Polynomial_regression_.ipynb

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      "source": [
        "# WOC 4.0\n",
        ">> ### Machine Learning\n",
        ">>>> ###### IIT(ISM) Dhanabad\n",
        ">>>> ###### Arushika"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "YHgMrkYJt4Gu"
      },
      "source": [
        "## Polynomial regression"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bC0W4PR05VFh"
      },
      "source": [
        ">> ### Training set"
      ]
    },
    {
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      "execution_count": 1,
      "metadata": {
        "id": "kcY9B-nlt-pk"
      },
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      "source": [
        "# Importing libraries needed for the project\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as pp"
      ]
    },
    {
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              "       Unnamed: 0         X         Y         Z        label\n",
              "0               0  0.643715 -9.866550 -5.836019   307.972927\n",
              "1               1 -1.366446 -3.761945 -8.756162   136.398375\n",
              "2               2 -4.090270 -1.836218 -1.846066  -310.724813\n",
              "3               3 -8.730478 -1.923651  3.892972     1.755447\n",
              "4               4  5.367169  0.358357  6.703989  -343.582590\n",
              "...           ...       ...       ...       ...          ...\n",
              "49995       49995  2.693877 -1.362685 -7.392968   683.405727\n",
              "49996       49996 -9.270188 -5.456920 -2.343480 -1874.385403\n",
              "49997       49997  6.616753 -2.847288 -0.504040   663.873655\n",
              "49998       49998  3.558199  4.507526 -4.823674  -421.004005\n",
              "49999       49999  0.623431  8.863234 -3.231040  -699.718682\n",
              "\n",
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              "      <th>49995</th>\n",
              "      <td>49995</td>\n",
              "      <td>2.693877</td>\n",
              "      <td>-1.362685</td>\n",
              "      <td>-7.392968</td>\n",
              "      <td>683.405727</td>\n",
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              "      <td>-9.270188</td>\n",
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              "      <td>8.863234</td>\n",
              "      <td>-3.231040</td>\n",
              "      <td>-699.718682</td>\n",
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          "metadata": {},
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        }
      ],
      "source": [
        "# Loading dataset \n",
        "data = pd.read_csv('Polynomial_train.csv')\n",
        "data"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yuthU9YaFUTQ"
      },
      "source": [
        "The Algorithm\n",
        "* Modify the hypothesis function of Linear Regression according to the data you have.\n",
        "* Add new higher (whichever) degree features you want to the input.\n",
        "* Do the Gradient Descent/mini-batch Gradient Descent to the modified input to find the parameters — weights and bias.\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data = (data - data.mean())/data.std()"
      ],
      "metadata": {
        "id": "GUycha2DqY7e"
      },
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "id": "GeUcz8B-Hb-k"
      },
      "outputs": [],
      "source": [
        "# Seperating the x and y matrices\n",
        "\n",
        "# Like in the training set\n",
        "# X-matrice is supposed to be a m x (n+1) dimensional matrice\n",
        "# where n = Number of different features present \n",
        "#       m = Number of enteries in each feature\n",
        "x= data.iloc[:,1:2].values # for m x 1 dimensional \n",
        "\n",
        "# y-matrice is supposed to be a m x 1 dimensional matrice \n",
        "Y = data.iloc[:,2:3].values\n",
        "\n",
        "# z-matrice is supposed to be a m x 1 dimensional matrice\n",
        "Z = data.iloc[:,3:4].values\n",
        "\n",
        "features = data.iloc[:,1:4].values\n",
        "\n",
        "# Label matrices is supposed to a m x 1 dimensional matrice\n",
        "Label_1 = data.iloc[:,4:5].values"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wgbrJQR8yHu5"
      },
      "source": [
        "` Hypothesis function` for polynomial regression will seem like this:\n",
        "\n",
        "<b> h_theta (x,y,z) = theta_0 + theta_1 * x + theta_2 * y + theta_3 * z + theta_4 * x^2 + theta_5 * y^2 + theta_6 * z^2 + theta_7 * xy + theta_8 * yz + theta_9 * zx + theta_10 * x^3 + theta_11 * y^3 + theta_12 * z^3 + theta_13 * x^2(y) + theta_14 * x^2(z) + theta_15 * y^2(z) + theta_16 * y^2(x) + theta_17 * z^2(x) + theta_18 * z^2(y)+ theta_19 * xyz"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "id": "_CH2qYuN2FRF"
      },
      "outputs": [],
      "source": [
        "# Here we will construct the features matrix(X_5). \n",
        "# First we will create the individual columns and then append them together.\n",
        "\n",
        "# x_0 for simplicity is considered to be 1 matrices.\n",
        "ones = np.ones([x.shape[0],1]) #Dimension is m x 1\n",
        "x_0 = ones\n",
        "\n",
        "# x_1 is simply the x feature given in the dataset\n",
        "x_1 = x\n",
        "\n",
        "# x_2 is simply the y feature given in the dataset\n",
        "x_2 = Y\n",
        "\n",
        "# x_3 is simply the z feature given in the dataset\n",
        "x_3 = Z\n",
        "\n",
        "# x_4 is square of the x feature given in the dataset\n",
        "x_4 = x**2\n",
        "\n",
        "# x_5 is square of the y feature given in the dataset \n",
        "x_5 = Y**2\n",
        "\n",
        "# x_6 is square of the z feature given in the dataset \n",
        "x_6 = Z**2\n",
        "\n",
        "# x_7 is the multiplycation of x and y matrice \n",
        "x_7 = x*(Y)\n",
        "\n",
        "# x_8 is the multiplication of y and z matrice \n",
        "x_8 = Y*(Z)\n",
        "\n",
        "# x_9 is the multiplication of z and x matrice\n",
        "x_9 = Z*(x)\n",
        "\n",
        "# x_10 is the cube of the x feature given in the dataset\n",
        "x_10 = x**3\n",
        "\n",
        "# x_11 is the cube of the y feature given in the dataset\n",
        "x_11 = Y**3\n",
        "\n",
        "# x_12 is the cube of the z feature given in the dataset\n",
        "x_12 = Z**3\n",
        "\n",
        "# x_13 is the multiplication of square of x and y matrice\n",
        "x_13 = (x**2)*Y\n",
        "\n",
        "# x_14 is the multiplication of square of x and z matrice\n",
        "x_14 = (x**2)*Z\n",
        "\n",
        "# x_15 is the multplication of square of y and x matrice\n",
        "x_15 = (Y**2)*x\n",
        "\n",
        "# x_16 is the multiplication of square of y and z matrice\n",
        "x_16 = (Y**2)*Z\n",
        "\n",
        "# x_17 is the multiplication of square of z and x matrice\n",
        "x_17 = (Z**2)*x\n",
        "\n",
        "# x_18 is the multiplication of square of z and y matrice \n",
        "x_18 = (Z**2)*Y\n",
        "\n",
        "# x_19 is the multiplcation of all three features givven in the dataset x,y and z\n",
        "x_19 = (x*Y)*Z"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
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        "outputId": "9ec32764-2d1b-4e79-807a-0582110be4c0"
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      "outputs": [
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          "name": "stdout",
          "text": [
            "[[ 1.          0.1057533  -1.69738613 ...  0.10797556 -1.73305432\n",
            "   0.1813804 ]\n",
            " [ 1.         -0.2427338  -0.64326391 ... -0.55714537 -1.47647961\n",
            "  -0.23655851]\n",
            " [ 1.         -0.71494348 -0.31073582 ... -0.07368195 -0.03202438\n",
            "  -0.07131941]\n",
            " ...\n",
            " [ 1.          1.1412558  -0.48532404 ...  0.00906858 -0.00385646\n",
            "   0.0493734 ]\n",
            " [ 1.          0.61101634  0.78468006 ...  0.42655612  0.54779235\n",
            "  -0.40059647]\n",
            " [ 1.          0.10223675  1.53680881 ...  0.03210022  0.48252616\n",
            "  -0.08803946]]\n"
          ]
        }
      ],
      "source": [
        "# Appending the featueres together\n",
        "X1 = np.concatenate((x_0,x_1,x_2,x_3,x_4,x_5,x_6,x_7,x_8,x_9,x_10,x_11,x_12,x_13,x_14,x_15,x_16,x_17,x_18,x_19),axis=1)\n",
        "X1 = np.asarray(X1)\n",
        "print(X1)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X1.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TTHA_1a0apul",
        "outputId": "572f5288-7076-462a-9fe2-f73a9e6a2c91"
      },
      "execution_count": 7,
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              "(50000, 20)"
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          "metadata": {},
          "execution_count": 7
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    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "id": "VaVEsmkaAe3I"
      },
      "outputs": [],
      "source": [
        "# Matrice of theta(coefficient of the features in hypothesis function) is supposed to a 1 x (n+1) dimensional matrice\n",
        "theta = np.zeros([1,20])"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#@title Setting Hyperparameters\n",
        "Alpha = 0.0015 #@param {type:\"slider\", min:0, max:1, step:0.01}\n",
        "iters = 1200 #@param {type:\"slider\", min:100, max:3000, step:100}\n",
        "alpha_3 = Alpha\n",
        "iters_3 = iters"
      ],
      "metadata": {
        "id": "HnK0ohbkii1l"
      },
      "execution_count": 91,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#Defining Cost function\n",
        "def computeCost(X,y,theta):\n",
        "    tobesummed = np.power(((X @ theta.T)-y),2)\n",
        "    return np.sum(tobesummed)/(2 * len(X))"
      ],
      "metadata": {
        "id": "Gcc1uoGqsS5f"
      },
      "execution_count": 92,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#Defining gradient descent\n",
        "def gradientDescent(X,y,theta,iters,alpha):\n",
        "    cost = np.zeros(iters)\n",
        "    for i in range(iters):\n",
        "        theta = theta - (alpha/len(X)) * np.sum(X * (X @ theta.T - y), axis=0)\n",
        "        cost[i] = computeCost(X, y, theta)\n",
        "    \n",
        "    return theta,cost"
      ],
      "metadata": {
        "id": "2lijThdWsTct"
      },
      "execution_count": 93,
      "outputs": []
    },
    {
      "cell_type": "code",
      "execution_count": 94,
      "metadata": {
        "id": "BteM8a_HAYOO",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9bca4071-c176-462b-ff3c-913472f7022b"
      },
      "outputs": [
        {
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          "name": "stdout",
          "text": [
            "[[-5.10909647e-03  2.03975302e-03 -1.24836278e-03 -3.03204123e-03\n",
            "   2.15717463e-02 -1.06865962e-01  8.28434608e-02 -7.38995076e-01\n",
            "   1.64933847e-01 -3.24882778e-01  3.73292220e-03 -1.66596609e-03\n",
            "  -6.90895252e-04  1.88343047e-03  5.34941106e-04 -1.93441179e-03\n",
            "   2.01254239e-03 -7.63185624e-04  1.14422015e-04 -7.65883200e-04]]\n",
            "0.014045599419497666\n"
          ]
        }
      ],
      "source": [
        "#running the gd and cost function\n",
        "g,cost = gradientDescent(X1,Label_1,theta,iters_3,alpha_3)\n",
        "print(g)\n",
        "\n",
        "finalCost = computeCost(X1,Label_1,g)\n",
        "print(finalCost)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 95,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "id": "_KkWVjtUBZZo",
        "outputId": "7a1ab338-2660-40bf-ec7b-814909fbed64"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Error vs. Training Epoch')"
            ]
          },
          "metadata": {},
          "execution_count": 95
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "#plot the cost\n",
        "fig, ax = pp.subplots()  \n",
        "ax.plot(np.arange(iters), cost, 'r')  \n",
        "ax.set_xlabel('Iterations')  \n",
        "ax.set_ylabel('Cost')  \n",
        "ax.set_title('Error vs. Training Epoch')"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pQLlTaKxB0Yp"
      },
      "source": [
        "### Test Set"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 96,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 423
        },
        "id": "YE74MQ2kCFKO",
        "outputId": "f99535d8-c8d4-4f8d-9ef9-35774c6baa59"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "      Unnamed: 0         X         Y         Z        label\n",
              "0              0  9.322078  0.413096  5.984731  -657.669309\n",
              "1              1  2.811964  6.142752  6.419237  -545.362524\n",
              "2              2 -2.669784  7.775091 -6.931907   -75.044187\n",
              "3              3 -6.992156 -9.205548  0.852580 -2403.124902\n",
              "4              4  1.574294 -2.213266  6.029188     8.595325\n",
              "...          ...       ...       ...       ...          ...\n",
              "9995        9995 -0.992449 -7.853677  7.748156  -635.006038\n",
              "9996        9996  8.574451  6.271919 -5.734962 -1275.855209\n",
              "9997        9997  6.640997  6.864877  4.511685 -1771.640694\n",
              "9998        9998 -6.262414  1.323203 -3.917748   -22.746921\n",
              "9999        9999  8.289792 -0.371541  2.099039   -64.853446\n",
              "\n",
              "[10000 rows x 5 columns]"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-f57884f0-dbb4-4279-9d34-8daa73cdddc8\">\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>Unnamed: 0</th>\n",
              "      <th>X</th>\n",
              "      <th>Y</th>\n",
              "      <th>Z</th>\n",
              "      <th>label</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>9.322078</td>\n",
              "      <td>0.413096</td>\n",
              "      <td>5.984731</td>\n",
              "      <td>-657.669309</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>2.811964</td>\n",
              "      <td>6.142752</td>\n",
              "      <td>6.419237</td>\n",
              "      <td>-545.362524</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2</td>\n",
              "      <td>-2.669784</td>\n",
              "      <td>7.775091</td>\n",
              "      <td>-6.931907</td>\n",
              "      <td>-75.044187</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3</td>\n",
              "      <td>-6.992156</td>\n",
              "      <td>-9.205548</td>\n",
              "      <td>0.852580</td>\n",
              "      <td>-2403.124902</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4</td>\n",
              "      <td>1.574294</td>\n",
              "      <td>-2.213266</td>\n",
              "      <td>6.029188</td>\n",
              "      <td>8.595325</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>9995</th>\n",
              "      <td>9995</td>\n",
              "      <td>-0.992449</td>\n",
              "      <td>-7.853677</td>\n",
              "      <td>7.748156</td>\n",
              "      <td>-635.006038</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9996</th>\n",
              "      <td>9996</td>\n",
              "      <td>8.574451</td>\n",
              "      <td>6.271919</td>\n",
              "      <td>-5.734962</td>\n",
              "      <td>-1275.855209</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9997</th>\n",
              "      <td>9997</td>\n",
              "      <td>6.640997</td>\n",
              "      <td>6.864877</td>\n",
              "      <td>4.511685</td>\n",
              "      <td>-1771.640694</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9998</th>\n",
              "      <td>9998</td>\n",
              "      <td>-6.262414</td>\n",
              "      <td>1.323203</td>\n",
              "      <td>-3.917748</td>\n",
              "      <td>-22.746921</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9999</th>\n",
              "      <td>9999</td>\n",
              "      <td>8.289792</td>\n",
              "      <td>-0.371541</td>\n",
              "      <td>2.099039</td>\n",
              "      <td>-64.853446</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>10000 rows × 5 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-f57884f0-dbb4-4279-9d34-8daa73cdddc8')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
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              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-f57884f0-dbb4-4279-9d34-8daa73cdddc8');\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": 96
        }
      ],
      "source": [
        "data_ = pd.read_csv('Polynomial_test.csv')\n",
        "data_"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "vSFcZ1KmChcp"
      },
      "source": [
        "Normalizing the dataset "
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data_ = (data_ - data_.mean()) / data_.std()\n",
        "data_"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 423
        },
        "id": "Ejp6cn5Iq1hX",
        "outputId": "2d876b29-14a7-4b2e-fc77-8c839473b9a1"
      },
      "execution_count": 97,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "      Unnamed: 0         X         Y         Z     label\n",
              "0      -1.731791  1.602895  0.057199  1.034578 -0.563902\n",
              "1      -1.731445  0.474656  1.049657  1.109700 -0.470760\n",
              "2      -1.731098 -0.475360  1.332401 -1.198596 -0.080700\n",
              "3      -1.730752 -1.224451 -1.608887  0.147274 -2.011504\n",
              "4      -1.730405  0.260161 -0.397724  1.042264 -0.011333\n",
              "...          ...       ...       ...       ...       ...\n",
              "9995    1.730405 -0.184669 -1.374724  1.339458 -0.545107\n",
              "9996    1.730752  1.473327  1.072031 -0.991655 -1.076598\n",
              "9997    1.731098  1.138249  1.174739  0.779901 -1.487780\n",
              "9998    1.731445 -1.097983  0.214842 -0.677474 -0.037327\n",
              "9999    1.731791  1.423994 -0.078711  0.362776 -0.072248\n",
              "\n",
              "[10000 rows x 5 columns]"
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              "      <th>Unnamed: 0</th>\n",
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              "      <th>1</th>\n",
              "      <td>-1.731445</td>\n",
              "      <td>0.474656</td>\n",
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              "      <td>1.109700</td>\n",
              "      <td>-0.470760</td>\n",
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              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>-1.731098</td>\n",
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              "      <td>-1.198596</td>\n",
              "      <td>-0.080700</td>\n",
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              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>-1.730752</td>\n",
              "      <td>-1.224451</td>\n",
              "      <td>-1.608887</td>\n",
              "      <td>0.147274</td>\n",
              "      <td>-2.011504</td>\n",
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              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>-1.730405</td>\n",
              "      <td>0.260161</td>\n",
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              "      <th>9995</th>\n",
              "      <td>1.730405</td>\n",
              "      <td>-0.184669</td>\n",
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              "      <td>1.339458</td>\n",
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              "    <tr>\n",
              "      <th>9996</th>\n",
              "      <td>1.730752</td>\n",
              "      <td>1.473327</td>\n",
              "      <td>1.072031</td>\n",
              "      <td>-0.991655</td>\n",
              "      <td>-1.076598</td>\n",
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              "    <tr>\n",
              "      <th>9997</th>\n",
              "      <td>1.731098</td>\n",
              "      <td>1.138249</td>\n",
              "      <td>1.174739</td>\n",
              "      <td>0.779901</td>\n",
              "      <td>-1.487780</td>\n",
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              "    <tr>\n",
              "      <th>9998</th>\n",
              "      <td>1.731445</td>\n",
              "      <td>-1.097983</td>\n",
              "      <td>0.214842</td>\n",
              "      <td>-0.677474</td>\n",
              "      <td>-0.037327</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>9999</th>\n",
              "      <td>1.731791</td>\n",
              "      <td>1.423994</td>\n",
              "      <td>-0.078711</td>\n",
              "      <td>0.362776</td>\n",
              "      <td>-0.072248</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>10000 rows × 5 columns</p>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-218948a9-2699-4feb-9ecd-48bc82c98a10')\"\n",
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              "            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",
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              "  "
            ]
          },
          "metadata": {},
          "execution_count": 97
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 98,
      "metadata": {
        "id": "RXTQCobCCgU2"
      },
      "outputs": [],
      "source": [
        "# Seperating the columns provided in the dataset.\n",
        "\n",
        "# Like in the training set\n",
        "# X-matrice is supposed to be a m x (n+1) dimensional matrice\n",
        "# where n = Number of different features present \n",
        "#       m = Number of enteries in each feature\n",
        "x_test= data_.iloc[:,1:2] # for m x 1 dimensional \n",
        "\n",
        "# y-matrice is supposed to be a m x 1 dimensional matrice \n",
        "Y_test = data_.iloc[:,2:3].values\n",
        "\n",
        "# z-matrice is supposed to be a m x 1 dimensional matrice\n",
        "Z_test = data_.iloc[:,3:4].values\n",
        " \n",
        "# Label matrices is supposed to a m x 1 dimensional matrice\n",
        "Label_2 = data_.iloc[:,4:5].values"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 99,
      "metadata": {
        "id": "k6CTKy_VDXqH"
      },
      "outputs": [],
      "source": [
        "# Here we will construct the features matrix(X_6). \n",
        "# First we will create the individual columns and then append them together.\n",
        "\n",
        "# x_0 for simplicity is considered to be 1 matrices.\n",
        "ones = np.ones([x_test.shape[0],1]) #Dimension is m x 1\n",
        "x_0 = ones\n",
        "\n",
        "# x_1 is simply the x feature given in the dataset\n",
        "x_1 = x_test\n",
        "\n",
        "# x_2 is simply the y feature given in the dataset\n",
        "x_2 = Y_test\n",
        "\n",
        "# x_3 is simply the z feature given in the dataset\n",
        "x_3 = Z_test\n",
        "\n",
        "# x_4 is square of the x feature given in the dataset\n",
        "x_4 = x_test**2\n",
        "\n",
        "# x_5 is square of the y feature given in the dataset \n",
        "x_5 = Y_test**2\n",
        "\n",
        "# x_6 is square of the z feature given in the dataset \n",
        "x_6 = Z_test**2\n",
        "\n",
        "# x_7 is the multiplycation of x and y matrice \n",
        "x_7 = x_test*(Y_test)\n",
        "\n",
        "# x_8 is the multiplication of y and z matrice \n",
        "x_8 = Y_test*(Z_test)\n",
        "\n",
        "# x_9 is the multiplication of z and x matrice\n",
        "x_9 = Z_test*(x_test)\n",
        "\n",
        "# x_10 is the cube of the x feature given in the dataset\n",
        "x_10 = x_test**3\n",
        "\n",
        "# x_11 is the cube of the y feature given in the dataset\n",
        "x_11 = Y_test**3\n",
        "\n",
        "# x_12 is the cube of the z feature given in the dataset\n",
        "x_12 = Z_test**3\n",
        "\n",
        "# x_13 is the multiplication of square of x and y matrice\n",
        "x_13 = (x_test**2)*Y_test\n",
        "\n",
        "# x_14 is the multiplication of square of x and z matrice\n",
        "x_14 = (x_test**2)*Z_test\n",
        "\n",
        "# x_15 is the multplication of square of y and x matrice\n",
        "x_15 = (Y_test**2)*x_test\n",
        "\n",
        "# x_16 is the multiplication of square of y and z matrice\n",
        "x_16 = (Y_test**2)*Z_test\n",
        "\n",
        "# x_17 is the multiplication of square of z and x matrice\n",
        "x_17 = (Z_test**2)*x_test\n",
        "\n",
        "# x_18 is the multiplication of square of z and y matrice \n",
        "x_18 = (Z_test**2)*Y_test\n",
        "\n",
        "# x_19 is the multiplcation of all three features givven in the dataset x,y and z\n",
        "x_19 = (x_test*Y_test)*Z_test"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 100,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nEv1xKCLEG1l",
        "outputId": "b185ec77-03ec-4d9e-d1b7-c24d435bac97"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[ 1.          1.6028949   0.05719898 ...  1.71565996  0.06122298\n",
            "   0.09485416]\n",
            " [ 1.          0.47465649  1.04965702 ...  0.58450814  1.29258334\n",
            "   0.55288195]\n",
            " [ 1.         -0.4753605   1.33240142 ... -0.68291824  1.91417091\n",
            "   0.75915593]\n",
            " ...\n",
            " [ 1.          1.13824884  1.17473941 ...  0.69233481  0.71453003\n",
            "   1.04284132]\n",
            " [ 1.         -1.09798296  0.21484245 ... -0.50394282  0.09860655\n",
            "   0.15981168]\n",
            " [ 1.          1.42399409 -0.07871134 ...  0.18740637 -0.0103589\n",
            "  -0.04066152]]\n"
          ]
        }
      ],
      "source": [
        "X_1= np.concatenate((x_0,x_1,x_2,x_3,x_4,x_5,x_6,x_7,x_8,x_9,x_10,x_11,x_12,x_13,x_14,x_15,x_16,x_17,x_18,x_19),axis=1)\n",
        "X_1 = np.asarray(X_1)\n",
        "print(X_1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 101,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "heVKYBGXFqX0",
        "outputId": "b8645eed-278d-43c9-fff2-0fd4947464e1"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[-0.44312715]\n",
            " [-0.36804302]\n",
            " [-0.05560715]\n",
            " ...\n",
            " [-1.19743177]\n",
            " [-0.04219779]\n",
            " [-0.0282203 ]]\n"
          ]
        }
      ],
      "source": [
        "# Y values (or Labels) can be found by multiplying the arrays of x and theta which is g(gradient)\n",
        "y_2 = X_1.dot(g.T)\n",
        "print(y_2) "
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 102,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5EoHiLkoLkC4",
        "outputId": "8e7023ee-baf3-4f4d-ad38-bc71baad7dc3"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[-0.56390249]\n",
            " [-0.47076032]\n",
            " [-0.08069956]\n",
            " ...\n",
            " [-1.48777998]\n",
            " [-0.03732658]\n",
            " [-0.07224782]]\n"
          ]
        }
      ],
      "source": [
        "print(Label_2)"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#combined rmse value\n",
        "rss=((Label_2-y_2)**2).sum()\n",
        "mse=np.mean((Label_2-y_2)**2)\n",
        "print(\"Final rmse value is =\",np.sqrt(np.mean((Label_2-y_2)**2)))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RhFm7soo4naF",
        "outputId": "5c5711ff-01c7-49af-ad67-9be11db3f9cb"
      },
      "execution_count": 103,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Final rmse value is = 0.16691423439082115\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cHl942CHLwlb"
      },
      "source": [
        "# Plotting (Polynomial Regression)\n",
        "Plotting traing dataset and test dataset together"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 77,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "emTrrKGIL95w",
        "outputId": "a08ad0f4-f993-46ef-93ba-df533da7812f"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "fig = pp.figure()\n",
        "ax1 = fig.add_subplot(111)\n",
        "ax1.scatter(x, Label_1, s = 10, c = 'b', label = 'training set')\n",
        "ax1.scatter(x_test, Label_2, s = 10, c = 'r', label = 'test set')\n",
        "pp.legend(loc='upper right');\n",
        "pp.show()"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "N7AOAXrnG2F4"
      },
      "execution_count": 77,
      "outputs": []
    }
  ],
  "metadata": {
    "colab": {
      "collapsed_sections": [],
      "name": "Polynomial regression .ipynb",
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}