Linear_regression_model.ipynb

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      "name": "Linear regression model.ipynb",
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      "name": "python"
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      "cell_type": "markdown",
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        "<a href=\"https://colab.research.google.com/github/omache/Simple-Linear-Regression/blob/main/Linear_regression_model.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "execution_count": null,
      "metadata": {
        "id": "mljip3cj5bbV"
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      "outputs": [],
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#Import the data and assign the x and y variables to their respective variables\n",
        "data = pd.read_csv(\"/content/sample_data/tvmarketing.csv\")\n",
        "x = data['TV']\n",
        "y = data['Sales']"
      ],
      "metadata": {
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      },
      "execution_count": null,
      "outputs": []
    },
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      "source": [
        "data.head()"
      ],
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          "height": 206
        },
        "outputId": "d2e317f2-c9c7-4700-9b8a-bb6b91e22276"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "      TV  Sales\n",
              "0  230.1   22.1\n",
              "1   44.5   10.4\n",
              "2   17.2    9.3\n",
              "3  151.5   18.5\n",
              "4  180.8   12.9"
            ],
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>TV</th>\n",
              "      <th>Sales</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>230.1</td>\n",
              "      <td>22.1</td>\n",
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              "      <th>1</th>\n",
              "      <td>44.5</td>\n",
              "      <td>10.4</td>\n",
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              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>17.2</td>\n",
              "      <td>9.3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>151.5</td>\n",
              "      <td>18.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>180.8</td>\n",
              "      <td>12.9</td>\n",
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      "cell_type": "code",
      "source": [
        "#We draw a scatterplpot using matplotlib's `scatter`\n",
        "plt.scatter(x,y)\n",
        "plt.xlabel('TV Marketing Budget')\n",
        "plt.ylabel('Sales')\n",
        "plt.title('Relationship Between TV and Sales')\n",
        "plt.figure(figsize= (10,6))\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 312
        },
        "id": "qJxgTXt99X4q",
        "outputId": "d3d1432f-24b0-4cef-ed31-c83c998d91c7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 720x432 with 0 Axes>"
            ]
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "data.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "M4npY3RQx__i",
        "outputId": "429054dc-a809-41b7-f06c-9622d003a831"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "      TV  Sales\n",
              "0  230.1   22.1\n",
              "1   44.5   10.4\n",
              "2   17.2    9.3\n",
              "3  151.5   18.5\n",
              "4  180.8   12.9"
            ],
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              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
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              "\n",
              "    .dataframe tbody tr th {\n",
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>TV</th>\n",
              "      <th>Sales</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>230.1</td>\n",
              "      <td>22.1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>44.5</td>\n",
              "      <td>10.4</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>17.2</td>\n",
              "      <td>9.3</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>151.5</td>\n",
              "      <td>18.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>180.8</td>\n",
              "      <td>12.9</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
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              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-3d1e7535-edb7-4619-931f-140813ed1b70')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
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              "      border: none;\n",
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              "      fill: #174EA6;\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
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              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
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              "        const buttonEl =\n",
              "          document.querySelector('#df-3d1e7535-edb7-4619-931f-140813ed1b70 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-3d1e7535-edb7-4619-931f-140813ed1b70');\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",
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              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 155
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "2. Calculating the regression line"
      ],
      "metadata": {
        "id": "jltP_hAB_pNT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "#we define b0 and b1 as global variables so that we are able to use them outside the function\n",
        "b0 = 0\n",
        "b1 = 1\n",
        "def linear_regression(x,y):\n",
        "  #evaluating b0: b0 = my - b1*mx\n",
        "  my = sum(y)/len(y)\n",
        "  mx = sum(x)/len(x)\n",
        "  \n",
        "  #evaluating b1; b1 = sp/ssx\n",
        "  sp = sum((x-mx)*(y-my))\n",
        "  ssx = sum((x-mx)*(x-mx))\n",
        "  global b1 #make the variable global\n",
        "  b1 = sp/ssx\n",
        "  \n",
        "  #evaluating b0: b0 = my - b1*mx\n",
        "  global b0\n",
        "  b0 = my - b1*mx\n",
        "  \n",
        "  #return combined model: y = b1x + b0 equation\n",
        "  print ('y = ' +str('{:.3f}'.format(b1))+'x'+' +' + str('{:.3f}'.format(b0)))\n",
        "  return f'The value of b0 is: {b0},and the value of b1 is: {b1}' \n",
        "\n",
        "\n",
        "\n"
      ],
      "metadata": {
        "id": "EsJnAzv_EfnS"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "linear_regression(a,b)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 53
        },
        "id": "NJpI0dGJ_tmP",
        "outputId": "84ddceed-8d6e-44c2-833c-04a02861d9f7"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "y = 9449.962x +25792.200\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "'The value of b0 is: 25792.20019866869,and the value of b1 is: 9449.962321455077'"
            ],
            "application/vnd.google.colaboratory.intrinsic+json": {
              "type": "string"
            }
          },
          "metadata": {},
          "execution_count": 192
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "b0"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "o1L8fTW7C7EQ",
        "outputId": "fded0d31-cf21-45d5-a5af-4a54f1875386"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "7.032593549127705"
            ]
          },
          "metadata": {},
          "execution_count": 187
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "3. Evaluating the model"
      ],
      "metadata": {
        "id": "-kltTPoOQ_th"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "R = 4\n",
        "# Correlation coefficient R\n",
        "def corr_coef(x, y):\n",
        "  N = len(x)\n",
        "  num = (N * (x*y).sum()) - (x.sum() * y.sum())\n",
        "  den = np.sqrt((N * (x**2).sum() - x.sum()**2) * (N * (y**2).sum() - y.sum()**2))\n",
        "  global R\n",
        "  R = num / den\n",
        "  return R\n"
      ],
      "metadata": {
        "id": "xtwv1fHYRBty"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "corr_coef(x,y)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JM47Tn0V_nIH",
        "outputId": "b56e8c02-f064-4259-9b19-7c2e071395ec"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.7822244248616065"
            ]
          },
          "metadata": {},
          "execution_count": 207
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "R\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0-_gGIrQDxj1",
        "outputId": "90efb713-f3db-44b8-a369-d6803b5df5d0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.97824161848876"
            ]
          },
          "metadata": {},
          "execution_count": 206
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "vqtYU9UhM-9n"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "## Finally we make predictions using the model\n",
        "def predict(new_x):\n",
        "  y = b1*new_x + b0\n",
        "  return y"
      ],
      "metadata": {
        "id": "WIs8-t_xEWNV"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "predict (4)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Mmr8StTWY4UA",
        "outputId": "ff1be629-5b73-43e1-a5dc-47043aeb2f3d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "63592.049484489"
            ]
          },
          "metadata": {},
          "execution_count": 129
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## We can try using a new set of data on our model to see if the model works\n",
        "new_data = pd.read_csv(\"/content/MyDataSets/Salary_Data.csv\")\n",
        "new_data.head()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "RtEej6DNZsno",
        "outputId": "fe20c6b4-bd05-4661-fa8c-0c89fdbe26db"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   YearsExperience   Salary\n",
              "0              1.1  39343.0\n",
              "1              1.3  46205.0\n",
              "2              1.5  37731.0\n",
              "3              2.0  43525.0\n",
              "4              2.2  39891.0"
            ],
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              "  <thead>\n",
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              "      <th>YearsExperience</th>\n",
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          "metadata": {},
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      ]
    },
    {
      "cell_type": "code",
      "source": [
        "a = new_data['YearsExperience']\n",
        "b = new_data['Salary']"
      ],
      "metadata": {
        "id": "Oz8Sovu3aBD5"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "e4QbTNzRcvo6"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#we define b0 and b1 as global variables so that we are able to use them outside the function\n",
        "b0 = 0\n",
        "b1 = 1\n",
        "def linear_regression(x,y):\n",
        "  #evaluating b0: b0 = my - b1*mx\n",
        "  my = sum(y)/len(y)\n",
        "  mx = sum(x)/len(x)\n",
        "  \n",
        "  #evaluating b1; b1 = sp/ssx\n",
        "  sp = sum((x-mx)*(y-my))\n",
        "  ssx = sum((x-mx)*(x-mx))\n",
        "  global b1 #make the variable global\n",
        "  b1 = sp/ssx\n",
        "  \n",
        "  #evaluating b0: b0 = my - b1*mx\n",
        "  global b0\n",
        "  b0 = my - b1*mx\n",
        "  \n",
        "  #return combined model: y = b1x + b0 equation\n",
        "  print ('y = ' +str('{:.3f}'.format(b1))+'x'+' +' + str('{:.3f}'.format(b0)))\n",
        "  return f'The value of b0 is: {b0},and the value of b1 is: {b1}' \n"
      ],
      "metadata": {
        "id": "2MLNMLUt3H7r"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}