CerealRatingAnalysis.ipynb

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      "name": "Week3-KhusheeKapoor-200968052-Cereals.ipynb",
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ce1b3b73"
      },
      "source": [
        "## Cereal Rating Analysis"
      ],
      "id": "ce1b3b73"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ca985076"
      },
      "source": [
        "Author: Khushee Kapoor\n",
        "\n",
        "Last Updated: 28/11/21\n",
        "\n",
        "Week: 3\n",
        "\n",
        "\n",
        "**Meta-Data** of the Cereals Dataset:\n",
        "\n",
        "*   name: cereal name \n",
        "*   mfr: Manufacturers are represented by their first initial: A=American Home Food Products, G=General Mills, K=Kelloggs, N=Nabisco, P=Post, Q=Quaker Oats, R=Ralston Purina)\n",
        "*   type: type (cold/hot)\n",
        "*   calories: calories (number) \n",
        "*   protein: protein(g) \n",
        "*   fat: fat(g) \n",
        "*   sodium: sodium(mg) \n",
        "*   fiber: dietary fiber(g) \n",
        "*   carbo: complex carbohydrates(g) \n",
        "*   sugars: sugars(g) \n",
        "*   shelf: display shelf (1, 2, or 3, counting from the floor) \n",
        "*   potass: potassium(mg) \n",
        "*   vitamins: vitamins & minerals (0, 25, or 100, respectively indicating 'none added'; 'enriched, often to 25% FDA recommended'; '100% of FDA recommended')\n",
        "*   weight: weight (in ounces) of one serving (serving size) \n",
        "*   cups: cups per serving \n",
        "*   rating: health rating of the cereal out of 100"
      ],
      "id": "ca985076"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "b5739dbe"
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      "source": [
        "First, we import the libraries:\n",
        "\n",
        "*   NumPy - for data manipulation.\n",
        "*   Pandas - for data manipulation.\n",
        "*   MatPlotLib - for data visualization.\n",
        "*   Seaborn - for data visualization.\n",
        "*   SciPy - for correlation stats."
      ],
      "id": "b5739dbe"
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2d604014"
      },
      "source": [
        "# importing the libraries\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "from matplotlib import pyplot as plt\n",
        "import seaborn as sns\n",
        "from scipy import stats"
      ],
      "id": "2d604014",
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "669307aa"
      },
      "source": [
        "Next, we read the excel file into a Pandas dataframe using the function read_excel() from the Pandas library."
      ],
      "id": "669307aa"
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2846cf98"
      },
      "source": [
        "# reading the dataset\n",
        "df = pd.read_excel('Cereals.xls')"
      ],
      "id": "2846cf98",
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9a4773d0"
      },
      "source": [
        "After reading the dataset, we view the first few rows of the dataframe using the head() function from the Pandas library."
      ],
      "id": "9a4773d0"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "896a8a4f",
        "outputId": "8d4e8a17-2c42-4a72-bea6-35e294cde553"
      },
      "source": [
        "# viewing the first few rows of the dataset\n",
        "# the head() function displays the first 5 rows of the dataframe\n",
        "df.head()"
      ],
      "id": "896a8a4f",
      "execution_count": 3,
      "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>name</th>\n",
              "      <th>mfr</th>\n",
              "      <th>type</th>\n",
              "      <th>calories</th>\n",
              "      <th>protein</th>\n",
              "      <th>fat</th>\n",
              "      <th>sodium</th>\n",
              "      <th>fiber</th>\n",
              "      <th>carbo</th>\n",
              "      <th>sugars</th>\n",
              "      <th>potass</th>\n",
              "      <th>vitamins</th>\n",
              "      <th>shelf</th>\n",
              "      <th>weight</th>\n",
              "      <th>cups</th>\n",
              "      <th>rating</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>100%_Natural_Bran</td>\n",
              "      <td>Q</td>\n",
              "      <td>C</td>\n",
              "      <td>120</td>\n",
              "      <td>3</td>\n",
              "      <td>5</td>\n",
              "      <td>15</td>\n",
              "      <td>2.0</td>\n",
              "      <td>8.0</td>\n",
              "      <td>8</td>\n",
              "      <td>135</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.00</td>\n",
              "      <td>33.983679</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>All-Bran</td>\n",
              "      <td>K</td>\n",
              "      <td>C</td>\n",
              "      <td>70</td>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>260</td>\n",
              "      <td>9.0</td>\n",
              "      <td>7.0</td>\n",
              "      <td>5</td>\n",
              "      <td>320</td>\n",
              "      <td>25</td>\n",
              "      <td>3</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.33</td>\n",
              "      <td>59.425505</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>All-Bran_with_Extra_Fiber</td>\n",
              "      <td>K</td>\n",
              "      <td>C</td>\n",
              "      <td>50</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>140</td>\n",
              "      <td>14.0</td>\n",
              "      <td>8.0</td>\n",
              "      <td>0</td>\n",
              "      <td>330</td>\n",
              "      <td>25</td>\n",
              "      <td>3</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.50</td>\n",
              "      <td>93.704912</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Almond_Delight</td>\n",
              "      <td>R</td>\n",
              "      <td>C</td>\n",
              "      <td>110</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>200</td>\n",
              "      <td>1.0</td>\n",
              "      <td>14.0</td>\n",
              "      <td>8</td>\n",
              "      <td>-1</td>\n",
              "      <td>25</td>\n",
              "      <td>3</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.75</td>\n",
              "      <td>34.384843</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Apple_Cinnamon_Cheerios</td>\n",
              "      <td>G</td>\n",
              "      <td>C</td>\n",
              "      <td>110</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>180</td>\n",
              "      <td>1.5</td>\n",
              "      <td>10.5</td>\n",
              "      <td>10</td>\n",
              "      <td>70</td>\n",
              "      <td>25</td>\n",
              "      <td>1</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.75</td>\n",
              "      <td>29.509541</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                        name mfr type  calories  ...  shelf  weight  cups     rating\n",
              "0          100%_Natural_Bran   Q    C       120  ...      3     1.0  1.00  33.983679\n",
              "1                   All-Bran   K    C        70  ...      3     1.0  0.33  59.425505\n",
              "2  All-Bran_with_Extra_Fiber   K    C        50  ...      3     1.0  0.50  93.704912\n",
              "3             Almond_Delight   R    C       110  ...      3     1.0  0.75  34.384843\n",
              "4    Apple_Cinnamon_Cheerios   G    C       110  ...      1     1.0  0.75  29.509541\n",
              "\n",
              "[5 rows x 16 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
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      "cell_type": "markdown",
      "metadata": {
        "id": "143378e4"
      },
      "source": [
        "Now, we start answering the lab questions."
      ],
      "id": "143378e4"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e14fe988"
      },
      "source": [
        "#### **Q1.** Create a table with the 5-number summary of all the nutrients."
      ],
      "id": "e14fe988"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2QstPT6A4n2J"
      },
      "source": [
        "To solve Question 1, we use the describe() function from the Pandas library on the columns protein, fat, carbo, vitamins, sodium, sugars, potass and fiber. "
      ],
      "id": "2QstPT6A4n2J"
    },
    {
      "cell_type": "code",
      "metadata": {
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        },
        "id": "773dc5ca",
        "outputId": "d2d4e17b-dcf0-4021-95c8-d37c08ccbe97"
      },
      "source": [
        "# selecting only the nutrients and displaying the five number summary\n",
        "df[['protein', 'fat', 'carbo', 'vitamins', 'sodium', 'sugars', 'potass', 'fiber']].describe()"
      ],
      "id": "773dc5ca",
      "execution_count": 4,
      "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>protein</th>\n",
              "      <th>fat</th>\n",
              "      <th>carbo</th>\n",
              "      <th>vitamins</th>\n",
              "      <th>sodium</th>\n",
              "      <th>sugars</th>\n",
              "      <th>potass</th>\n",
              "      <th>fiber</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>76.000000</td>\n",
              "      <td>76.000000</td>\n",
              "      <td>76.000000</td>\n",
              "      <td>76.000000</td>\n",
              "      <td>76.000000</td>\n",
              "      <td>76.000000</td>\n",
              "      <td>76.000000</td>\n",
              "      <td>76.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>2.526316</td>\n",
              "      <td>1.013158</td>\n",
              "      <td>14.723684</td>\n",
              "      <td>28.289474</td>\n",
              "      <td>160.065789</td>\n",
              "      <td>6.934211</td>\n",
              "      <td>93.657895</td>\n",
              "      <td>2.048684</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>1.089020</td>\n",
              "      <td>1.013159</td>\n",
              "      <td>4.160444</td>\n",
              "      <td>22.487813</td>\n",
              "      <td>84.318813</td>\n",
              "      <td>4.473136</td>\n",
              "      <td>68.502565</td>\n",
              "      <td>2.219038</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>-1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>-1.000000</td>\n",
              "      <td>-1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>2.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>12.000000</td>\n",
              "      <td>25.000000</td>\n",
              "      <td>132.500000</td>\n",
              "      <td>3.000000</td>\n",
              "      <td>40.000000</td>\n",
              "      <td>0.750000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>2.500000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>14.500000</td>\n",
              "      <td>25.000000</td>\n",
              "      <td>180.000000</td>\n",
              "      <td>7.000000</td>\n",
              "      <td>90.000000</td>\n",
              "      <td>1.750000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>3.000000</td>\n",
              "      <td>2.000000</td>\n",
              "      <td>17.000000</td>\n",
              "      <td>25.000000</td>\n",
              "      <td>212.500000</td>\n",
              "      <td>11.000000</td>\n",
              "      <td>120.000000</td>\n",
              "      <td>3.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>6.000000</td>\n",
              "      <td>5.000000</td>\n",
              "      <td>23.000000</td>\n",
              "      <td>100.000000</td>\n",
              "      <td>320.000000</td>\n",
              "      <td>15.000000</td>\n",
              "      <td>330.000000</td>\n",
              "      <td>14.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         protein        fat      carbo  ...     sugars      potass      fiber\n",
              "count  76.000000  76.000000  76.000000  ...  76.000000   76.000000  76.000000\n",
              "mean    2.526316   1.013158  14.723684  ...   6.934211   93.657895   2.048684\n",
              "std     1.089020   1.013159   4.160444  ...   4.473136   68.502565   2.219038\n",
              "min     1.000000   0.000000  -1.000000  ...  -1.000000   -1.000000   0.000000\n",
              "25%     2.000000   0.000000  12.000000  ...   3.000000   40.000000   0.750000\n",
              "50%     2.500000   1.000000  14.500000  ...   7.000000   90.000000   1.750000\n",
              "75%     3.000000   2.000000  17.000000  ...  11.000000  120.000000   3.000000\n",
              "max     6.000000   5.000000  23.000000  ...  15.000000  330.000000  14.000000\n",
              "\n",
              "[8 rows x 8 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MJXotHXW47pp"
      },
      "source": [
        "As we can see, the minimum values of carbo, sugars and potass is -1, which cannot be possible in a real-life scenario. This is caused by the presence of null values which are represented by -1 in our dataset. Hence, we must deal with them and then do our analysis."
      ],
      "id": "MJXotHXW47pp"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "49acf16b"
      },
      "source": [
        "#### **Q2.**  For each of the numeric attributes (proteins upto vitamins) , identify and replace all missing data(indicated with -1) with the arithmetic mean of the attribute."
      ],
      "id": "49acf16b"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ElGeE1hVaRVe"
      },
      "source": [
        "To solve Question 2, we use the mask() function from the Pandas library. This function first replaces -1 with NA and then fills them with the mean of the rest of the data using the mean() function from the Pandas library."
      ],
      "id": "ElGeE1hVaRVe"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "6ee5ab2d",
        "outputId": "e2adc45d-3577-4d2d-fd49-21f43660d157"
      },
      "source": [
        "# filling values -1 with mean\n",
        "df = df.mask(df==-1).fillna(df.mean())\n",
        "df.head()"
      ],
      "id": "6ee5ab2d",
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>name</th>\n",
              "      <th>mfr</th>\n",
              "      <th>type</th>\n",
              "      <th>calories</th>\n",
              "      <th>protein</th>\n",
              "      <th>fat</th>\n",
              "      <th>sodium</th>\n",
              "      <th>fiber</th>\n",
              "      <th>carbo</th>\n",
              "      <th>sugars</th>\n",
              "      <th>potass</th>\n",
              "      <th>vitamins</th>\n",
              "      <th>shelf</th>\n",
              "      <th>weight</th>\n",
              "      <th>cups</th>\n",
              "      <th>rating</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>100%_Natural_Bran</td>\n",
              "      <td>Q</td>\n",
              "      <td>C</td>\n",
              "      <td>120</td>\n",
              "      <td>3</td>\n",
              "      <td>5</td>\n",
              "      <td>15</td>\n",
              "      <td>2.0</td>\n",
              "      <td>8.0</td>\n",
              "      <td>8.0</td>\n",
              "      <td>135.000000</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>1.0</td>\n",
              "      <td>1.00</td>\n",
              "      <td>33.983679</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>All-Bran</td>\n",
              "      <td>K</td>\n",
              "      <td>C</td>\n",
              "      <td>70</td>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "      <td>260</td>\n",
              "      <td>9.0</td>\n",
              "      <td>7.0</td>\n",
              "      <td>5.0</td>\n",
              "      <td>320.000000</td>\n",
              "      <td>25</td>\n",
              "      <td>3</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.33</td>\n",
              "      <td>59.425505</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>All-Bran_with_Extra_Fiber</td>\n",
              "      <td>K</td>\n",
              "      <td>C</td>\n",
              "      <td>50</td>\n",
              "      <td>4</td>\n",
              "      <td>0</td>\n",
              "      <td>140</td>\n",
              "      <td>14.0</td>\n",
              "      <td>8.0</td>\n",
              "      <td>0.0</td>\n",
              "      <td>330.000000</td>\n",
              "      <td>25</td>\n",
              "      <td>3</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.50</td>\n",
              "      <td>93.704912</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Almond_Delight</td>\n",
              "      <td>R</td>\n",
              "      <td>C</td>\n",
              "      <td>110</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>200</td>\n",
              "      <td>1.0</td>\n",
              "      <td>14.0</td>\n",
              "      <td>8.0</td>\n",
              "      <td>93.657895</td>\n",
              "      <td>25</td>\n",
              "      <td>3</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.75</td>\n",
              "      <td>34.384843</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>Apple_Cinnamon_Cheerios</td>\n",
              "      <td>G</td>\n",
              "      <td>C</td>\n",
              "      <td>110</td>\n",
              "      <td>2</td>\n",
              "      <td>2</td>\n",
              "      <td>180</td>\n",
              "      <td>1.5</td>\n",
              "      <td>10.5</td>\n",
              "      <td>10.0</td>\n",
              "      <td>70.000000</td>\n",
              "      <td>25</td>\n",
              "      <td>1</td>\n",
              "      <td>1.0</td>\n",
              "      <td>0.75</td>\n",
              "      <td>29.509541</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                        name mfr type  calories  ...  shelf  weight  cups     rating\n",
              "0          100%_Natural_Bran   Q    C       120  ...      3     1.0  1.00  33.983679\n",
              "1                   All-Bran   K    C        70  ...      3     1.0  0.33  59.425505\n",
              "2  All-Bran_with_Extra_Fiber   K    C        50  ...      3     1.0  0.50  93.704912\n",
              "3             Almond_Delight   R    C       110  ...      3     1.0  0.75  34.384843\n",
              "4    Apple_Cinnamon_Cheerios   G    C       110  ...      1     1.0  0.75  29.509541\n",
              "\n",
              "[5 rows x 16 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "492de21f"
      },
      "source": [
        "#### **Q3.**  Create a table with the 5-number summary of all the numeric attributes after treating missing values. Do you think the strategy used in dealing with missing values was effective? "
      ],
      "id": "492de21f"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PE8eQN3oaoY2"
      },
      "source": [
        "To solve Question 3, we use the describe() function from the Pandas library on the columns protein, fat, carbo, vitamins, sodium, sugars, potass and fiber. "
      ],
      "id": "PE8eQN3oaoY2"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "id": "c4eb2719",
        "outputId": "d51c0387-3a02-4795-a1cf-6bbae21dee4c"
      },
      "source": [
        "# selecting only the numeric datatypes and displaying the five number summary\n",
        "df[['protein', 'fat', 'carbo', 'vitamins', 'sodium', 'sugars', 'potass', 'fiber']].describe()"
      ],
      "id": "c4eb2719",
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<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>protein</th>\n",
              "      <th>fat</th>\n",
              "      <th>carbo</th>\n",
              "      <th>vitamins</th>\n",
              "      <th>sodium</th>\n",
              "      <th>sugars</th>\n",
              "      <th>potass</th>\n",
              "      <th>fiber</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>76.000000</td>\n",
              "      <td>76.000000</td>\n",
              "      <td>76.000000</td>\n",
              "      <td>76.000000</td>\n",
              "      <td>76.000000</td>\n",
              "      <td>76.000000</td>\n",
              "      <td>76.000000</td>\n",
              "      <td>76.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>2.526316</td>\n",
              "      <td>1.013158</td>\n",
              "      <td>14.930575</td>\n",
              "      <td>28.289474</td>\n",
              "      <td>160.065789</td>\n",
              "      <td>7.038608</td>\n",
              "      <td>96.148892</td>\n",
              "      <td>2.048684</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>1.089020</td>\n",
              "      <td>1.013159</td>\n",
              "      <td>3.737575</td>\n",
              "      <td>22.487813</td>\n",
              "      <td>84.318813</td>\n",
              "      <td>4.377048</td>\n",
              "      <td>66.688658</td>\n",
              "      <td>2.219038</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>7.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>15.000000</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>2.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>12.000000</td>\n",
              "      <td>25.000000</td>\n",
              "      <td>132.500000</td>\n",
              "      <td>3.000000</td>\n",
              "      <td>43.750000</td>\n",
              "      <td>0.750000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>2.500000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>14.861842</td>\n",
              "      <td>25.000000</td>\n",
              "      <td>180.000000</td>\n",
              "      <td>7.000000</td>\n",
              "      <td>90.000000</td>\n",
              "      <td>1.750000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>3.000000</td>\n",
              "      <td>2.000000</td>\n",
              "      <td>17.000000</td>\n",
              "      <td>25.000000</td>\n",
              "      <td>212.500000</td>\n",
              "      <td>11.000000</td>\n",
              "      <td>120.000000</td>\n",
              "      <td>3.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>6.000000</td>\n",
              "      <td>5.000000</td>\n",
              "      <td>23.000000</td>\n",
              "      <td>100.000000</td>\n",
              "      <td>320.000000</td>\n",
              "      <td>15.000000</td>\n",
              "      <td>330.000000</td>\n",
              "      <td>14.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         protein        fat      carbo  ...     sugars      potass      fiber\n",
              "count  76.000000  76.000000  76.000000  ...  76.000000   76.000000  76.000000\n",
              "mean    2.526316   1.013158  14.930575  ...   7.038608   96.148892   2.048684\n",
              "std     1.089020   1.013159   3.737575  ...   4.377048   66.688658   2.219038\n",
              "min     1.000000   0.000000   7.000000  ...   0.000000   15.000000   0.000000\n",
              "25%     2.000000   0.000000  12.000000  ...   3.000000   43.750000   0.750000\n",
              "50%     2.500000   1.000000  14.861842  ...   7.000000   90.000000   1.750000\n",
              "75%     3.000000   2.000000  17.000000  ...  11.000000  120.000000   3.000000\n",
              "max     6.000000   5.000000  23.000000  ...  15.000000  330.000000  14.000000\n",
              "\n",
              "[8 rows x 8 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0AinG7-7a2YT"
      },
      "source": [
        "As we can see, the minimum values of carbo, sugars and potass are now 7, 0, and 15 respectively. This is possible in real life. Hence, the strategy in dealing with the missing values was effective. However, we see that the maximum values of the columns protein, vitamins, potass and fiber and the minimum values of the columns vitamins and sodium are not on the scale of the Q1, Q2, and Q3 values of the respective columns. This indicates the presence of outliers in the data. Hence, we must deal with them and do our analysis."
      ],
      "id": "0AinG7-7a2YT"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "03924e13"
      },
      "source": [
        "#### **Q4.** For each of the numeric attributes (proteins upto vitamins), identify and replace all noisy data with the median of attribute. "
      ],
      "id": "03924e13"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dWZ8pxXUdyKS"
      },
      "source": [
        "To solve Question 5, we loop over the nutrient columns and find out the Q1, Q2, Q3 and IQR values from the data columns using the quantile() and median() functions from the NumPy and Pandas libraries and then calculate the lower and upper bounds. After that, we replace the outliers, which are outside the lower and upper bounds, with the median of the data using the where() function from the NumPy library."
      ],
      "id": "dWZ8pxXUdyKS"
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7820a843"
      },
      "source": [
        "# replacing the outliers with median\n",
        "for column in df[['protein', 'fat', 'carbo', 'vitamins', 'sodium', 'sugars', 'potass', 'fiber']]:\n",
        "    \n",
        "    q1 = np.quantile(df[column], 0.25)\n",
        "    q3 = np.quantile(df[column], 0.75)\n",
        "    iqr = q3 - q1\n",
        "    \n",
        "    upper_bound = q3 + 1.5*iqr\n",
        "    lower_bound = q1 - 1.5*iqr\n",
        "    \n",
        "    q2 = df[column].median()\n",
        "    \n",
        "    df[column] = np.where(df[column]>upper_bound, q2, df[column])\n",
        "    df[column] = np.where(df[column]<lower_bound, q2, df[column])"
      ],
      "id": "7820a843",
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e3e57878"
      },
      "source": [
        "#### **Q5.** Create a table with the 5-number summary of all the numeric attributes after treating noisy values. Do you think the strategy used in dealing with noisy values was  effective?"
      ],
      "id": "e3e57878"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0YPK6ygR3P0Z"
      },
      "source": [
        "To solve Question 5, we use the describe() function from the Pandas library on the columns protein, fat, carbo, vitamins, sodium, sugars, potass and fiber."
      ],
      "id": "0YPK6ygR3P0Z"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "id": "17d9990d",
        "outputId": "a772c61c-dbbf-4870-b4b2-f6c6061e7c7f"
      },
      "source": [
        "# selecting only the numeric datatypes and displaying the five number summary\n",
        "df[['protein', 'fat', 'carbo', 'vitamins', 'sodium', 'sugars', 'potass', 'fiber']].describe()"
      ],
      "id": "17d9990d",
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<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",
              "        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>protein</th>\n",
              "      <th>fat</th>\n",
              "      <th>carbo</th>\n",
              "      <th>vitamins</th>\n",
              "      <th>sodium</th>\n",
              "      <th>sugars</th>\n",
              "      <th>potass</th>\n",
              "      <th>fiber</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>count</th>\n",
              "      <td>76.000000</td>\n",
              "      <td>76.000000</td>\n",
              "      <td>76.000000</td>\n",
              "      <td>76.0</td>\n",
              "      <td>76.000000</td>\n",
              "      <td>76.000000</td>\n",
              "      <td>76.000000</td>\n",
              "      <td>76.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>2.401316</td>\n",
              "      <td>1.013158</td>\n",
              "      <td>14.930575</td>\n",
              "      <td>25.0</td>\n",
              "      <td>181.381579</td>\n",
              "      <td>7.038608</td>\n",
              "      <td>85.754155</td>\n",
              "      <td>1.792105</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>0.875670</td>\n",
              "      <td>1.013159</td>\n",
              "      <td>3.737575</td>\n",
              "      <td>0.0</td>\n",
              "      <td>60.186370</td>\n",
              "      <td>4.377048</td>\n",
              "      <td>48.049515</td>\n",
              "      <td>1.520220</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>7.000000</td>\n",
              "      <td>25.0</td>\n",
              "      <td>15.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>15.000000</td>\n",
              "      <td>0.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>2.000000</td>\n",
              "      <td>0.000000</td>\n",
              "      <td>12.000000</td>\n",
              "      <td>25.0</td>\n",
              "      <td>147.500000</td>\n",
              "      <td>3.000000</td>\n",
              "      <td>43.750000</td>\n",
              "      <td>0.750000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>2.250000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>14.861842</td>\n",
              "      <td>25.0</td>\n",
              "      <td>180.000000</td>\n",
              "      <td>7.000000</td>\n",
              "      <td>90.000000</td>\n",
              "      <td>1.625000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>3.000000</td>\n",
              "      <td>2.000000</td>\n",
              "      <td>17.000000</td>\n",
              "      <td>25.0</td>\n",
              "      <td>212.500000</td>\n",
              "      <td>11.000000</td>\n",
              "      <td>110.000000</td>\n",
              "      <td>3.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>4.000000</td>\n",
              "      <td>5.000000</td>\n",
              "      <td>23.000000</td>\n",
              "      <td>25.0</td>\n",
              "      <td>320.000000</td>\n",
              "      <td>15.000000</td>\n",
              "      <td>230.000000</td>\n",
              "      <td>6.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "         protein        fat      carbo  ...     sugars      potass      fiber\n",
              "count  76.000000  76.000000  76.000000  ...  76.000000   76.000000  76.000000\n",
              "mean    2.401316   1.013158  14.930575  ...   7.038608   85.754155   1.792105\n",
              "std     0.875670   1.013159   3.737575  ...   4.377048   48.049515   1.520220\n",
              "min     1.000000   0.000000   7.000000  ...   0.000000   15.000000   0.000000\n",
              "25%     2.000000   0.000000  12.000000  ...   3.000000   43.750000   0.750000\n",
              "50%     2.250000   1.000000  14.861842  ...   7.000000   90.000000   1.625000\n",
              "75%     3.000000   2.000000  17.000000  ...  11.000000  110.000000   3.000000\n",
              "max     4.000000   5.000000  23.000000  ...  15.000000  230.000000   6.000000\n",
              "\n",
              "[8 rows x 8 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "zBAN2oz73Rp6"
      },
      "source": [
        "As we can see, the minimum and maximum values are now within the scale of the Q1, Q2, and Q3 values of all the columns. Hence, the strategy of dealing with outliers was effective."
      ],
      "id": "zBAN2oz73Rp6"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "33iqL7aT3i4A"
      },
      "source": [
        "Hence, the data has now been pre-processed - we have replaced the missing values with the mean of the data and the outliers with the median of the data. Now, we will proceed with the analysis."
      ],
      "id": "33iqL7aT3i4A"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "34576997"
      },
      "source": [
        "#### **Q6.** Cross tabulate the type of cereal (hot vs cold) against the manufacturer"
      ],
      "id": "34576997"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "H9Hnhcd67Yy3"
      },
      "source": [
        "To solve Question 6, we use the crosstab() function from the Pandas library and pass the columns mfr and type."
      ],
      "id": "H9Hnhcd67Yy3"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 300
        },
        "id": "41be4732",
        "outputId": "9c210a1a-84ec-4082-a039-cdef5d3b89c9"
      },
      "source": [
        "# cross-tabulation\n",
        "pd.crosstab(df.mfr, df.type)"
      ],
      "id": "41be4732",
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
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              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
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              "    .dataframe thead th {\n",
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              "    }\n",
              "</style>\n",
              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th>type</th>\n",
              "      <th>C</th>\n",
              "      <th>H</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mfr</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>A</th>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>G</th>\n",
              "      <td>22</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>K</th>\n",
              "      <td>23</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>N</th>\n",
              "      <td>4</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>P</th>\n",
              "      <td>9</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Q</th>\n",
              "      <td>7</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>R</th>\n",
              "      <td>8</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "type   C  H\n",
              "mfr        \n",
              "A      0  1\n",
              "G     22  0\n",
              "K     23  0\n",
              "N      4  1\n",
              "P      9  0\n",
              "Q      7  1\n",
              "R      8  0"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xchYCIjK7ku6"
      },
      "source": [
        "As we can see, there are:\n",
        "*   0 cold and 1 hot cereals that American Home Food Products sells.\n",
        "*   22 cold and 0 hot cereals that General Mills sells.\n",
        "*   23 cold and 0 hot cereals that Kelloggs sells.\n",
        "*   4 cold and 1 hot cereals that Nabisco sells.\n",
        "*   9 cold and 0 hot cereals that Post sells.\n",
        "*   7 cold and 1 hot cereals that Quaker Oats sells.\n",
        "*   8 cold and 0 hot cereals that Ralston Purina sells."
      ],
      "id": "xchYCIjK7ku6"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c132faf1"
      },
      "source": [
        "#### **Q7.** Which is the cereal with the best rating, worst rating?"
      ],
      "id": "c132faf1"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-RUrrd7W8Tkb"
      },
      "source": [
        "To solve part a of Question 7, we filter the dataframe with the condition that the rating observation matches the maximum value of the rating. In this filtered dataframe, we check the observation in the name column. "
      ],
      "id": "-RUrrd7W8Tkb"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "218484b8",
        "outputId": "496b82a2-f425-4e1c-a97a-f81e18ef6bc1"
      },
      "source": [
        "# best rating\n",
        "df[df.rating==df.rating.max()].name"
      ],
      "id": "218484b8",
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2    All-Bran_with_Extra_Fiber\n",
              "Name: name, dtype: object"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "P3LXIRV-8hH3"
      },
      "source": [
        "As we can see, All-Bran_with_Extra_Fiber has the best rating."
      ],
      "id": "P3LXIRV-8hH3"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Fr41Y7wL806W"
      },
      "source": [
        "To solve part b of Question 7, we filter the dataframe with the condition that the rating observation matches the minimum value of the rating. In this filtered dataframe, we check the observation in the name column. "
      ],
      "id": "Fr41Y7wL806W"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "f68de616",
        "outputId": "20943d49-13b8-44d1-8b28-6e3c5b350320"
      },
      "source": [
        "# worst rating\n",
        "df[df.rating==df.rating.min()].name"
      ],
      "id": "f68de616",
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "9    Cap'n'Crunch\n",
              "Name: name, dtype: object"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GDGMyZYC8461"
      },
      "source": [
        "As we can see, Cap'n'Crunch has the worst rating."
      ],
      "id": "GDGMyZYC8461"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2cf8f8cb"
      },
      "source": [
        "#### **Q8.** Plot a side-by-side boxplot comparing the consumer rating of hot vs. cold cereals. "
      ],
      "id": "2cf8f8cb"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "m59C8IBC9OED"
      },
      "source": [
        "To solve Question 8, we use the boxplot() function from the Seaborn library and pass the values type to be plotted on the x-axis and rating to be plotted on the y-axis."
      ],
      "id": "m59C8IBC9OED"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "239146df",
        "outputId": "080bb4e5-b853-4eee-e102-ed6df300a31d"
      },
      "source": [
        "# boxplot of consumer rating vs type\n",
        "sns.boxplot(x='type', y='rating', data=df)"
      ],
      "id": "239146df",
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fe0138ee190>"
            ]
          },
          "metadata": {},
          "execution_count": 12
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "36bGk_uM9irG"
      },
      "source": [
        "As we can see, the boxplot() function plots boxplots for each cereal type in different colours to make it easily distinguishable. The cold type cereal has one outlier in the higher range and is right skewed with a wider distribution. The hot type cereal has no outliers and has a more or less normal distribution with a narrower distribution."
      ],
      "id": "36bGk_uM9irG"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c9749343"
      },
      "source": [
        "#### **Q9.** Is there a relation between sugars, calories, carbs, and fat?"
      ],
      "id": "c9749343"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Mr7qNhX3bv6w"
      },
      "source": [
        "To solve Question 9, use the pearson's correlation, as all the variables are continuous. To do this, we use the corr() function from the Pandas library."
      ],
      "id": "Mr7qNhX3bv6w"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 174
        },
        "id": "1080cfd3",
        "outputId": "9ee7b9a3-ce3b-425a-c3c8-c4ea80e8cc2a"
      },
      "source": [
        "# pearson's correlation value\n",
        "corr = df[['sugars', 'calories', 'carbo', 'fat']].corr()\n",
        "corr"
      ],
      "id": "1080cfd3",
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "\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>sugars</th>\n",
              "      <th>calories</th>\n",
              "      <th>carbo</th>\n",
              "      <th>fat</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>sugars</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.574304</td>\n",
              "      <td>-0.501056</td>\n",
              "      <td>0.300349</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>calories</th>\n",
              "      <td>0.574304</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.207615</td>\n",
              "      <td>0.510630</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>carbo</th>\n",
              "      <td>-0.501056</td>\n",
              "      <td>0.207615</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.312341</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>fat</th>\n",
              "      <td>0.300349</td>\n",
              "      <td>0.510630</td>\n",
              "      <td>-0.312341</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "            sugars  calories     carbo       fat\n",
              "sugars    1.000000  0.574304 -0.501056  0.300349\n",
              "calories  0.574304  1.000000  0.207615  0.510630\n",
              "carbo    -0.501056  0.207615  1.000000 -0.312341\n",
              "fat       0.300349  0.510630 -0.312341  1.000000"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "n2xoMKgEb9Z3"
      },
      "source": [
        "As we can see: \n",
        "*   The variables sugars and calories have a moderate degree of positive linear correlation, having correlation coefficient 0.57.\n",
        "*   The variables sugars and carbo have a moderate degree of negative linear correlation, having correlation coefficient -0.50.\n",
        "*   The variables sugars and fat have only the possibility of positive linear correlation, having correlation coefficient 0.30.\n",
        "*   The variables calories and carbo have only the possibility of positive linear correlation, having correlation coefficient 0.21.\n",
        "*   The variables calories and fat have a moderate degree of positive linear correlation, having correlation coefficient 0.51.\n",
        "*   The variables carbo and fat have only the possibility of negative linear correlation, having correlation coefficient -0.31."
      ],
      "id": "n2xoMKgEb9Z3"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2PJazukSvkY_"
      },
      "source": [
        "To visualize the correlation, we use the heatmap() function from the Seaborn library."
      ],
      "id": "2PJazukSvkY_"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 286
        },
        "id": "6ab99ce9",
        "outputId": "7f0808a6-375a-42c9-cfdc-8e42d83aa936"
      },
      "source": [
        "# visualizing\n",
        "sns.heatmap(corr, annot=True)"
      ],
      "id": "6ab99ce9",
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fe012cf4290>"
            ]
          },
          "metadata": {},
          "execution_count": 14
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "sa2mnXL1diat"
      },
      "source": [
        "As we can see: \n",
        "*   The variables sugars and calories have a moderate degree of positive linear correlation, having correlation coefficient 0.57.\n",
        "*   The variables sugars and carbo have a moderate degree of negative linear correlation, having correlation coefficient -0.50.\n",
        "*   The variables sugars and fat have only the possibility of positive linear correlation, having correlation coefficient 0.30.\n",
        "*   The variables calories and carbo have only the possibility of positive linear correlation, having correlation coefficient 0.21.\n",
        "*   The variables calories and fat have a moderate degree of positive linear correlation, having correlation coefficient 0.51.\n",
        "*   The variables carbo and fat have only the possibility of negative linear correlation, having correlation coefficient -0.31."
      ],
      "id": "sa2mnXL1diat"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ye_u4NNzvt2B"
      },
      "source": [
        "To visualize the correlation, we also use the pairplot() function from the Seaborn library."
      ],
      "id": "Ye_u4NNzvt2B"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 743
        },
        "id": "xhYYo9HFdNcN",
        "outputId": "809dd920-e9a2-4444-dca8-a3771eac4cc0"
      },
      "source": [
        "# visualization\n",
        "sns.pairplot(df[['sugars', 'calories', 'carbo', 'fat']])"
      ],
      "id": "xhYYo9HFdNcN",
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<seaborn.axisgrid.PairGrid at 0x7fe009fa4790>"
            ]
          },
          "metadata": {},
          "execution_count": 15
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x720 with 20 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "xCtbTb3zdpo7"
      },
      "source": [
        "As we can see: \n",
        "*   The variables sugars and calories have a moderate degree of positive linear correlation.\n",
        "*   The variables sugars and carbo have a moderate degree of negative linear correlation.\n",
        "*   The variables sugars and fat have only the possibility of positive linear correlation.\n",
        "*   The variables calories and carbo have only the possibility of positive linear correlation.\n",
        "*   The variables calories and fat have a moderate degree of positive linear correlation.\n",
        "*   The variables carbo and fat have only the possibility of negative linear correlation."
      ],
      "id": "xCtbTb3zdpo7"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2b07efea"
      },
      "source": [
        "#### **Q10.** Which manufacturers produce cereal with highest calories?"
      ],
      "id": "2b07efea"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OLTwx7EJd4Wn"
      },
      "source": [
        "To solve Question 10, we filter the dataframe with the condition that the calories observation matches the maximum value of calories. In this filtered dataframe, we check the observation in the mfr column."
      ],
      "id": "OLTwx7EJd4Wn"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "75a99a41",
        "outputId": "74634d62-7e93-407a-de45-3c9c58df98d3"
      },
      "source": [
        "# manufacturers with highest calories\n",
        "df[df.calories==df.calories.max()].mfr"
      ],
      "id": "75a99a41",
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "45    K\n",
              "Name: mfr, dtype: object"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OkjNz9E_eYJt"
      },
      "source": [
        "As we can see, Kelloggs produces the cereal with the highest calories."
      ],
      "id": "OkjNz9E_eYJt"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "38d8d1fa"
      },
      "source": [
        "#### **Q11.** Use correlation tests and visualization to identify if the two variables calories and consumer rating associated ?"
      ],
      "id": "38d8d1fa"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "04EDmRJAsgiM"
      },
      "source": [
        "To solve Question 11, we use the ANOVA test, since one variable - calories is discrete and one variable - rating is continuous. Here, the Null Hypothesis is that the ratings are not affected by the calories (sample means are equal) and the Alternate Hypothesis is that the ratings are affected by the calories (sample means are not equal). To do so, we use the f_oneway() function from the SciPy Stats library and group the ratings by calories."
      ],
      "id": "04EDmRJAsgiM"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8dccde42",
        "outputId": "6feaa891-fc71-4782-99d5-00de93139761"
      },
      "source": [
        "# anova test\n",
        "F, p = stats.f_oneway(df[df.calories==50].rating, df[df.calories==70].rating, df[df.calories==80].rating, df[df.calories==90].rating, df[df.calories==100].rating, df[df.calories==110].rating, df[df.calories==120].rating, df[df.calories==130].rating, df[df.calories==140].rating, df[df.calories==150].rating, df[df.calories==160].rating)\n",
        "print('F-critical: 2.79')\n",
        "print('F-calculated: ', F)"
      ],
      "id": "8dccde42",
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "F-critical: 2.79\n",
            "F-calculated:  11.448496433877295\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8PkC7nI9srSL"
      },
      "source": [
        "As we can see, the calculate F-statistic value is greater than the critical F-statistic value for the dof. Hence, we reject the Null Hypothesis and accept the Alternate Hypothesis which states that the variables calories and rating are associated."
      ],
      "id": "8PkC7nI9srSL"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8JKH6sVeuRwj"
      },
      "source": [
        "To visualize the relation, we find the mean ratings of all the values of calories and then make a scatterplot using the scatterplot() function from the Seaborn library."
      ],
      "id": "8JKH6sVeuRwj"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 282
        },
        "id": "36a70a6f",
        "outputId": "1ca5456e-f79d-4832-ab94-553a4c60d1d0"
      },
      "source": [
        "# visualization\n",
        "ratings_mean = list(df.groupby(by='calories').rating.mean())\n",
        "calories = list(df.calories.unique())\n",
        "calories.sort()\n",
        "\n",
        "sns.scatterplot(x=calories, y=ratings_mean)"
      ],
      "id": "36a70a6f",
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fe009867050>"
            ]
          },
          "metadata": {},
          "execution_count": 18
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eoQRTAJZub-a"
      },
      "source": [
        "As we can see, as the calories increase, the ratings decrease, indicating a negative correlation."
      ],
      "id": "eoQRTAJZub-a"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "39a3e5b3"
      },
      "source": [
        "#### **Q12.** Use correlation tests and visualization to identify if the two variables shelf and calories associated?"
      ],
      "id": "39a3e5b3"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VzAa4SV9fY4w"
      },
      "source": [
        "To solve Question 12, we use the Chi-Squared Test, since the variables calories and shelf are discrete. Here the Null Hypothesis is that the variables are independent, and the Alternate Hypothesis is that they are dependent.\n",
        "\n",
        "To do this, first we form a contingency table using the crosstab() function from the Pandas library."
      ],
      "id": "VzAa4SV9fY4w"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 174
        },
        "id": "e1145e67",
        "outputId": "1620a3f5-e493-4178-9521-b579ee97849e"
      },
      "source": [
        "# chi-square test\n",
        "contingency = pd.crosstab(df.shelf, df.calories)\n",
        "contingency"
      ],
      "id": "e1145e67",
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<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>calories</th>\n",
              "      <th>50</th>\n",
              "      <th>70</th>\n",
              "      <th>80</th>\n",
              "      <th>90</th>\n",
              "      <th>100</th>\n",
              "      <th>110</th>\n",
              "      <th>120</th>\n",
              "      <th>130</th>\n",
              "      <th>140</th>\n",
              "      <th>150</th>\n",
              "      <th>160</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>shelf</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>3</td>\n",
              "      <td>6</td>\n",
              "      <td>10</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>1</td>\n",
              "      <td>4</td>\n",
              "      <td>11</td>\n",
              "      <td>5</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "      <td>0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3</td>\n",
              "      <td>1</td>\n",
              "      <td>0</td>\n",
              "      <td>3</td>\n",
              "      <td>7</td>\n",
              "      <td>8</td>\n",
              "      <td>5</td>\n",
              "      <td>2</td>\n",
              "      <td>3</td>\n",
              "      <td>2</td>\n",
              "      <td>1</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "calories  50   70   80   90   100  110  120  130  140  150  160\n",
              "shelf                                                          \n",
              "1           0    0    1    3    6   10    0    0    0    0    0\n",
              "2           0    0    0    1    4   11    5    0    0    0    0\n",
              "3           3    1    0    3    7    8    5    2    3    2    1"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B8YmYWq_h7Mx"
      },
      "source": [
        "As we can see, on shelf:    \n",
        "*  1, there are 1 80 cal, 3 90 cal, 6 100 cal, and 10 110 cal cereals.\n",
        "*  2, there are 1 90 cal, 4 100 cal, 11 110 cal, and 5 120 cal cereals.\n",
        "*  3, there are 3 50 cal, 1 70 cal, 3 90 cal, 7 100 cal, 8 110 cal, 5 120 cal, 2 130 cal, 3 140 cal, 2 150 cal, and 1 160 cal cereals."
      ],
      "id": "B8YmYWq_h7Mx"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 296
        },
        "id": "a4d59d25",
        "outputId": "52448884-492a-4ccf-c1b1-831b8c71872a"
      },
      "source": [
        "# visualization\n",
        "sns.heatmap(contingency, annot=True)"
      ],
      "id": "a4d59d25",
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7fe00977e9d0>"
            ]
          },
          "metadata": {},
          "execution_count": 20
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 2 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4kWW59kDidg1"
      },
      "source": [
        "As we can see, on shelf:    \n",
        "*  1, there are 1 80 cal, 3 90 cal, 6 100 cal, and 10 110 cal cereals.\n",
        "*  2, there are 1 90 cal, 4 100 cal, 11 110 cal, and 5 120 cal cereals.\n",
        "*  3, there are 3 50 cal, 1 70 cal, 3 90 cal, 7 100 cal, 8 110 cal, 5 120 cal, 2 130 cal, 3 140 cal, 2 150 cal, and 1 160 cal cereals."
      ],
      "id": "4kWW59kDidg1"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kCl0_RuSifcg"
      },
      "source": [
        "Next, we perform the Chi-Squared Test using the chi2_contingency() function from the SciPy Stats library. "
      ],
      "id": "kCl0_RuSifcg"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2f682e91",
        "outputId": "44054a3d-0b1d-4a73-ef59-81b7349d5682"
      },
      "source": [
        "# chi-square test\n",
        "c, p, dof, expected = stats.chi2_contingency(contingency)\n",
        "print('p-value: ', p)"
      ],
      "id": "2f682e91",
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "p-value:  0.12876294513924283\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UaRx2rLoieo3"
      },
      "source": [
        "Since the p-value returned is more than 0.05, we reject the Null Hypothesis, and accept the Alternate Hypothesis that states that the variables shelf and calories are related."
      ],
      "id": "UaRx2rLoieo3"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "58915197"
      },
      "source": [
        "#### **Q13.** Is there a relation between manufacturer and rating?"
      ],
      "id": "58915197"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "no_ehiWyi-HX"
      },
      "source": [
        "To solve Question 13, we use the ANOVA test, since one variable - manufacturer is categorical and one variable - rating is continuous. Here, the Null Hypothesis is that the ratings are not affected by the manufacturer (sample means are equal) and the Alternate Hypothesis is that the ratings are affected by the manufacturer (sample means are not equal). To do so, we use the f_oneway() function from the SciPy Stats library and group the ratings by manufacturer."
      ],
      "id": "no_ehiWyi-HX"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "a257427d",
        "outputId": "49bac82f-6d7d-491b-9495-6da7f41244e0"
      },
      "source": [
        "# anova test\n",
        "F, p = stats.f_oneway(df[df.mfr=='A'].rating, df[df.mfr=='G'].rating, df[df.mfr=='K'].rating, df[df.mfr=='N'].rating, df[df.mfr=='P'].rating, df[df.mfr=='Q'].rating, df[df.mfr=='R'].rating)\n",
        "print('F-critical: 2.22')\n",
        "print('F-calculated: ', F)"
      ],
      "id": "a257427d",
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "F-critical: 2.22\n",
            "F-calculated:  5.892057149371146\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lEaPCIySkNjn"
      },
      "source": [
        "As we can see, the calculate F-statistic value is greater than the critical F-statistic value for the dof. Hence, we reject the Null Hypothesis and accept the Alternate Hypothesis which states that the variables manufacturer and rating are associated."
      ],
      "id": "lEaPCIySkNjn"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "be837cfa"
      },
      "source": [
        "#### **Q14.** Which nutrients are essential for a good rating for a cereal?"
      ],
      "id": "be837cfa"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "qLw5ZCqIlMa4"
      },
      "source": [
        "To solve Question 14, we calculate the Pearson's correlation for the variables as all of them are continuous. To do this, we use the corr() function from the Pandas library."
      ],
      "id": "qLw5ZCqIlMa4"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 331
        },
        "id": "441dc205",
        "outputId": "6b4c30c5-8655-4265-80fa-16af5f1164aa"
      },
      "source": [
        "# pearson's correlation\n",
        "corr = df[['protein', 'fat', 'carbo', 'vitamins', 'sodium', 'sugars', 'potass', 'fiber', 'rating']].corr()\n",
        "corr"
      ],
      "id": "441dc205",
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<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>protein</th>\n",
              "      <th>fat</th>\n",
              "      <th>carbo</th>\n",
              "      <th>vitamins</th>\n",
              "      <th>sodium</th>\n",
              "      <th>sugars</th>\n",
              "      <th>potass</th>\n",
              "      <th>fiber</th>\n",
              "      <th>rating</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>protein</th>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.226913</td>\n",
              "      <td>-0.016380</td>\n",
              "      <td>NaN</td>\n",
              "      <td>-0.120710</td>\n",
              "      <td>-0.226848</td>\n",
              "      <td>0.671223</td>\n",
              "      <td>0.587843</td>\n",
              "      <td>0.466606</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>fat</th>\n",
              "      <td>0.226913</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.312341</td>\n",
              "      <td>NaN</td>\n",
              "      <td>-0.248478</td>\n",
              "      <td>0.300349</td>\n",
              "      <td>0.357217</td>\n",
              "      <td>0.135546</td>\n",
              "      <td>-0.418439</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>carbo</th>\n",
              "      <td>-0.016380</td>\n",
              "      <td>-0.312341</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>NaN</td>\n",
              "      <td>0.444677</td>\n",
              "      <td>-0.501056</td>\n",
              "      <td>-0.095005</td>\n",
              "      <td>-0.110386</td>\n",
              "      <td>0.160481</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>vitamins</th>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "      <td>NaN</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sodium</th>\n",
              "      <td>-0.120710</td>\n",
              "      <td>-0.248478</td>\n",
              "      <td>0.444677</td>\n",
              "      <td>NaN</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>-0.288444</td>\n",
              "      <td>-0.157435</td>\n",
              "      <td>-0.124328</td>\n",
              "      <td>-0.050622</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sugars</th>\n",
              "      <td>-0.226848</td>\n",
              "      <td>0.300349</td>\n",
              "      <td>-0.501056</td>\n",
              "      <td>NaN</td>\n",
              "      <td>-0.288444</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.030380</td>\n",
              "      <td>-0.000373</td>\n",
              "      <td>-0.774390</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>potass</th>\n",
              "      <td>0.671223</td>\n",
              "      <td>0.357217</td>\n",
              "      <td>-0.095005</td>\n",
              "      <td>NaN</td>\n",
              "      <td>-0.157435</td>\n",
              "      <td>0.030380</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.792123</td>\n",
              "      <td>0.209746</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>fiber</th>\n",
              "      <td>0.587843</td>\n",
              "      <td>0.135546</td>\n",
              "      <td>-0.110386</td>\n",
              "      <td>NaN</td>\n",
              "      <td>-0.124328</td>\n",
              "      <td>-0.000373</td>\n",
              "      <td>0.792123</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.335319</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>rating</th>\n",
              "      <td>0.466606</td>\n",
              "      <td>-0.418439</td>\n",
              "      <td>0.160481</td>\n",
              "      <td>NaN</td>\n",
              "      <td>-0.050622</td>\n",
              "      <td>-0.774390</td>\n",
              "      <td>0.209746</td>\n",
              "      <td>0.335319</td>\n",
              "      <td>1.000000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "           protein       fat     carbo  ...    potass     fiber    rating\n",
              "protein   1.000000  0.226913 -0.016380  ...  0.671223  0.587843  0.466606\n",
              "fat       0.226913  1.000000 -0.312341  ...  0.357217  0.135546 -0.418439\n",
              "carbo    -0.016380 -0.312341  1.000000  ... -0.095005 -0.110386  0.160481\n",
              "vitamins       NaN       NaN       NaN  ...       NaN       NaN       NaN\n",
              "sodium   -0.120710 -0.248478  0.444677  ... -0.157435 -0.124328 -0.050622\n",
              "sugars   -0.226848  0.300349 -0.501056  ...  0.030380 -0.000373 -0.774390\n",
              "potass    0.671223  0.357217 -0.095005  ...  1.000000  0.792123  0.209746\n",
              "fiber     0.587843  0.135546 -0.110386  ...  0.792123  1.000000  0.335319\n",
              "rating    0.466606 -0.418439  0.160481  ...  0.209746  0.335319  1.000000\n",
              "\n",
              "[9 rows x 9 columns]"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rtQMpQALl9Hc"
      },
      "source": [
        "As we can see, the top 3 nutrients that affect the rating are sugars, protein and fat, having correlation coefficients -0.77 (high negative linear correlation), 0.46 (moderate positive linear correlation), and -0.41 (moderate negative linear correlation). The variable vitamin returns a NaN value, since after preprocessing, all the values turn to 25."
      ],
      "id": "rtQMpQALl9Hc"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "41bcce34"
      },
      "source": [
        "#### **Q15.** Design a Linear regression model to predict the rating of a cereal based on top 3 related nutrients. Tabulate the accuracy of the model using a 70 ,30 split"
      ],
      "id": "41bcce34"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HNRQusYQmhVX"
      },
      "source": [
        "To solve Question 15, we first split the data into dependent and independent variables x and y. x has the variables protein, fat, and sugars (from the previous question), and y has the variable rating."
      ],
      "id": "HNRQusYQmhVX"
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "84ebbefa"
      },
      "source": [
        "# splitting dataset into dependent and independent variables\n",
        "x = df[['protein', 'fat', 'sugars']]\n",
        "y = df['rating']"
      ],
      "id": "84ebbefa",
      "execution_count": 24,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nAKSCQj3mz2U"
      },
      "source": [
        "Next, we split the dataset into training and testing sets. To do this, we use the train_test_split() method from the sklearn.model_selection library. Here we, fix the training size to be 0.7 and random_state to be 109 to maintain consistency."
      ],
      "id": "nAKSCQj3mz2U"
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0b9de851"
      },
      "source": [
        "# splitting dataset into training and testing sets\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=109)"
      ],
      "id": "0b9de851",
      "execution_count": 25,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HCT2G2V4nLLy"
      },
      "source": [
        "Finally, we use the LinearRegression method from the sklearn.linear_model library to design a linear regression model by training it on the training sets and then predicting the score on the testing set."
      ],
      "id": "HCT2G2V4nLLy"
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "b1825d89",
        "outputId": "75e9d88a-d819-4c28-d6e3-c54c487c3b47"
      },
      "source": [
        "# training the model and calculating the score\n",
        "from sklearn.linear_model import LinearRegression\n",
        "model = LinearRegression()\n",
        "model.fit(x_train, y_train)\n",
        "model.score(x_test, y_test)"
      ],
      "id": "b1825d89",
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.8630735791969519"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WB8vF0lPniOS"
      },
      "source": [
        "As we can see, our model has a score 0f 0.86, which is very high. Hence, the model has high explanatory power and the variables protein, fat and sugars can predict the rating accurately."
      ],
      "id": "WB8vF0lPniOS"
    }
  ]
}