Simple+linear+regression.ipynb

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        "<a href=\"https://colab.research.google.com/github/Nargis45/Regression-techniques/blob/master/Simple%2Blinear%2Bregression.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-K2G2oIj5LDp"
      },
      "source": [
        "# Simple linear regression"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "oq4ab7HC5LD2"
      },
      "source": [
        "## Import the relevant libraries"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "ZCS5SZMg5LD4"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import statsmodels.api as sm\n",
        "# We can override the default matplotlib styles with those of Seaborn\n",
        "#import seaborn as sns\n",
        "#sns.set()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r-O-tpCA5LD9"
      },
      "source": [
        "## Load the data"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "5oW-w93A5LD-"
      },
      "outputs": [],
      "source": [
        "# Load the data from a .csv in the same folder\n",
        "data = pd.read_csv('/content/1.01.+Simple+linear+regression.csv')"
      ]
    },
    {
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      "execution_count": 4,
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        "id": "4C9Zfykd5LEA",
        "outputId": "8046bfbf-a2a6-4b7f-8bc5-ceca7e1078f5"
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      "outputs": [
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              "     SAT   GPA\n",
              "0   1714  2.40\n",
              "1   1664  2.52\n",
              "2   1760  2.54\n",
              "3   1685  2.74\n",
              "4   1693  2.83\n",
              "..   ...   ...\n",
              "79  1936  3.71\n",
              "80  1810  3.71\n",
              "81  1987  3.73\n",
              "82  1962  3.76\n",
              "83  2050  3.81\n",
              "\n",
              "[84 rows x 2 columns]"
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              "      <td>2.52</td>\n",
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              "      <th>2</th>\n",
              "      <td>1760</td>\n",
              "      <td>2.54</td>\n",
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              "      <td>2.74</td>\n",
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              "      <td>3.76</td>\n",
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              "    <tr>\n",
              "      <th>83</th>\n",
              "      <td>2050</td>\n",
              "      <td>3.81</td>\n",
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              "<p>84 rows × 2 columns</p>\n",
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              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
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              "\n",
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      "source": [
        "# Let's check what's inside this data frame\n",
        "data"
      ]
    },
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      "cell_type": "code",
      "execution_count": 5,
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        "scrolled": true,
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          "data": {
            "text/plain": [
              "               SAT        GPA\n",
              "count    84.000000  84.000000\n",
              "mean   1845.273810   3.330238\n",
              "std     104.530661   0.271617\n",
              "min    1634.000000   2.400000\n",
              "25%    1772.000000   3.190000\n",
              "50%    1846.000000   3.380000\n",
              "75%    1934.000000   3.502500\n",
              "max    2050.000000   3.810000"
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              "      <th>GPA</th>\n",
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              "  </thead>\n",
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              "      <th>count</th>\n",
              "      <td>84.000000</td>\n",
              "      <td>84.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>1845.273810</td>\n",
              "      <td>3.330238</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>104.530661</td>\n",
              "      <td>0.271617</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>1634.000000</td>\n",
              "      <td>2.400000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>1772.000000</td>\n",
              "      <td>3.190000</td>\n",
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              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>1846.000000</td>\n",
              "      <td>3.380000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>1934.000000</td>\n",
              "      <td>3.502500</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>2050.000000</td>\n",
              "      <td>3.810000</td>\n",
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              "                                                     [key], {});\n",
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              "\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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          },
          "metadata": {},
          "execution_count": 5
        }
      ],
      "source": [
        "# This method gives us very nice descriptive statistics. We don't need this as of now, but will later on!\n",
        "data.describe()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gLredtr25LEE"
      },
      "source": [
        "# Create your first regression"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "l_V8Tqdi5LEG"
      },
      "source": [
        "## Define the dependent and the independent variables"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "id": "TxBGFeWc5LEJ"
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      "outputs": [],
      "source": [
        "# Following the regression equation, our dependent variable (y) is the GPA\n",
        "y = data ['GPA']\n",
        "# Similarly, our independent variable (x) is the SAT score\n",
        "x1 = data ['SAT']"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o3uhUJyD5LEN"
      },
      "source": [
        "## Explore the data"
      ]
    },
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      "execution_count": 7,
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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
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            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "# Plot a scatter plot (first we put the horizontal axis, then the vertical axis)\n",
        "plt.scatter(x1,y)\n",
        "# Name the axes\n",
        "plt.xlabel('SAT', fontsize = 20)\n",
        "plt.ylabel('GPA', fontsize = 20)\n",
        "# Show the plot\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Be-x8B3R5LEQ"
      },
      "source": [
        "## Regression itself"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "scrolled": false,
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 533
        },
        "id": "XI8Tcs8K5LER",
        "outputId": "19bceeef-0db4-470b-c120-68a5b0d06d7c"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/statsmodels/tsa/tsatools.py:142: FutureWarning: In a future version of pandas all arguments of concat except for the argument 'objs' will be keyword-only\n",
            "  x = pd.concat(x[::order], 1)\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<class 'statsmodels.iolib.summary.Summary'>\n",
              "\"\"\"\n",
              "                            OLS Regression Results                            \n",
              "==============================================================================\n",
              "Dep. Variable:                    GPA   R-squared:                       0.406\n",
              "Model:                            OLS   Adj. R-squared:                  0.399\n",
              "Method:                 Least Squares   F-statistic:                     56.05\n",
              "Date:                Thu, 10 Nov 2022   Prob (F-statistic):           7.20e-11\n",
              "Time:                        09:36:42   Log-Likelihood:                 12.672\n",
              "No. Observations:                  84   AIC:                            -21.34\n",
              "Df Residuals:                      82   BIC:                            -16.48\n",
              "Df Model:                           1                                         \n",
              "Covariance Type:            nonrobust                                         \n",
              "==============================================================================\n",
              "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
              "------------------------------------------------------------------------------\n",
              "const          0.2750      0.409      0.673      0.503      -0.538       1.088\n",
              "SAT            0.0017      0.000      7.487      0.000       0.001       0.002\n",
              "==============================================================================\n",
              "Omnibus:                       12.839   Durbin-Watson:                   0.950\n",
              "Prob(Omnibus):                  0.002   Jarque-Bera (JB):               16.155\n",
              "Skew:                          -0.722   Prob(JB):                     0.000310\n",
              "Kurtosis:                       4.590   Cond. No.                     3.29e+04\n",
              "==============================================================================\n",
              "\n",
              "Notes:\n",
              "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
              "[2] The condition number is large, 3.29e+04. This might indicate that there are\n",
              "strong multicollinearity or other numerical problems.\n",
              "\"\"\""
            ],
            "text/html": [
              "<table class=\"simpletable\">\n",
              "<caption>OLS Regression Results</caption>\n",
              "<tr>\n",
              "  <th>Dep. Variable:</th>           <td>GPA</td>       <th>  R-squared:         </th> <td>   0.406</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.399</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   56.05</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Date:</th>             <td>Thu, 10 Nov 2022</td> <th>  Prob (F-statistic):</th> <td>7.20e-11</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Time:</th>                 <td>09:36:42</td>     <th>  Log-Likelihood:    </th> <td>  12.672</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>No. Observations:</th>      <td>    84</td>      <th>  AIC:               </th> <td>  -21.34</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Residuals:</th>          <td>    82</td>      <th>  BIC:               </th> <td>  -16.48</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "    <td></td>       <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
              "</tr>\n",
              "<tr>\n",
              "  <th>const</th> <td>    0.2750</td> <td>    0.409</td> <td>    0.673</td> <td> 0.503</td> <td>   -0.538</td> <td>    1.088</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>SAT</th>   <td>    0.0017</td> <td>    0.000</td> <td>    7.487</td> <td> 0.000</td> <td>    0.001</td> <td>    0.002</td>\n",
              "</tr>\n",
              "</table>\n",
              "<table class=\"simpletable\">\n",
              "<tr>\n",
              "  <th>Omnibus:</th>       <td>12.839</td> <th>  Durbin-Watson:     </th> <td>   0.950</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Prob(Omnibus):</th> <td> 0.002</td> <th>  Jarque-Bera (JB):  </th> <td>  16.155</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Skew:</th>          <td>-0.722</td> <th>  Prob(JB):          </th> <td>0.000310</td>\n",
              "</tr>\n",
              "<tr>\n",
              "  <th>Kurtosis:</th>      <td> 4.590</td> <th>  Cond. No.          </th> <td>3.29e+04</td>\n",
              "</tr>\n",
              "</table><br/><br/>Notes:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.<br/>[2] The condition number is large, 3.29e+04. This might indicate that there are<br/>strong multicollinearity or other numerical problems."
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ],
      "source": [
        "# Add a constant. Essentially, we are adding a new column (equal in lenght to x), which consists only of 1s\n",
        "x = sm.add_constant(x1)\n",
        "# Fit the model, according to the OLS (ordinary least squares) method with a dependent variable y and an idependent x\n",
        "results = sm.OLS(y,x).fit()\n",
        "# Print a nice summary of the regression. That's one of the strong points of statsmodels -> the summaries\n",
        "results.summary()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 288
        },
        "id": "tsOGcAOD5LES",
        "outputId": "4c48676a-025f-47f2-d7c6-072557f55ebd"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "# Create a scatter plot\n",
        "plt.scatter(x1,y)\n",
        "# Define the regression equation, so we can plot it later\n",
        "yhat = 0.0017*x1 + 0.275\n",
        "# Plot the regression line against the independent variable (SAT)\n",
        "fig = plt.plot(x1,yhat, lw=4, c='orange', label ='regression line')\n",
        "# Label the axes\n",
        "plt.xlabel('SAT', fontsize = 20)\n",
        "plt.ylabel('GPA', fontsize = 20)\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "VWulpmcR5krV"
      },
      "execution_count": null,
      "outputs": []
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.6.4"
    },
    "colab": {
      "provenance": [],
      "include_colab_link": true
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}