    </tr>\n","    <tr>\n","      <th>4</th>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","    </tr>\n","    <tr>\n","      <th>...</th>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","    </tr>\n","    <tr>\n","      <th>16995</th>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","    </tr>\n","    <tr>\n","      <th>16996</th>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","    </tr>\n","    <tr>\n","      <th>16997</th>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","    </tr>\n","    <tr>\n","      <th>16998</th>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","    </tr>\n","    <tr>\n","      <th>16999</th>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","      <td>False</td>\n","    </tr>\n","  </tbody>\n","</table>\n","<p>17000 rows × 8 columns</p>\n","</div>\n","      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-34c8001b-bed2-4448-b7f7-fdb06d5157a2')\"\n","              title=\"Convert this dataframe to an interactive table.\"\n","              style=\"display:none;\">\n","        \n","  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n","       width=\"24px\">\n","    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n","    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n","  </svg>\n","      </button>\n","      \n","  <style>\n","    .colab-df-container {\n","      display:flex;\n","      flex-wrap:wrap;\n","      gap: 12px;\n","    }\n","\n","    .colab-df-convert {\n","      background-color: #E8F0FE;\n","      border: none;\n","      border-radius: 50%;\n","      cursor: pointer;\n","      display: none;\n","      fill: #1967D2;\n","      height: 32px;\n","      padding: 0 0 0 0;\n","      width: 32px;\n","    }\n","\n","    .colab-df-convert:hover {\n","      background-color: #E2EBFA;\n","      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n","      fill: #174EA6;\n","    }\n","\n","    [theme=dark] .colab-df-convert {\n","      background-color: #3B4455;\n","      fill: #D2E3FC;\n","    }\n","\n","    [theme=dark] .colab-df-convert:hover {\n","      background-color: #434B5C;\n","      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n","      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n","      fill: #FFFFFF;\n","    }\n","  </style>\n","\n","      <script>\n","        const buttonEl =\n","          document.querySelector('#df-34c8001b-bed2-4448-b7f7-fdb06d5157a2 button.colab-df-convert');\n","        buttonEl.style.display =\n","          google.colab.kernel.accessAllowed ? 'block' : 'none';\n","\n","        async function convertToInteractive(key) {\n","          const element = document.querySelector('#df-34c8001b-bed2-4448-b7f7-fdb06d5157a2');\n","          const dataTable =\n","            await google.colab.kernel.invokeFunction('convertToInteractive',\n","                                                     [key], {});\n","          if (!dataTable) return;\n","\n","          const docLinkHtml = 'Like what you see? Visit the ' +\n","            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n","            + ' to learn more about interactive tables.';\n","          element.innerHTML = '';\n","          dataTable['output_type'] = 'display_data';\n","          await google.colab.output.renderOutput(dataTable, element);\n","          const docLink = document.createElement('div');\n","          docLink.innerHTML = docLinkHtml;\n","          element.appendChild(docLink);\n","        }\n","      </script>\n","    </div>\n","  </div>\n","  "]},"metadata":{},"execution_count":49}]},{"cell_type":"code","source":["test = pd.read_csv(\"/content/sample_data/california_housing_test.csv\")"],"metadata":{"id":"7XyYC3a4uaBk"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["test.iloc[:,:-1]"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":423},"id":"Lzrx9yxPudsl","executionInfo":{"status":"ok","timestamp":1681400609620,"user_tz":-330,"elapsed":51,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"4cd61105-b279-4c21-976e-981a342dcfc5"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["      longitude  latitude  housing_median_age  total_rooms  total_bedrooms  \\\n","0       -122.05     37.37                27.0       3885.0           661.0   \n","1       -118.30     34.26                43.0       1510.0           310.0   \n","2       -117.81     33.78                27.0       3589.0           507.0   \n","3       -118.36     33.82                28.0         67.0            15.0   \n","4       -119.67     36.33                19.0       1241.0           244.0   \n","...         ...       ...                 ...          ...             ...   \n","2995    -119.86     34.42                23.0       1450.0           642.0   \n","2996    -118.14     34.06                27.0       5257.0          1082.0   \n","2997    -119.70     36.30                10.0        956.0           201.0   \n","2998    -117.12     34.10                40.0         96.0            14.0   \n","2999    -119.63     34.42                42.0       1765.0           263.0   \n","\n","      population  households  median_income  \n","0         1537.0       606.0         6.6085  \n","1          809.0       277.0         3.5990  \n","2         1484.0       495.0         5.7934  \n","3           49.0        11.0         6.1359  \n","4          850.0       237.0         2.9375  \n","...          ...         ...            ...  \n","2995      1258.0       607.0         1.1790  \n","2996      3496.0      1036.0         3.3906  \n","2997       693.0       220.0         2.2895  \n","2998        46.0        14.0         3.2708  \n","2999       753.0       260.0         8.5608  \n","\n","[3000 rows x 8 columns]"],"text/html":["\n","  <div id=\"df-dee2fb4d-4ec0-4b5a-bf4f-0017228dcfa7\">\n","    <div class=\"colab-df-container\">\n","      <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>longitude</th>\n","      <th>latitude</th>\n","      <th>housing_median_age</th>\n","      <th>total_rooms</th>\n","      <th>total_bedrooms</th>\n","      <th>population</th>\n","      <th>households</th>\n","      <th>median_income</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>0</th>\n","      <td>-122.05</td>\n","      <td>37.37</td>\n","      <td>27.0</td>\n","      <td>3885.0</td>\n","      <td>661.0</td>\n","      <td>1537.0</td>\n","      <td>606.0</td>\n","      <td>6.6085</td>\n","    </tr>\n","    <tr>\n","      <th>1</th>\n","      <td>-118.30</td>\n","      <td>34.26</td>\n","      <td>43.0</td>\n","      <td>1510.0</td>\n","      <td>310.0</td>\n","      <td>809.0</td>\n","      <td>277.0</td>\n","      <td>3.5990</td>\n","    </tr>\n","    <tr>\n","      <th>2</th>\n","      <td>-117.81</td>\n","      <td>33.78</td>\n","      <td>27.0</td>\n","      <td>3589.0</td>\n","      <td>507.0</td>\n","      <td>1484.0</td>\n","      <td>495.0</td>\n","      <td>5.7934</td>\n","    </tr>\n","    <tr>\n","      <th>3</th>\n","      <td>-118.36</td>\n","      <td>33.82</td>\n","      <td>28.0</td>\n","      <td>67.0</td>\n","      <td>15.0</td>\n","      <td>49.0</td>\n","      <td>11.0</td>\n","      <td>6.1359</td>\n","    </tr>\n","    <tr>\n","      <th>4</th>\n","      <td>-119.67</td>\n","      <td>36.33</td>\n","      <td>19.0</td>\n","      <td>1241.0</td>\n","      <td>244.0</td>\n","      <td>850.0</td>\n","      <td>237.0</td>\n","      <td>2.9375</td>\n","    </tr>\n","    <tr>\n","      <th>...</th>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","    </tr>\n","    <tr>\n","      <th>2995</th>\n","      <td>-119.86</td>\n","      <td>34.42</td>\n","      <td>23.0</td>\n","      <td>1450.0</td>\n","      <td>642.0</td>\n","      <td>1258.0</td>\n","      <td>607.0</td>\n","      <td>1.1790</td>\n","    </tr>\n","    <tr>\n","      <th>2996</th>\n","      <td>-118.14</td>\n","      <td>34.06</td>\n","      <td>27.0</td>\n","      <td>5257.0</td>\n","      <td>1082.0</td>\n","      <td>3496.0</td>\n","      <td>1036.0</td>\n","      <td>3.3906</td>\n","    </tr>\n","    <tr>\n","      <th>2997</th>\n","      <td>-119.70</td>\n","      <td>36.30</td>\n","      <td>10.0</td>\n","      <td>956.0</td>\n","      <td>201.0</td>\n","      <td>693.0</td>\n","      <td>220.0</td>\n","      <td>2.2895</td>\n","    </tr>\n","    <tr>\n","      <th>2998</th>\n","      <td>-117.12</td>\n","      <td>34.10</td>\n","      <td>40.0</td>\n","      <td>96.0</td>\n","      <td>14.0</td>\n","      <td>46.0</td>\n","      <td>14.0</td>\n","      <td>3.2708</td>\n","    </tr>\n","    <tr>\n","      <th>2999</th>\n","      <td>-119.63</td>\n","      <td>34.42</td>\n","      <td>42.0</td>\n","      <td>1765.0</td>\n","      <td>263.0</td>\n","      <td>753.0</td>\n","      <td>260.0</td>\n","      <td>8.5608</td>\n","    </tr>\n","  </tbody>\n","</table>\n","<p>3000 rows × 8 columns</p>\n","</div>\n","      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-dee2fb4d-4ec0-4b5a-bf4f-0017228dcfa7')\"\n","              title=\"Convert this dataframe to an interactive table.\"\n","              style=\"display:none;\">\n","        \n","  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n","       width=\"24px\">\n","    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n","    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n","  </svg>\n","      </button>\n","      \n","  <style>\n","    .colab-df-container {\n","      display:flex;\n","      flex-wrap:wrap;\n","      gap: 12px;\n","    }\n","\n","    .colab-df-convert {\n","      background-color: #E8F0FE;\n","      border: none;\n","      border-radius: 50%;\n","      cursor: pointer;\n","      display: none;\n","      fill: #1967D2;\n","      height: 32px;\n","      padding: 0 0 0 0;\n","      width: 32px;\n","    }\n","\n","    .colab-df-convert:hover {\n","      background-color: #E2EBFA;\n","      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n","      fill: #174EA6;\n","    }\n","\n","    [theme=dark] .colab-df-convert {\n","      background-color: #3B4455;\n","      fill: #D2E3FC;\n","    }\n","\n","    [theme=dark] .colab-df-convert:hover {\n","      background-color: #434B5C;\n","      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n","      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n","      fill: #FFFFFF;\n","    }\n","  </style>\n","\n","      <script>\n","        const buttonEl =\n","          document.querySelector('#df-dee2fb4d-4ec0-4b5a-bf4f-0017228dcfa7 button.colab-df-convert');\n","        buttonEl.style.display =\n","          google.colab.kernel.accessAllowed ? 'block' : 'none';\n","\n","        async function convertToInteractive(key) {\n","          const element = document.querySelector('#df-dee2fb4d-4ec0-4b5a-bf4f-0017228dcfa7');\n","          const dataTable =\n","            await google.colab.kernel.invokeFunction('convertToInteractive',\n","                                                     [key], {});\n","          if (!dataTable) return;\n","\n","          const docLinkHtml = 'Like what you see? Visit the ' +\n","            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n","            + ' to learn more about interactive tables.';\n","          element.innerHTML = '';\n","          dataTable['output_type'] = 'display_data';\n","          await google.colab.output.renderOutput(dataTable, element);\n","          const docLink = document.createElement('div');\n","          docLink.innerHTML = docLinkHtml;\n","          element.appendChild(docLink);\n","        }\n","      </script>\n","    </div>\n","  </div>\n","  "]},"metadata":{},"execution_count":51}]},{"cell_type":"code","source":["df"],"metadata":{"colab":{"base_uri":"https://localhost:8080/","height":423},"id":"kLHPCu0LSwHm","executionInfo":{"status":"ok","timestamp":1681400730895,"user_tz":-330,"elapsed":801,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}},"outputId":"6285b9bb-bab4-4c0f-dc96-6df544474678"},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["       longitude  latitude  housing_median_age  total_rooms  total_bedrooms  \\\n","0        -114.31     34.19                15.0       5612.0          1283.0   \n","1        -114.47     34.40                19.0       7650.0          1901.0   \n","2        -114.56     33.69                17.0        720.0           174.0   \n","3        -114.57     33.64                14.0       1501.0           337.0   \n","4        -114.57     33.57                20.0       1454.0           326.0   \n","...          ...       ...                 ...          ...             ...   \n","16995    -124.26     40.58                52.0       2217.0           394.0   \n","16996    -124.27     40.69                36.0       2349.0           528.0   \n","16997    -124.30     41.84                17.0       2677.0           531.0   \n","16998    -124.30     41.80                19.0       2672.0           552.0   \n","16999    -124.35     40.54                52.0       1820.0           300.0   \n","\n","       population  households  median_income  median_house_value  \n","0          1015.0       472.0         1.4936             66900.0  \n","1          1129.0       463.0         1.8200             80100.0  \n","2           333.0       117.0         1.6509             85700.0  \n","3           515.0       226.0         3.1917             73400.0  \n","4           624.0       262.0         1.9250             65500.0  \n","...           ...         ...            ...                 ...  \n","16995       907.0       369.0         2.3571            111400.0  \n","16996      1194.0       465.0         2.5179             79000.0  \n","16997      1244.0       456.0         3.0313            103600.0  \n","16998      1298.0       478.0         1.9797             85800.0  \n","16999       806.0       270.0         3.0147             94600.0  \n","\n","[17000 rows x 9 columns]"],"text/html":["\n","  <div id=\"df-13d91234-ef8f-4122-a8c7-bcb18a3e7dd0\">\n","    <div class=\"colab-df-container\">\n","      <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>longitude</th>\n","      <th>latitude</th>\n","      <th>housing_median_age</th>\n","      <th>total_rooms</th>\n","      <th>total_bedrooms</th>\n","      <th>population</th>\n","      <th>households</th>\n","      <th>median_income</th>\n","      <th>median_house_value</th>\n","    </tr>\n","  </thead>\n","  <tbody>\n","    <tr>\n","      <th>0</th>\n","      <td>-114.31</td>\n","      <td>34.19</td>\n","      <td>15.0</td>\n","      <td>5612.0</td>\n","      <td>1283.0</td>\n","      <td>1015.0</td>\n","      <td>472.0</td>\n","      <td>1.4936</td>\n","      <td>66900.0</td>\n","    </tr>\n","    <tr>\n","      <th>1</th>\n","      <td>-114.47</td>\n","      <td>34.40</td>\n","      <td>19.0</td>\n","      <td>7650.0</td>\n","      <td>1901.0</td>\n","      <td>1129.0</td>\n","      <td>463.0</td>\n","      <td>1.8200</td>\n","      <td>80100.0</td>\n","    </tr>\n","    <tr>\n","      <th>2</th>\n","      <td>-114.56</td>\n","      <td>33.69</td>\n","      <td>17.0</td>\n","      <td>720.0</td>\n","      <td>174.0</td>\n","      <td>333.0</td>\n","      <td>117.0</td>\n","      <td>1.6509</td>\n","      <td>85700.0</td>\n","    </tr>\n","    <tr>\n","      <th>3</th>\n","      <td>-114.57</td>\n","      <td>33.64</td>\n","      <td>14.0</td>\n","      <td>1501.0</td>\n","      <td>337.0</td>\n","      <td>515.0</td>\n","      <td>226.0</td>\n","      <td>3.1917</td>\n","      <td>73400.0</td>\n","    </tr>\n","    <tr>\n","      <th>4</th>\n","      <td>-114.57</td>\n","      <td>33.57</td>\n","      <td>20.0</td>\n","      <td>1454.0</td>\n","      <td>326.0</td>\n","      <td>624.0</td>\n","      <td>262.0</td>\n","      <td>1.9250</td>\n","      <td>65500.0</td>\n","    </tr>\n","    <tr>\n","      <th>...</th>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","      <td>...</td>\n","    </tr>\n","    <tr>\n","      <th>16995</th>\n","      <td>-124.26</td>\n","      <td>40.58</td>\n","      <td>52.0</td>\n","      <td>2217.0</td>\n","      <td>394.0</td>\n","      <td>907.0</td>\n","      <td>369.0</td>\n","      <td>2.3571</td>\n","      <td>111400.0</td>\n","    </tr>\n","    <tr>\n","      <th>16996</th>\n","      <td>-124.27</td>\n","      <td>40.69</td>\n","      <td>36.0</td>\n","      <td>2349.0</td>\n","      <td>528.0</td>\n","      <td>1194.0</td>\n","      <td>465.0</td>\n","      <td>2.5179</td>\n","      <td>79000.0</td>\n","    </tr>\n","    <tr>\n","      <th>16997</th>\n","      <td>-124.30</td>\n","      <td>41.84</td>\n","      <td>17.0</td>\n","      <td>2677.0</td>\n","      <td>531.0</td>\n","      <td>1244.0</td>\n","      <td>456.0</td>\n","      <td>3.0313</td>\n","      <td>103600.0</td>\n","    </tr>\n","    <tr>\n","      <th>16998</th>\n","      <td>-124.30</td>\n","      <td>41.80</td>\n","      <td>19.0</td>\n","      <td>2672.0</td>\n","      <td>552.0</td>\n","      <td>1298.0</td>\n","      <td>478.0</td>\n","      <td>1.9797</td>\n","      <td>85800.0</td>\n","    </tr>\n","    <tr>\n","      <th>16999</th>\n","      <td>-124.35</td>\n","      <td>40.54</td>\n","      <td>52.0</td>\n","      <td>1820.0</td>\n","      <td>300.0</td>\n","      <td>806.0</td>\n","      <td>270.0</td>\n","      <td>3.0147</td>\n","      <td>94600.0</td>\n","    </tr>\n","  </tbody>\n","</table>\n","<p>17000 rows × 9 columns</p>\n","</div>\n","      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-13d91234-ef8f-4122-a8c7-bcb18a3e7dd0')\"\n","              title=\"Convert this dataframe to an interactive table.\"\n","              style=\"display:none;\">\n","        \n","  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n","       width=\"24px\">\n","    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n","    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n","  </svg>\n","      </button>\n","      \n","  <style>\n","    .colab-df-container {\n","      display:flex;\n","      flex-wrap:wrap;\n","      gap: 12px;\n","    }\n","\n","    .colab-df-convert {\n","      background-color: #E8F0FE;\n","      border: none;\n","      border-radius: 50%;\n","      cursor: pointer;\n","      display: none;\n","      fill: #1967D2;\n","      height: 32px;\n","      padding: 0 0 0 0;\n","      width: 32px;\n","    }\n","\n","    .colab-df-convert:hover {\n","      background-color: #E2EBFA;\n","      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n","      fill: #174EA6;\n","    }\n","\n","    [theme=dark] .colab-df-convert {\n","      background-color: #3B4455;\n","      fill: #D2E3FC;\n","    }\n","\n","    [theme=dark] .colab-df-convert:hover {\n","      background-color: #434B5C;\n","      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n","      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n","      fill: #FFFFFF;\n","    }\n","  </style>\n","\n","      <script>\n","        const buttonEl =\n","          document.querySelector('#df-13d91234-ef8f-4122-a8c7-bcb18a3e7dd0 button.colab-df-convert');\n","        buttonEl.style.display =\n","          google.colab.kernel.accessAllowed ? 'block' : 'none';\n","\n","        async function convertToInteractive(key) {\n","          const element = document.querySelector('#df-13d91234-ef8f-4122-a8c7-bcb18a3e7dd0');\n","          const dataTable =\n","            await google.colab.kernel.invokeFunction('convertToInteractive',\n","                                                     [key], {});\n","          if (!dataTable) return;\n","\n","          const docLinkHtml = 'Like what you see? Visit the ' +\n","            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n","            + ' to learn more about interactive tables.';\n","          element.innerHTML = '';\n","          dataTable['output_type'] = 'display_data';\n","          await google.colab.output.renderOutput(dataTable, element);\n","          const docLink = document.createElement('div');\n","          docLink.innerHTML = docLinkHtml;\n","          element.appendChild(docLink);\n","        }\n","      </script>\n","    </div>\n","  </div>\n","  "]},"metadata":{},"execution_count":52}]},{"cell_type":"code","source":["algo.fit(df.iloc[:,:-1],df.iloc[:,-1])\n","predictions = algo.predict(test.iloc[:,:-1])"],"metadata":{"id":"8hZ7vCxZSq2Q"},"execution_count":null,"outputs":[]},{"cell_type":"code","source":["from sklearn.metrics import r2_score\n","percentage = r2_score(y_true = test.iloc[:,-1],y_pred=predictions)\n","percentage"],"metadata":{"id":"eICHDh1CFzHE","colab":{"base_uri":"https://localhost:8080/"},"outputId":"1c19f639-3ab5-4738-fd83-95ca9265e12f","executionInfo":{"status":"ok","timestamp":1681400893229,"user_tz":-330,"elapsed":11,"user":{"displayName":"Mohit Manghwani","userId":"11157237833313497817"}}},"execution_count":null,"outputs":[{"output_type":"execute_result","data":{"text/plain":["0.6195057678312047"]},"metadata":{},"execution_count":59}]},{"cell_type":"code","source":[],"metadata":{"id":"Ows5xCvixyt1"},"execution_count":null,"outputs":[]}]}