Mission730Solutions.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Mission730Solutions.ipynb",
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Purpose of Notebook\n",
        "\n",
        "The purpose of this notebook is to offer as a an example answer to the Guided Project for Linear Regression in Python course. Since the choice of model predictors is up to the student, results can differ. Use this solution as a guide to how to structure your own answer."
      ],
      "metadata": {
        "id": "OsSvDQ0Y3yNk"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.metrics import mean_squared_error, r2_score\n",
        "from sklearn.model_selection import train_test_split"
      ],
      "metadata": {
        "id": "lmpsg5fi4t8d"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "# Load in the insurance dataset\n",
        "insurance = pd.read_csv(\"insurance.csv\")"
      ],
      "metadata": {
        "id": "y6aqBHg-5cJT"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Exploring The Dataset"
      ],
      "metadata": {
        "id": "wS1GbH1g7ta5"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Columns in the dataset\n",
        "insurance.columns"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JuqpqwPd5l6d",
        "outputId": "470c6b14-184b-4489-e151-0a6cfe235d08"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Index(['age', 'sex', 'bmi', 'children', 'smoker', 'region', 'charges'], dtype='object')"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The `charges` column is our outcome, while everything else are the potential predictors to use in the model"
      ],
      "metadata": {
        "id": "M5zR7HAr8tsb"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "insurance.hist(\"charges\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 316
        },
        "id": "SMObDGAlOci0",
        "outputId": "82673471-fdbe-48fe-fc14-5974fab5f95f"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7fdf38c164d0>]],\n",
              "      dtype=object)"
            ]
          },
          "metadata": {},
          "execution_count": 4
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The `charges` column is highly skewed to the right. Extremely costly insurance charges are more common than extremely small ones. This makes it unlikely that the errors in the model will truly be centered at zero. It might be worth it to log-transform the outcome."
      ],
      "metadata": {
        "id": "5rSOAfQHOr_8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "insurance[\"log_charges\"] = np.log2(insurance[\"charges\"])\n",
        "\n",
        "insurance.hist(\"log_charges\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 316
        },
        "id": "FG2IyzGFPHF2",
        "outputId": "c0f8e3d8-57fd-4467-e164-6797960c871f"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7fdf38b11ad0>]],\n",
              "      dtype=object)"
            ]
          },
          "metadata": {},
          "execution_count": 5
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The log-transformed `charges` values are more centered, which is what we wanted. This makes it more likely that the errors will be unbiased."
      ],
      "metadata": {
        "id": "sFiFbsCUQHv8"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Checking the correlation between the continuous columns in the insurance data\n",
        "insurance.corr()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "uSRq96HH8AAR",
        "outputId": "ace3b1fc-0cbc-4cce-b57e-38b26b1dbfe7"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "                  age       bmi  children   charges  log_charges\n",
              "age          1.000000  0.109272  0.042469  0.299008     0.527834\n",
              "bmi          0.109272  1.000000  0.012759  0.198341     0.132669\n",
              "children     0.042469  0.012759  1.000000  0.067998     0.161336\n",
              "charges      0.299008  0.198341  0.067998  1.000000     0.892964\n",
              "log_charges  0.527834  0.132669  0.161336  0.892964     1.000000"
            ],
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              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Comments on correlation\n",
        "\n",
        "`age` has 30% correlation with `charges`, `bmi` has 19.8% correlation, and number of children has 6.7% correlation."
      ],
      "metadata": {
        "id": "-ghJAB_59B9Z"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "insurance.boxplot(column = [\"log_charges\"], by = \"sex\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 373
        },
        "id": "amZ_91bU8352",
        "outputId": "dec66ac2-8799-432a-9aa5-344d5a6eaac6"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/matplotlib/cbook/__init__.py:1376: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
            "  X = np.atleast_1d(X.T if isinstance(X, np.ndarray) else np.asarray(X))\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fdf385f8690>"
            ]
          },
          "metadata": {},
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "insurance.boxplot(column = [\"log_charges\"], by = \"smoker\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 373
        },
        "id": "9_gIr-7AJ1Uo",
        "outputId": "61cfc34b-4718-429c-ff27-2e9ee9e39d22"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/matplotlib/cbook/__init__.py:1376: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
            "  X = np.atleast_1d(X.T if isinstance(X, np.ndarray) else np.asarray(X))\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fdf385c4510>"
            ]
          },
          "metadata": {},
          "execution_count": 8
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "insurance.boxplot(column = [\"log_charges\"], by = \"region\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 373
        },
        "id": "Z5-n30hmKH_Y",
        "outputId": "aeabd663-0781-432c-954f-7ce33dc5c4f0"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/matplotlib/cbook/__init__.py:1376: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
            "  X = np.atleast_1d(X.T if isinstance(X, np.ndarray) else np.asarray(X))\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fdf38466110>"
            ]
          },
          "metadata": {},
          "execution_count": 9
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "insurance.boxplot(column = [\"log_charges\"], by = \"region\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 373
        },
        "id": "lVogyvIOKK6o",
        "outputId": "30499162-adaf-4260-f26d-b650759d4b73"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/matplotlib/cbook/__init__.py:1376: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n",
            "  X = np.atleast_1d(X.T if isinstance(X, np.ndarray) else np.asarray(X))\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fdf385da190>"
            ]
          },
          "metadata": {},
          "execution_count": 10
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Comments on plots\n",
        "\n",
        "Males seem to have a wider distribution of charges compared to women. Smokers have much higher costs than non-smokers. There doesn't seem tobe many appreciable differences between regions. "
      ],
      "metadata": {
        "id": "EcQUy2RaKPNh"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Dividing The Data\n",
        "\n",
        "Based on the univariate relationships shown above, `age`, `bmi` and `smoker` are positively associated with higher `charges`. We'll include these predictors in our final model."
      ],
      "metadata": {
        "id": "Q4f6SIK8Kv-k"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Splitting the data up into a training and test set\n",
        "insurance[\"is_smoker\"] = (insurance[\"smoker\"] == \"yes\")\n",
        "X = insurance[[\"age\", \"bmi\", \"is_smoker\"]]\n",
        "y = insurance[\"log_charges\"]\n",
        "\n",
        "# 75% for training set, 25% for test set\n",
        "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.25, \n",
        "                                                    random_state = 1)"
      ],
      "metadata": {
        "id": "lihP2kTALKL-"
      },
      "execution_count": 11,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Build The Model"
      ],
      "metadata": {
        "id": "YE-XKUr_428I"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Training and checking model performance on training set\n",
        "insurance_model = LinearRegression()\n",
        "insurance_model.fit(X_train, y_train)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jCHcD-PcLfxu",
        "outputId": "93957439-f797-4f85-e5fc-1149ae619dd0"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression()"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        ""
      ],
      "metadata": {
        "id": "r9pR9V2TOYdT"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Get predicted values by model\n",
        "y_pred = insurance_model.predict(X_train)\n",
        "\n",
        "# MSE on the log scale for the insurance charges\n",
        "mean_squared_error(y_train, y_pred)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "WY4gnJJpMqNN",
        "outputId": "ac7676db-6ccf-4b35-aa30-d81905dac57d"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.4546665339270644"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# MSE on the original scale for the insurance charges\n",
        "np.exp(mean_squared_error(y_train, y_pred))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YvUvASEyQ0aN",
        "outputId": "5f99b5a4-317f-47cc-93b1-8d22464612a6"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.575647870310887"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Coefficient of determination\n",
        "r2_score(y_train, y_pred)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tOFi1oxFRFPk",
        "outputId": "351d9bd3-2b78-4ff0-fec0-f5ca559b5d1c"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.7421118855283421"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Comments\n",
        "\n",
        "The training MSE for the model is 0.454 and is 1.57 on the original scale. The $R^2$ indicates that the model can explain 74% of the variation in the log-insurance charges. These preliminary results are promising, but we must remember that these are optimistic values."
      ],
      "metadata": {
        "id": "70BciwrTQucW"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Residual Diagnostics"
      ],
      "metadata": {
        "id": "Op2iO4grSZBZ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Quick visual check of residuals\n",
        "check = pd.DataFrame()\n",
        "check[\"residuals\"] = y_train - y_pred\n",
        "check[\"fitted\"] = y_pred\n",
        "\n",
        "check.plot.scatter(x = \"fitted\", y = \"residuals\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "dLCBNJMuNb-x",
        "outputId": "626a7509-6890-4932-cd42-8b443001d99f"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fdf383015d0>"
            ]
          },
          "metadata": {},
          "execution_count": 16
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The residuals suggest some violations to the assumptions of linear regression. As fitted values get larger, the residuals trend downward. We expect an even band, centered around zero. This does not necessarily make the model predictions unusable, but it puts into question the linear regression assumptions."
      ],
      "metadata": {
        "id": "PW19C6k5TgUS"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Interpreting The Model"
      ],
      "metadata": {
        "id": "2NpUAgXgUI0Z"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Getting the non-intercept coefficients\n",
        "insurance_model.coef_"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "YmfjKyIjSqr-",
        "outputId": "7e388b83-ffb1-4116-c711-7aabea9312d5"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0.04892865, 0.01523672, 2.23063344])"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "- A year increase in the subject is associated with a 0.04 increase in the log charges, holding smoking status and bmi constant. About a 4% increase in the charges on the regular scale.\n",
        "- A unit increase in the subject BMI is associated with a 0.01 increase in the log charges, holding smoking status and age constant.  About a 1.5% increase in the charges on the regular scale.\n",
        "- A smoker is associated with a 2.23 increase in the log charges, holding age and bmi constant. About a 930% increase in the charges on the regular scale.\n",
        "\n",
        "Note: we are not concerned about if these changes are *statistically significant*, so we don't know if these associations are truly non-zero. Our primary goal is prediction."
      ],
      "metadata": {
        "id": "guf4YyvQVSfq"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Final Model Evaluation"
      ],
      "metadata": {
        "id": "aYOK6CucWXBB"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Getting MSE on test model\n",
        "test_pred = insurance_model.predict(X_test)\n",
        "\n",
        "mean_squared_error(y_test, test_pred)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "tXrcpejXUNDv",
        "outputId": "fbbab0a6-4446-4b35-8626-dc4a5d47dd76"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.4355350875308211"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Putting the outcome (in log-terms) back into the original scale\n",
        "np.exp(mean_squared_error(y_test, test_pred))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "NjH8j9ZPXDHv",
        "outputId": "001d7c0a-70db-4be3-8a1d-84521e71ac8b"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.545789970635098"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Drawing Conclusions\n",
        "\n",
        "The test MSE was about 0.435, while the training MSE was about 0.454. In this case, the two errors match up pretty well, so we can conclude that the model is not overfit. The residuals suggest that the model is predicting much lower costs for subjects who were actually charged much higher. Therefore the model struggles with these higher costs. As a whole, the model predictions are too conservative. \n",
        "\n",
        "We might improve the model by including more complex terms in the regression, such as interactions or quadratic terms. "
      ],
      "metadata": {
        "id": "iZcGg2tgWpGx"
      }
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "sMKpzdDG5B7_"
      },
      "execution_count": 19,
      "outputs": []
    }
  ]
}