Case_study_Simple_Linear_Regression.ipynb

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        "<a href=\"https://colab.research.google.com/github/devzohaib/Simple-Linear-Regression/blob/master/Case_study_Simple_Linear_Regression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SeXvLc-1BW5y"
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      "source": [
        "# Simple Linear Regression "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JUPGS__xBW5y"
      },
      "source": [
        "In this example we will consider sales based on 'TV' marketing budget. \n",
        "\n",
        "In this notebook, we'll build a linear regression model to predict 'Sales' using 'TV' as the predictor variable.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "_xhhrRGiBW5y"
      },
      "source": [
        "## Understanding the Data"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5Hxz_OnuBW5y"
      },
      "source": [
        "Let's start with the following steps:\n",
        "\n",
        "1. Importing data using the pandas library\n",
        "2. Understanding the structure of the data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4YmE8-RiBW5y"
      },
      "source": [
        "import pandas as pd"
      ],
      "execution_count": 3,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LIadm3t6BW5z"
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      "source": [
        "# Reading csv file from github repo\n",
        "url  = \"https://raw.githubusercontent.com/devzohaib/Simple-Linear-Regression/master/tvmarketing.csv\"\n",
        "advertising = pd.read_csv(url)"
      ],
      "execution_count": 6,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9ZFSxwHPBW5z"
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      "source": [
        "Now, let's check the structure of the advertising dataset."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 202
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        "id": "pzkseQTcBW5z",
        "outputId": "450b1d4b-b243-455a-df62-e6b3c1211e6a"
      },
      "source": [
        "# Display the first 5 rows\n",
        "advertising.head()"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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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",
              "    </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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            ],
            "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"
            ]
          },
          "metadata": {
            "tags": []
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          "execution_count": 7
        }
      ]
    },
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        "id": "pbmsRO2YBW50",
        "outputId": "d513486d-be6f-4908-fc0f-78662e099e4f"
      },
      "source": [
        "# Display the last 5 rows\n",
        "advertising.tail()"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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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>195</th>\n",
              "      <td>38.2</td>\n",
              "      <td>7.6</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>196</th>\n",
              "      <td>94.2</td>\n",
              "      <td>9.7</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>197</th>\n",
              "      <td>177.0</td>\n",
              "      <td>12.8</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>198</th>\n",
              "      <td>283.6</td>\n",
              "      <td>25.5</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>199</th>\n",
              "      <td>232.1</td>\n",
              "      <td>13.4</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
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            ],
            "text/plain": [
              "        TV  Sales\n",
              "195   38.2    7.6\n",
              "196   94.2    9.7\n",
              "197  177.0   12.8\n",
              "198  283.6   25.5\n",
              "199  232.1   13.4"
            ]
          },
          "metadata": {
            "tags": []
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          "execution_count": 8
        }
      ]
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        "id": "HQDqzhdKBW51",
        "outputId": "1cb2a23e-8963-4629-b415-8fa68c5c383b"
      },
      "source": [
        "# Let's check the columns\n",
        "advertising.info()"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 200 entries, 0 to 199\n",
            "Data columns (total 2 columns):\n",
            " #   Column  Non-Null Count  Dtype  \n",
            "---  ------  --------------  -----  \n",
            " 0   TV      200 non-null    float64\n",
            " 1   Sales   200 non-null    float64\n",
            "dtypes: float64(2)\n",
            "memory usage: 3.2 KB\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
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        "id": "1fOGVz61BW51",
        "outputId": "81567bb2-0c1b-480c-9a4c-9f1d70c012e0"
      },
      "source": [
        "# Check the shape of the DataFrame (rows, columns)\n",
        "advertising.shape"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(200, 2)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        }
      ]
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    {
      "cell_type": "code",
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          "height": 294
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        "id": "VO4GoVyfBW51",
        "outputId": "29ea1da8-11c6-4cf1-9e1f-8cb9298afa92"
      },
      "source": [
        "# Let's look at some statistical information about the dataframe.\n",
        "advertising.describe()"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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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>count</th>\n",
              "      <td>200.000000</td>\n",
              "      <td>200.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>147.042500</td>\n",
              "      <td>14.022500</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>85.854236</td>\n",
              "      <td>5.217457</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>0.700000</td>\n",
              "      <td>1.600000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>74.375000</td>\n",
              "      <td>10.375000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>149.750000</td>\n",
              "      <td>12.900000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>218.825000</td>\n",
              "      <td>17.400000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>296.400000</td>\n",
              "      <td>27.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
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            ],
            "text/plain": [
              "               TV       Sales\n",
              "count  200.000000  200.000000\n",
              "mean   147.042500   14.022500\n",
              "std     85.854236    5.217457\n",
              "min      0.700000    1.600000\n",
              "25%     74.375000   10.375000\n",
              "50%    149.750000   12.900000\n",
              "75%    218.825000   17.400000\n",
              "max    296.400000   27.000000"
            ]
          },
          "metadata": {
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          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4tkuFialBW52"
      },
      "source": [
        "# Visualising Data Using Plot"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "3mEiKmvYCk8S",
        "outputId": "0fd94a12-8a44-4c99-fe22-13b786d02b61"
      },
      "source": [
        "# Visualise the relationship between the features and the response using scatterplots\n",
        "df.plot(x='TV',y='Sales',kind='scatter')"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f6b37e95588>"
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          "metadata": {
            "tags": []
          },
          "execution_count": 18
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          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "54eMqRWoBW52"
      },
      "source": [
        "# Perfroming Simple Linear Regression"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "R8O25fC6BW52"
      },
      "source": [
        "Equation of linear regression<br>\n",
        "$y = c + m_1x_1 + m_2x_2 + ... + m_nx_n$\n",
        "\n",
        "-  $y$ is the response\n",
        "-  $c$ is the intercept\n",
        "-  $m_1$ is the coefficient for the first feature\n",
        "-  $m_n$ is the coefficient for the nth feature<br>\n",
        "\n",
        "In our case:\n",
        "\n",
        "$y = c + m_1 \\times TV$\n",
        "\n",
        "The $m$ values are called the model **coefficients** or **model parameters**."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SdKPVlotBW52"
      },
      "source": [
        "### Generic Steps in Model Building using ```sklearn```\n",
        "\n",
        "Before you read further, it is good to understand the generic structure of modeling using the scikit-learn library. Broadly, the steps to build any model can be divided as follows: "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GaxpcxRABW52"
      },
      "source": [
        "## Preparing X and y\n",
        "\n",
        "-  The scikit-learn library expects X (feature variable) and y (response variable) to be NumPy arrays.\n",
        "-  However, X can be a dataframe as Pandas is built over NumPy."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0ySJx_RkBW52",
        "outputId": "cdcd677e-7d8e-4b24-e1f8-5a8fb85d9904"
      },
      "source": [
        "# Putting feature variable to X\n",
        "X = advertising['TV']\n",
        "\n",
        "# Print the first 5 rows\n",
        "X.head()"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0    230.1\n",
              "1     44.5\n",
              "2     17.2\n",
              "3    151.5\n",
              "4    180.8\n",
              "Name: TV, dtype: float64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RA6LC8R4BW52",
        "outputId": "4f7f2b72-2202-4d45-b077-1b8dde5935b0"
      },
      "source": [
        "# Putting response variable to y\n",
        "y = advertising['Sales']\n",
        "\n",
        "# Print the first 5 rows\n",
        "y.head()"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0    22.1\n",
              "1    10.4\n",
              "2     9.3\n",
              "3    18.5\n",
              "4    12.9\n",
              "Name: Sales, dtype: float64"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fRshsy8OBW52"
      },
      "source": [
        "## Splitting Data into Training and Testing Sets"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OD84Ss_hBW52"
      },
      "source": [
        "#random_state is the seed used by the random number generator, it can be any integer.\n",
        "\n",
        "from sklearn.model_selection import train_test_split\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, train_size=0.7 , random_state=0000)"
      ],
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rP9gRuF-BW52",
        "outputId": "979bec18-e023-4c18-a1be-d26c94f3bcab"
      },
      "source": [
        "print(type(X_train))\n",
        "print(type(X_test))\n",
        "print(type(y_train))\n",
        "print(type(y_test))"
      ],
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "<class 'pandas.core.series.Series'>\n",
            "<class 'pandas.core.series.Series'>\n",
            "<class 'pandas.core.series.Series'>\n",
            "<class 'pandas.core.series.Series'>\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "iaNZaViTBW52",
        "outputId": "ac72156d-2cff-4e49-c175-61aff59504fa"
      },
      "source": [
        "train_test_split      \n",
        "#Press Tab+Shift to read the documentation"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<function sklearn.model_selection._split.train_test_split>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XGx3CCXlBW52",
        "outputId": "149a721e-d422-4aa6-ce94-76cc7289a7ee"
      },
      "source": [
        "print(X_train.shape)\n",
        "print(y_train.shape)\n",
        "print(X_test.shape)\n",
        "print(y_test.shape)"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(140,)\n",
            "(140,)\n",
            "(60,)\n",
            "(60,)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SVKR9nQHBW52",
        "outputId": "8dfd1eeb-d1d9-4229-de3c-7e2e17508dea"
      },
      "source": [
        "#It is a general convention in scikit-learn that observations are rows, while features are columns. \n",
        "#This is needed only when you are using a single feature; in this case, 'TV'.\n",
        "\n",
        "import numpy as np\n",
        "#Simply put, numpy.newaxis is used to increase the dimension of the existing array by one more dimension,\n",
        "X_train = X_train[:, np.newaxis]\n",
        "X_test = X_test[:, np.newaxis]"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:6: FutureWarning: Support for multi-dimensional indexing (e.g. `obj[:, None]`) is deprecated and will be removed in a future version.  Convert to a numpy array before indexing instead.\n",
            "  \n",
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:7: FutureWarning: Support for multi-dimensional indexing (e.g. `obj[:, None]`) is deprecated and will be removed in a future version.  Convert to a numpy array before indexing instead.\n",
            "  import sys\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "P84R5ARrBW52",
        "outputId": "ef70bde7-5c3e-4f2e-f84a-ae1e031feb91"
      },
      "source": [
        "print(X_train.shape)\n",
        "print(y_train.shape)\n",
        "print(X_test.shape)\n",
        "print(y_test.shape)"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(140, 1)\n",
            "(140,)\n",
            "(60, 1)\n",
            "(60,)\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "EdeY_F9xBW52"
      },
      "source": [
        "## Performing Linear Regression"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "qL6yPFpABW52",
        "outputId": "fe24ad41-cfc8-4bb0-d11d-8c4b4eb9c6aa"
      },
      "source": [
        "# import LinearRegression from sklearn\n",
        "from sklearn.linear_model import LinearRegression\n",
        "\n",
        "# Representing LinearRegression as lr(Creating LinearRegression Object)\n",
        "lr = LinearRegression()\n",
        "\n",
        "# Fit the model using lr.fit()\n",
        "lr.fit(X_train, y_train)"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ZhChGqJ2BW52"
      },
      "source": [
        "## Coefficients Calculation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "527h4jGWBW52",
        "outputId": "45d60d59-59c1-4b1e-d66e-2c4e6e44f6f7"
      },
      "source": [
        "# Print the intercept and coefficients\n",
        "print(lr.intercept_)\n",
        "print(lr.coef_)"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "7.310810165411681\n",
            "[0.04581434]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Hm_44AKFBW53"
      },
      "source": [
        "$y = 6.989 + 0.0464 \\times TV $<br>\n",
        "\n",
        "Now, let's use this equation to predict our sales."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8t8Av_XXBW53"
      },
      "source": [
        "## Predictions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wJqlolZtBW53"
      },
      "source": [
        "# Making predictions on the testing set\n",
        "y_pred = lr.predict(X_test)"
      ],
      "execution_count": 34,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4u4Cz-xqBW53",
        "outputId": "b0d8415b-b6c7-4b39-d8d2-a13bc41c54d8"
      },
      "source": [
        "type(y_pred)"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "numpy.ndarray"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "collapsed": true,
        "id": "42DUHkQzBW53"
      },
      "source": [
        "#### Computing RMSE and R^2 Values\n",
        "RMSE is the standard deviation of the errors which occur when a prediction is made on a dataset. This is the same as MSE (Mean Squared Error) but the root of the value is considered while determining the accuracy of the model\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yRt2E6pIK9h1",
        "outputId": "64ea703a-d923-4c1d-d0bd-202be086239e"
      },
      "source": [
        "y_test.shape # cheek the shape to generate the index for plot"
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(60,)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 333
        },
        "id": "beUEVjg3Jb_h",
        "outputId": "bdb68398-759e-4f78-b568-a32fab391ec6"
      },
      "source": [
        "# Actual vs Predicted\n",
        "import matplotlib.pyplot as plt\n",
        "c = [i for i in range(1,61,1)]         # generating index \n",
        "fig = plt.figure()\n",
        "plt.plot(c,y_test, color=\"blue\", linewidth=2, linestyle=\"-\")\n",
        "plt.plot(c,y_pred, color=\"red\",  linewidth=2, linestyle=\"-\")\n",
        "fig.suptitle('Actual and Predicted', fontsize=20)              # Plot heading \n",
        "plt.xlabel('Index', fontsize=18)                               # X-label\n",
        "plt.ylabel('Sales', fontsize=16)                       # Y-label"
      ],
      "execution_count": 45,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'Sales')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 45
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 333
        },
        "id": "fHp6JU41BW53",
        "outputId": "6af7c0f5-526f-4b53-dd8c-476c8c795ea5"
      },
      "source": [
        "# Error terms\n",
        "c = [i for i in range(1,61,1)]\n",
        "fig = plt.figure()\n",
        "plt.plot(c,y_test-y_pred, color=\"blue\", linewidth=2, linestyle=\"-\")\n",
        "fig.suptitle('Error Terms', fontsize=20)              # Plot heading \n",
        "plt.xlabel('Index', fontsize=18)                      # X-label\n",
        "plt.ylabel('ytest-ypred', fontsize=16)                # Y-label"
      ],
      "execution_count": 46,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'ytest-ypred')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 46
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rJKwrhrABW53"
      },
      "source": [
        "from sklearn.metrics import mean_squared_error, r2_score\n",
        "mse = mean_squared_error(y_test, y_pred)"
      ],
      "execution_count": 47,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "v6OraM7mBW53"
      },
      "source": [
        "r_squared = r2_score(y_test, y_pred)"
      ],
      "execution_count": 48,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "osv85GbBBW53",
        "outputId": "8cd66d2c-988a-45ce-9f76-84518bed87a2"
      },
      "source": [
        "print('Mean_Squared_Error :' ,mse)\n",
        "print('r_square_value :',r_squared)"
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Mean_Squared_Error : 7.497479593464674\n",
            "r_square_value : 0.725606346597073\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "cvBH_rcAQFSv"
      },
      "source": [
        "# this mse =7.9 means that this model is not able to match the 7.9 percent of the values\n",
        "# r2 means that your model is 72% is accurate on test data ."
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "P1-nZjpyBW53",
        "outputId": "d770a694-3d01-4b22-d00e-9e73a5a39b83"
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "plt.scatter(y_test,y_pred,c='blue')\n",
        "plt.xlabel('Y Test')\n",
        "plt.ylabel('Predicted Y')\n",
        "plt.grid()\n"
      ],
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    }
  ]
}