Fourier_series_regression.ipynb

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      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import random\n",
        "from sklearn import preprocessing\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.linear_model import LinearRegression\n",
        "import seaborn as sns\n",
        "import statsmodels.api as sm"
      ],
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      "execution_count": 1,
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    {
      "cell_type": "markdown",
      "source": [
        "## Mod 3"
      ],
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        "id": "ea0YAgAnvbZ6"
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      "source": [
        "l1 = range(2**32-1)\n",
        "X = random.sample(l1,200)\n",
        "y = np.mod(X,3)\n",
        "train_df = pd.DataFrame(zip(X,y), columns=['int','mod3'])\n",
        "train_df['sin1'] = np.sin(2 * np.pi * 1 * train_df['int']/3)\n",
        "train_df['cos1'] = np.cos(2 * np.pi * 1 * train_df['int']/3)\n",
        "train_df['sin2'] = np.sin(2 * np.pi * 2 * train_df['int']/3)\n",
        "train_df['cos2'] = np.cos(2 * np.pi * 2 * train_df['int']/3)\n",
        "train_df.head(5)"
      ],
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              "          int  mod3      sin1      cos1      sin2      cos2\n",
              "0   202697092     1  0.866025 -0.500000 -0.866025 -0.500000\n",
              "1  4029289600     1  0.866026 -0.500000 -0.866025 -0.500001\n",
              "2  1140803188     1  0.866026 -0.500000 -0.866025 -0.500000\n",
              "3  3584204123     2 -0.866025 -0.500001  0.866026 -0.499999\n",
              "4  3949518374     2 -0.866025 -0.500001  0.866026 -0.499999"
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              "      <td>-0.866025</td>\n",
              "      <td>-0.500000</td>\n",
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      "source": [
        "X = train_df[['sin1','cos1']].iloc[:150]\n",
        "y = train_df['mod3'].iloc[:150]\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.1)"
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      "source": [
        "LM = LinearRegression()\n",
        "LM.fit(X_train,y_train)\n",
        "print(LM.score(X_test, y_test)) #R^2 value\n",
        "print(LM.intercept_)"
      ],
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          "text": [
            "0.9999999999998856\n",
            "1.0000000486403873\n"
          ]
        }
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        "pd.DataFrame(zip(X.columns, LM.coef_)).set_axis(['Feature','Coefficient'], axis='columns')"
      ],
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      "execution_count": 5,
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              "  Feature  Coefficient\n",
              "0    sin1     -0.57735\n",
              "1    cos1     -1.00000"
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              "            title=\"Suggest charts.\"\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",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-4592886f-4cb3-4012-91af-6c9433a87c73 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X_val = train_df[['sin1','cos1']].iloc[-50:]\n",
        "y_val = train_df['mod3'].iloc[-50:]\n",
        "y_val = y_val.to_list()\n",
        "y_val_predict = LM.predict(X_val)"
      ],
      "metadata": {
        "id": "a_hWwSPawpS_"
      },
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "error = 10 **(-5)\n",
        "y_val_pred_label = [0 if abs(y-0)< error else 1 if abs(y-1) < error else 2 for y in y_val_predict]"
      ],
      "metadata": {
        "id": "1BWNPKD6wrso"
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "count = 0\n",
        "for i in range(len(y_val_pred_label)):\n",
        "  if y_val[i] == y_val_pred_label[i]:\n",
        "    count += 1\n",
        "accuracy = count/len(y_val_pred_label)\n",
        "print(accuracy)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9ecgCV52wvpf",
        "outputId": "41fa5cc8-2671-46b2-daef-931b9f2c5f76"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Mod  7"
      ],
      "metadata": {
        "id": "yb-tmTPFw4us"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "l1 = range(2**32-1)\n",
        "X = random.sample(l1,200)\n",
        "y = np.mod(X,7)\n",
        "train_df = pd.DataFrame(zip(X,y), columns=['int','mod7'])\n",
        "train_df['sin1'] = np.sin(2 * np.pi * 1 * train_df['int']/7)\n",
        "train_df['cos1'] = np.cos(2 * np.pi * 1 * train_df['int']/7)\n",
        "train_df['sin2'] = np.sin(2 * np.pi * 2 * train_df['int']/7)\n",
        "train_df['cos2'] = np.cos(2 * np.pi * 2 * train_df['int']/7)\n",
        "train_df['sin3'] = np.sin(2 * np.pi * 3 * train_df['int']/7)\n",
        "train_df['cos3'] = np.cos(2 * np.pi * 3 * train_df['int']/7)\n",
        "train_df['sin4'] = np.sin(2 * np.pi * 4 * train_df['int']/7)\n",
        "train_df['cos4'] = np.cos(2 * np.pi * 4 * train_df['int']/7)\n",
        "train_df['sin5'] = np.sin(2 * np.pi * 5 * train_df['int']/7)\n",
        "train_df['cos5'] = np.cos(2 * np.pi * 5 * train_df['int']/7)\n",
        "train_df['sin6'] = np.sin(2 * np.pi * 6 * train_df['int']/7)\n",
        "train_df['cos6'] = np.cos(2 * np.pi * 6 * train_df['int']/7)\n",
        "train_df.head(5)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 221
        },
        "id": "1NaCGC39w38d",
        "outputId": "bc50b52e-23aa-4445-fecb-90336005c09e"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "          int  mod7      sin1      cos1      sin2      cos2      sin3  \\\n",
              "0  2309698898     3  0.433884 -0.900969 -0.781832  0.623490  0.974928   \n",
              "1   237322882     6 -0.781831  0.623490 -0.974928 -0.222521 -0.433884   \n",
              "2  3596214994     1  0.781831  0.623490  0.974928 -0.222521  0.433884   \n",
              "3   312183957     1  0.781831  0.623490  0.974928 -0.222521  0.433884   \n",
              "4  2986527711     6 -0.781831  0.623490 -0.974928 -0.222521 -0.433884   \n",
              "\n",
              "       cos3      sin4      cos4      sin5      cos5      sin6      cos6  \n",
              "0 -0.222521 -0.974928 -0.222521  0.781832  0.623490 -0.433884 -0.900969  \n",
              "1 -0.900969  0.433884 -0.900969  0.974928 -0.222521  0.781831  0.623490  \n",
              "2 -0.900969 -0.433883 -0.900969 -0.974928 -0.222522 -0.781832  0.623490  \n",
              "3 -0.900969 -0.433884 -0.900969 -0.974928 -0.222521 -0.781832  0.623490  \n",
              "4 -0.900969  0.433883 -0.900969  0.974928 -0.222519  0.781831  0.623490  "
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-eaf32b22-a9f9-49ff-8249-f6599c84fedf\" 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>int</th>\n",
              "      <th>mod7</th>\n",
              "      <th>sin1</th>\n",
              "      <th>cos1</th>\n",
              "      <th>sin2</th>\n",
              "      <th>cos2</th>\n",
              "      <th>sin3</th>\n",
              "      <th>cos3</th>\n",
              "      <th>sin4</th>\n",
              "      <th>cos4</th>\n",
              "      <th>sin5</th>\n",
              "      <th>cos5</th>\n",
              "      <th>sin6</th>\n",
              "      <th>cos6</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>2309698898</td>\n",
              "      <td>3</td>\n",
              "      <td>0.433884</td>\n",
              "      <td>-0.900969</td>\n",
              "      <td>-0.781832</td>\n",
              "      <td>0.623490</td>\n",
              "      <td>0.974928</td>\n",
              "      <td>-0.222521</td>\n",
              "      <td>-0.974928</td>\n",
              "      <td>-0.222521</td>\n",
              "      <td>0.781832</td>\n",
              "      <td>0.623490</td>\n",
              "      <td>-0.433884</td>\n",
              "      <td>-0.900969</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>237322882</td>\n",
              "      <td>6</td>\n",
              "      <td>-0.781831</td>\n",
              "      <td>0.623490</td>\n",
              "      <td>-0.974928</td>\n",
              "      <td>-0.222521</td>\n",
              "      <td>-0.433884</td>\n",
              "      <td>-0.900969</td>\n",
              "      <td>0.433884</td>\n",
              "      <td>-0.900969</td>\n",
              "      <td>0.974928</td>\n",
              "      <td>-0.222521</td>\n",
              "      <td>0.781831</td>\n",
              "      <td>0.623490</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>3596214994</td>\n",
              "      <td>1</td>\n",
              "      <td>0.781831</td>\n",
              "      <td>0.623490</td>\n",
              "      <td>0.974928</td>\n",
              "      <td>-0.222521</td>\n",
              "      <td>0.433884</td>\n",
              "      <td>-0.900969</td>\n",
              "      <td>-0.433883</td>\n",
              "      <td>-0.900969</td>\n",
              "      <td>-0.974928</td>\n",
              "      <td>-0.222522</td>\n",
              "      <td>-0.781832</td>\n",
              "      <td>0.623490</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>312183957</td>\n",
              "      <td>1</td>\n",
              "      <td>0.781831</td>\n",
              "      <td>0.623490</td>\n",
              "      <td>0.974928</td>\n",
              "      <td>-0.222521</td>\n",
              "      <td>0.433884</td>\n",
              "      <td>-0.900969</td>\n",
              "      <td>-0.433884</td>\n",
              "      <td>-0.900969</td>\n",
              "      <td>-0.974928</td>\n",
              "      <td>-0.222521</td>\n",
              "      <td>-0.781832</td>\n",
              "      <td>0.623490</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>2986527711</td>\n",
              "      <td>6</td>\n",
              "      <td>-0.781831</td>\n",
              "      <td>0.623490</td>\n",
              "      <td>-0.974928</td>\n",
              "      <td>-0.222521</td>\n",
              "      <td>-0.433884</td>\n",
              "      <td>-0.900969</td>\n",
              "      <td>0.433883</td>\n",
              "      <td>-0.900969</td>\n",
              "      <td>0.974928</td>\n",
              "      <td>-0.222519</td>\n",
              "      <td>0.781831</td>\n",
              "      <td>0.623490</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-eaf32b22-a9f9-49ff-8249-f6599c84fedf')\"\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 -960 960 960\">\n",
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              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\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",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\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-eaf32b22-a9f9-49ff-8249-f6599c84fedf 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-eaf32b22-a9f9-49ff-8249-f6599c84fedf');\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",
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              "\n",
              "\n",
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              "            title=\"Suggest charts.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
              "<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
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              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-17f8f9f7-220a-437e-8ffb-79a71e117c78 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X7 = train_df[['sin1','cos1','sin2','cos2','sin3','cos3']].iloc[:150]\n",
        "y7 = train_df['mod7'].iloc[:150]\n",
        "X7_train, X7_test, y7_train, y7_test = train_test_split(X7, y7, test_size = 0.1)"
      ],
      "metadata": {
        "id": "leGIIEb_xCDE"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "LM7 = LinearRegression()\n",
        "LM7.fit(X7_train,y7_train)\n",
        "print(LM7.score(X7_test, y7_test)) #R^2 value\n",
        "print(LM7.intercept_)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "f6BDQvlkxCyL",
        "outputId": "02a4e7a9-2c68-4c4d-b0ed-885dca7d8b66"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.9999999999999493\n",
            "3.000000009061278\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "pd.DataFrame(zip(X7.columns, LM7.coef_)).set_axis(['Feature','Coefficient'], axis='columns')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 252
        },
        "id": "XAfuUF6HxFum",
        "outputId": "2ba54f87-4053-48ce-80c5-86ca890fdd9a"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "  Feature  Coefficient\n",
              "0    sin1    -2.076521\n",
              "1    cos1    -1.000000\n",
              "2    sin2    -0.797473\n",
              "3    cos2    -1.000000\n",
              "4    sin3    -0.228243\n",
              "5    cos3    -1.000000"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-fe47afaf-5928-4389-a4b2-b55c1454fb39\" 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</th>\n",
              "      <th>Coefficient</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>sin1</td>\n",
              "      <td>-2.076521</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>cos1</td>\n",
              "      <td>-1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>sin2</td>\n",
              "      <td>-0.797473</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>cos2</td>\n",
              "      <td>-1.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>sin3</td>\n",
              "      <td>-0.228243</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>5</th>\n",
              "      <td>cos3</td>\n",
              "      <td>-1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "    <div class=\"colab-df-buttons\">\n",
              "\n",
              "  <div class=\"colab-df-container\">\n",
              "    <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-fe47afaf-5928-4389-a4b2-b55c1454fb39')\"\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 -960 960 960\">\n",
              "    <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
              "  </svg>\n",
              "    </button>\n",
              "\n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\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",
              "    .colab-df-buttons div {\n",
              "      margin-bottom: 4px;\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-fe47afaf-5928-4389-a4b2-b55c1454fb39 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-fe47afaf-5928-4389-a4b2-b55c1454fb39');\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",
              "\n",
              "\n",
              "<div id=\"df-d3e716b2-0b33-4aec-a608-53a8dab23dd4\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-d3e716b2-0b33-4aec-a608-53a8dab23dd4')\"\n",
              "            title=\"Suggest charts.\"\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",
              "    <g>\n",
              "        <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
              "    </g>\n",
              "</svg>\n",
              "  </button>\n",
              "\n",
              "<style>\n",
              "  .colab-df-quickchart {\n",
              "      --bg-color: #E8F0FE;\n",
              "      --fill-color: #1967D2;\n",
              "      --hover-bg-color: #E2EBFA;\n",
              "      --hover-fill-color: #174EA6;\n",
              "      --disabled-fill-color: #AAA;\n",
              "      --disabled-bg-color: #DDD;\n",
              "  }\n",
              "\n",
              "  [theme=dark] .colab-df-quickchart {\n",
              "      --bg-color: #3B4455;\n",
              "      --fill-color: #D2E3FC;\n",
              "      --hover-bg-color: #434B5C;\n",
              "      --hover-fill-color: #FFFFFF;\n",
              "      --disabled-bg-color: #3B4455;\n",
              "      --disabled-fill-color: #666;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart {\n",
              "    background-color: var(--bg-color);\n",
              "    border: none;\n",
              "    border-radius: 50%;\n",
              "    cursor: pointer;\n",
              "    display: none;\n",
              "    fill: var(--fill-color);\n",
              "    height: 32px;\n",
              "    padding: 0;\n",
              "    width: 32px;\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart:hover {\n",
              "    background-color: var(--hover-bg-color);\n",
              "    box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "    fill: var(--button-hover-fill-color);\n",
              "  }\n",
              "\n",
              "  .colab-df-quickchart-complete:disabled,\n",
              "  .colab-df-quickchart-complete:disabled:hover {\n",
              "    background-color: var(--disabled-bg-color);\n",
              "    fill: var(--disabled-fill-color);\n",
              "    box-shadow: none;\n",
              "  }\n",
              "\n",
              "  .colab-df-spinner {\n",
              "    border: 2px solid var(--fill-color);\n",
              "    border-color: transparent;\n",
              "    border-bottom-color: var(--fill-color);\n",
              "    animation:\n",
              "      spin 1s steps(1) infinite;\n",
              "  }\n",
              "\n",
              "  @keyframes spin {\n",
              "    0% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "      border-left-color: var(--fill-color);\n",
              "    }\n",
              "    20% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    30% {\n",
              "      border-color: transparent;\n",
              "      border-left-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    40% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-top-color: var(--fill-color);\n",
              "    }\n",
              "    60% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "    }\n",
              "    80% {\n",
              "      border-color: transparent;\n",
              "      border-right-color: var(--fill-color);\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "    90% {\n",
              "      border-color: transparent;\n",
              "      border-bottom-color: var(--fill-color);\n",
              "    }\n",
              "  }\n",
              "</style>\n",
              "\n",
              "  <script>\n",
              "    async function quickchart(key) {\n",
              "      const quickchartButtonEl =\n",
              "        document.querySelector('#' + key + ' button');\n",
              "      quickchartButtonEl.disabled = true;  // To prevent multiple clicks.\n",
              "      quickchartButtonEl.classList.add('colab-df-spinner');\n",
              "      try {\n",
              "        const charts = await google.colab.kernel.invokeFunction(\n",
              "            'suggestCharts', [key], {});\n",
              "      } catch (error) {\n",
              "        console.error('Error during call to suggestCharts:', error);\n",
              "      }\n",
              "      quickchartButtonEl.classList.remove('colab-df-spinner');\n",
              "      quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
              "    }\n",
              "    (() => {\n",
              "      let quickchartButtonEl =\n",
              "        document.querySelector('#df-d3e716b2-0b33-4aec-a608-53a8dab23dd4 button');\n",
              "      quickchartButtonEl.style.display =\n",
              "        google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "    })();\n",
              "  </script>\n",
              "</div>\n",
              "    </div>\n",
              "  </div>\n"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X7_val = train_df[['sin1','cos1','sin2','cos2','sin3','cos3']].iloc[-50:]\n",
        "y7_val = train_df['mod7'].iloc[-50:]\n",
        "y7_val = y7_val.to_list()\n",
        "y7_val_predict = LM7.predict(X7_val)"
      ],
      "metadata": {
        "id": "HE0CLOH1xR8v"
      },
      "execution_count": 13,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "error = 10 **(-5)\n",
        "y7_val_pred_label = [0 if abs(y-0)< error else 1 if abs(y-1) < error else 2 if abs(y-2) < error else 3 if abs(y-3) < error else 4 if abs(y-4) < error else 5 if abs(y-5) < error else 6 for y in y7_val_predict]\n",
        "count7 = 0\n",
        "for i in range(len(y7_val_pred_label)):\n",
        "  if y7_val[i] == y7_val_pred_label[i]:\n",
        "    count7 += 1\n",
        "accuracy7 = count7/len(y7_val_pred_label)\n",
        "print(accuracy7)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fScWONeHxqdd",
        "outputId": "efec7528-df7b-4573-eb76-8b8a5ba3902c"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "1.0\n"
          ]
        }
      ]
    }
  ]
}