Statistics.ipynb

{
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  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "display_name": "Julia",
      "language": "julia",
      "name": "julia"
    },
    "language_info": {
      "file_extension": ".jl",
      "mimetype": "application/julia",
      "name": "julia"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/xKDR/Julia-Workshop/blob/main/Statistics.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tQ1r1bbb0yBv"
      },
      "source": [
        "# <img src=\"https://github.com/JuliaLang/julia-logo-graphics/raw/master/images/julia-logo-color.png\" height=\"100\" /> _Colab Notebook Template_\n",
        "\n",
        "## Instructions\n",
        "1. Work on a copy of this notebook: _File_ > _Save a copy in Drive_ (you will need a Google account). Alternatively, you can download the notebook using _File_ > _Download .ipynb_, then upload it to [Colab](https://colab.research.google.com/).\n",
        "2. If you need a GPU: _Runtime_ > _Change runtime type_ > _Harware accelerator_ = _GPU_.\n",
        "3. Execute the following cell (click on it and press Ctrl+Enter) to install Julia, IJulia and other packages (if needed, update `JULIA_VERSION` and the other parameters). This takes a couple of minutes.\n",
        "4. Reload this page (press Ctrl+R, or ⌘+R, or the F5 key) and continue to the next section.\n",
        "\n",
        "_Notes_:\n",
        "* If your Colab Runtime gets reset (e.g., due to inactivity), repeat steps 2, 3 and 4.\n",
        "* After installation, if you want to change the Julia version or activate/deactivate the GPU, you will need to reset the Runtime: _Runtime_ > _Factory reset runtime_ and repeat steps 3 and 4."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GIeFXS0F0zww",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 88
        },
        "outputId": "56f6299f-93c5-4f1e-83ef-a05718d0d15d"
      },
      "source": [
        "%%shell\n",
        "set -e\n",
        "\n",
        "#---------------------------------------------------#\n",
        "JULIA_VERSION=\"1.10.4\" # any version ≥ 0.7.0\n",
        "JULIA_PACKAGES=\"IJulia BenchmarkTools\"\n",
        "JULIA_PACKAGES_IF_GPU=\"CUDA\" # or CuArrays for older Julia versions\n",
        "JULIA_NUM_THREADS=2\n",
        "#---------------------------------------------------#\n",
        "\n",
        "if [ -z `which julia` ]; then\n",
        "  # Install Julia\n",
        "  JULIA_VER=`cut -d '.' -f -2 <<< \"$JULIA_VERSION\"`\n",
        "  echo \"Installing Julia $JULIA_VERSION on the current Colab Runtime...\"\n",
        "  BASE_URL=\"https://julialang-s3.julialang.org/bin/linux/x64\"\n",
        "  URL=\"$BASE_URL/$JULIA_VER/julia-$JULIA_VERSION-linux-x86_64.tar.gz\"\n",
        "  wget -nv $URL -O /tmp/julia.tar.gz # -nv means \"not verbose\"\n",
        "  tar -x -f /tmp/julia.tar.gz -C /usr/local --strip-components 1\n",
        "  rm /tmp/julia.tar.gz\n",
        "\n",
        "  # Install Packages\n",
        "  nvidia-smi -L &> /dev/null && export GPU=1 || export GPU=0\n",
        "  if [ $GPU -eq 1 ]; then\n",
        "    JULIA_PACKAGES=\"$JULIA_PACKAGES $JULIA_PACKAGES_IF_GPU\"\n",
        "  fi\n",
        "  for PKG in `echo $JULIA_PACKAGES`; do\n",
        "    echo \"Installing Julia package $PKG...\"\n",
        "    julia -e 'using Pkg; pkg\"add '$PKG'; precompile;\"' &> /dev/null\n",
        "  done\n",
        "\n",
        "  # Install kernel and rename it to \"julia\"\n",
        "  echo \"Installing IJulia kernel...\"\n",
        "  julia -e 'using IJulia; IJulia.installkernel(\"julia\", env=Dict(\n",
        "      \"JULIA_NUM_THREADS\"=>\"'\"$JULIA_NUM_THREADS\"'\"))'\n",
        "  KERNEL_DIR=`julia -e \"using IJulia; print(IJulia.kerneldir())\"`\n",
        "  KERNEL_NAME=`ls -d \"$KERNEL_DIR\"/julia*`\n",
        "  mv -f $KERNEL_NAME \"$KERNEL_DIR\"/julia\n",
        "\n",
        "  echo ''\n",
        "  echo \"Successfully installed `julia -v`!\"\n",
        "  echo \"Please reload this page (press Ctrl+R, ⌘+R, or the F5 key) then\"\n",
        "  echo \"jump to the 'Checking the Installation' section.\"\n",
        "fi"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "  Unrecognized magic \u001b[36m%%shell\u001b[39m.\n",
              "\n",
              "  Julia does not use the IPython \u001b[36m%magic\u001b[39m syntax. To interact with the IJulia kernel, use\n",
              "  \u001b[36mIJulia.somefunction(...)\u001b[39m, for example. Julia macros, string macros, and functions can be used to\n",
              "  accomplish most of the other functionalities of IPython magics."
            ],
            "text/markdown": "Unrecognized magic `%%shell`.\n\nJulia does not use the IPython `%magic` syntax.   To interact with the IJulia kernel, use `IJulia.somefunction(...)`, for example.  Julia macros, string macros, and functions can be used to accomplish most of the other functionalities of IPython magics.\n",
            "text/latex": "Unrecognized magic \\texttt{\\%\\%shell}.\n\nJulia does not use the IPython \\texttt{\\%magic} syntax.   To interact with the IJulia kernel, use \\texttt{IJulia.somefunction(...)}, for example.  Julia macros, string macros, and functions can be used to accomplish most of the other functionalities of IPython magics.\n\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-OS3Ac017T1i"
      },
      "source": [
        "# Checking the Installation\n",
        "The `versioninfo()` function should print your Julia version and some other info about the system:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EEzvvzCl1i0F",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e365b466-4cda-4929-9e2a-fd6bffb9cc67"
      },
      "source": [
        "versioninfo()"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Julia Version 1.10.4\n",
            "Commit 48d4fd48430 (2024-06-04 10:41 UTC)\n",
            "Build Info:\n",
            "  Official https://julialang.org/ release\n",
            "Platform Info:\n",
            "  OS: Linux (x86_64-linux-gnu)\n",
            "  CPU: 2 × Intel(R) Xeon(R) CPU @ 2.20GHz\n",
            "  WORD_SIZE: 64\n",
            "  LIBM: libopenlibm\n",
            "  LLVM: libLLVM-15.0.7 (ORCJIT, broadwell)\n",
            "Threads: 2 default, 0 interactive, 1 GC (on 2 virtual cores)\n",
            "Environment:\n",
            "  LD_LIBRARY_PATH = /usr/local/nvidia/lib:/usr/local/nvidia/lib64\n",
            "  JULIA_NUM_THREADS = 2\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "using BenchmarkTools\n",
        "\n",
        "M = rand(2^11, 2^11)\n",
        "\n",
        "@btime $M * $M;"
      ],
      "metadata": {
        "id": "YjM_qq54lCcs",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d3498a5f-727e-4f32-e08e-e1391f4f8755"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "  571.981 ms (2 allocations: 32.00 MiB)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XciCcMAJOT3_",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "396591fc-547f-4f0f-bd38-da368924a308"
      },
      "source": [
        "try\n",
        "    using CUDA\n",
        "catch\n",
        "    println(\"No GPU found.\")\n",
        "else\n",
        "    run(`nvidia-smi`)\n",
        "    # Create a new random matrix directly on the GPU:\n",
        "    M_on_gpu = CUDA.CURAND.rand(2^11, 2^11)\n",
        "    @btime $M_on_gpu * $M_on_gpu; nothing\n",
        "end"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "No GPU found.\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8RC1QNNqk6h1"
      },
      "source": [
        "# Need Help?\n",
        "\n",
        "* Learning: https://julialang.org/learning/\n",
        "* Documentation: https://docs.julialang.org/\n",
        "* Questions & Discussions:\n",
        "  * https://discourse.julialang.org/\n",
        "  * http://julialang.slack.com/\n",
        "  * https://stackoverflow.com/questions/tagged/julia\n",
        "\n",
        "If you ever ask for help or file an issue about Julia, you should generally provide the output of `versioninfo()`."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2UMidUQB03vJ"
      },
      "source": [
        "Add new code cells by clicking the `+ Code` button (or _Insert_ > _Code cell_).\n",
        "\n",
        "Have fun!\n",
        "\n",
        "<img src=\"https://raw.githubusercontent.com/JuliaLang/julia-logo-graphics/master/images/julia-logo-mask.png\" height=\"100\" />"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **Introduction to Statistics using Julia**\n",
        "\n",
        "This notebook serves as an introductory guide to using Julia for statistical analysis. Statistics is the foundation of data-driven decision-making, enabling us to describe, understand, and infer patterns in data. With Julia, a high-performance programming language, we can efficiently handle statistical computations and visualise data insights.\n",
        "\n",
        "In this notebook, we will:\n",
        "\n",
        "1. **Explore Basic Concepts in Statistics**  \n",
        "   - Learn about key terms such as population, sample, mean, median, variance, and standard deviation.\n",
        "   - Understand the distinction between descriptive and inferential statistics and their real-world applications.\n",
        "\n",
        "2. **Perform Descriptive Statistical Analysis Using Julia**  \n",
        "   - Compute measures of central tendency (mean, median) and dispersion (variance, standard deviation, interquartile range).\n",
        "   - Summarise data to identify patterns, trends, and outliers.\n",
        "\n",
        "3. **Implement Inferential Statistics**  \n",
        "   - Learn the fundamentals of hypothesis testing and its importance in decision-making.\n",
        "   - Conduct hypothesis tests (e.g., one-sample t-tests) to draw conclusions from sample data.\n",
        "   - Explore basic linear regression for modelling relationships between variables.\n",
        "\n",
        "4. **Visualise Data for Better Insights**  \n",
        "   - Create histograms, box plots, and scatter plots to visualise data distributions and relationships.\n",
        "   - Understand how data visualisation aids in identifying patterns and communicating findings effectively.\n",
        "\n",
        "By the end of this session, you will have a hands-on understanding of how Julia simplifies statistical analysis and serves as a powerful tool for tackling data-centric problems. Whether you are a beginner in statistics or an experienced data scientist exploring Julia, this notebook is designed to get you started with confidence.\n",
        "\n",
        "## Let’s dive in!"
      ],
      "metadata": {
        "id": "I1X66MG_MpBD"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "using Pkg\n",
        "Pkg.add(\"CRRao\")\n",
        "Pkg.add(\"Distributions\")\n",
        "Pkg.add(\"Statistics\")\n",
        "Pkg.add(\"GLM\")\n",
        "Pkg.add(\"DataFrames\")\n",
        "Pkg.add(\"Plots\")\n",
        "Pkg.add(\"HypothesisTests\")\n",
        "Pkg.add(\"CSV\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "R2O0XFUCPmqT",
        "outputId": "b9fb2e56-a5b4-48ab-b355-0b852460a241"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\u001b[32m\u001b[1m    Updating\u001b[22m\u001b[39m registry at `~/.julia/registries/General.toml`\n",
            "\u001b[32m\u001b[1m   Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Project.toml`\n",
            "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n",
            "\u001b[32m\u001b[1m   Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Project.toml`\n",
            "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n",
            "\u001b[32m\u001b[1m   Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Project.toml`\n",
            "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n",
            "\u001b[32m\u001b[1m   Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Project.toml`\n",
            "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n",
            "\u001b[32m\u001b[1m   Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Project.toml`\n",
            "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n",
            "\u001b[32m\u001b[1m   Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Project.toml`\n",
            "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n",
            "\u001b[32m\u001b[1m   Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Project.toml`\n",
            "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n",
            "\u001b[32m\u001b[1m   Resolving\u001b[22m\u001b[39m package versions...\n",
            "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Project.toml`\n",
            "\u001b[32m\u001b[1m  No Changes\u001b[22m\u001b[39m to `~/.julia/environments/v1.10/Manifest.toml`\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Importing essential packages\n",
        "using Distributions\n",
        "using Statistics\n",
        "using DataFrames\n",
        "using Plots\n",
        "using HypothesisTests\n",
        "using GLM\n",
        "using CRRao\n",
        "using CSV\n",
        "\n",
        "println(\"Welcome to Julia for Statistics!\")\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "G8mQZ44QMcqa",
        "outputId": "53e84fab-d7a1-41e6-c2c7-c3f29a65ab55"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Welcome to Julia for Statistics!\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Define the URL of the CSV file\n",
        "url = \"https://www.football-data.co.uk/mmz4281/2324/E0.csv\"\n",
        "\n",
        "# Read the CSV file directly from the URL into a DataFrame\n",
        "df = CSV.read(download(url), DataFrame)\n",
        "\n",
        "# Display the first few rows of the DataFrame\n",
        "first(df, 5)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 244
        },
        "id": "3Nsrd0vGFbEW",
        "outputId": "02001fa1-06cd-4ae5-802a-01d6cb7202f3"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "\u001b[1m5×106 DataFrame\u001b[0m\n",
              "\u001b[1m Row \u001b[0m│\u001b[1m Div     \u001b[0m\u001b[1m Date       \u001b[0m\u001b[1m Time     \u001b[0m\u001b[1m HomeTeam    \u001b[0m\u001b[1m AwayTeam      \u001b[0m\u001b[1m FTHG  \u001b[0m\u001b[1m FTAG  \u001b[0m\u001b[1m FTR     \u001b[0m\u001b[1m HTHG  \u001b[0m\u001b[1m HT\u001b[0m ⋯\n",
              "     │\u001b[90m String3 \u001b[0m\u001b[90m String15   \u001b[0m\u001b[90m Time     \u001b[0m\u001b[90m String31    \u001b[0m\u001b[90m String31      \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m String1 \u001b[0m\u001b[90m Int64 \u001b[0m\u001b[90m In\u001b[0m ⋯\n",
              "─────┼──────────────────────────────────────────────────────────────────────────────────────────────\n",
              "   1 │ E0       11/08/2023  20:00:00  Burnley      Man City           0      3  A            0     ⋯\n",
              "   2 │ E0       12/08/2023  12:30:00  Arsenal      Nott'm Forest      2      1  H            2\n",
              "   3 │ E0       12/08/2023  15:00:00  Bournemouth  West Ham           1      1  D            0\n",
              "   4 │ E0       12/08/2023  15:00:00  Brighton     Luton              4      1  H            1\n",
              "   5 │ E0       12/08/2023  15:00:00  Everton      Fulham             0      1  A            0     ⋯\n",
              "\u001b[36m                                                                                  97 columns omitted\u001b[0m"
            ],
            "text/html": [
              "<div><div style = \"float: left;\"><span>5×106 DataFrame</span></div><div style = \"float: right;\"><span style = \"font-style: italic;\">6 columns omitted</span></div><div style = \"clear: both;\"></div></div><div class = \"data-frame\" style = \"overflow-x: scroll;\"><table class = \"data-frame\" style = \"margin-bottom: 6px;\"><thead><tr class = \"header\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">Row</th><th style = \"text-align: left;\">Div</th><th style = \"text-align: left;\">Date</th><th style = \"text-align: left;\">Time</th><th style = \"text-align: left;\">HomeTeam</th><th style = \"text-align: left;\">AwayTeam</th><th style = \"text-align: left;\">FTHG</th><th style = \"text-align: left;\">FTAG</th><th style = \"text-align: left;\">FTR</th><th style = \"text-align: left;\">HTHG</th><th style = \"text-align: left;\">HTAG</th><th style = \"text-align: left;\">HTR</th><th style = \"text-align: left;\">Referee</th><th style = \"text-align: left;\">HS</th><th style = \"text-align: left;\">AS</th><th style = \"text-align: left;\">HST</th><th style = \"text-align: left;\">AST</th><th style = \"text-align: left;\">HF</th><th style = \"text-align: left;\">AF</th><th style = \"text-align: left;\">HC</th><th style = \"text-align: left;\">AC</th><th style = \"text-align: left;\">HY</th><th style = \"text-align: left;\">AY</th><th style = \"text-align: left;\">HR</th><th style = \"text-align: left;\">AR</th><th style = \"text-align: left;\">B365H</th><th style = \"text-align: left;\">B365D</th><th style = \"text-align: left;\">B365A</th><th style = \"text-align: left;\">BWH</th><th style = \"text-align: left;\">BWD</th><th style = \"text-align: left;\">BWA</th><th style = \"text-align: left;\">IWH</th><th style = \"text-align: left;\">IWD</th><th style = \"text-align: left;\">IWA</th><th style = \"text-align: left;\">PSH</th><th style = \"text-align: left;\">PSD</th><th style = \"text-align: left;\">PSA</th><th style = \"text-align: left;\">WHH</th><th style = \"text-align: left;\">WHD</th><th style = \"text-align: left;\">WHA</th><th style = \"text-align: left;\">VCH</th><th style = \"text-align: left;\">VCD</th><th style = \"text-align: left;\">VCA</th><th style = \"text-align: left;\">MaxH</th><th style = \"text-align: left;\">MaxD</th><th style = \"text-align: left;\">MaxA</th><th style = \"text-align: left;\">AvgH</th><th style = \"text-align: left;\">AvgD</th><th style = \"text-align: left;\">AvgA</th><th style = \"text-align: left;\">B365&gt;2.5</th><th style = \"text-align: left;\">B365&lt;2.5</th><th style = \"text-align: left;\">P&gt;2.5</th><th style = \"text-align: left;\">P&lt;2.5</th><th style = \"text-align: left;\">Max&gt;2.5</th><th style = \"text-align: left;\">Max&lt;2.5</th><th style = \"text-align: left;\">Avg&gt;2.5</th><th style = \"text-align: left;\">Avg&lt;2.5</th><th style = \"text-align: left;\">AHh</th><th style = \"text-align: left;\">B365AHH</th><th style = \"text-align: left;\">B365AHA</th><th style = \"text-align: left;\">PAHH</th><th style = \"text-align: left;\">PAHA</th><th style = \"text-align: left;\">MaxAHH</th><th style = \"text-align: left;\">MaxAHA</th><th style = \"text-align: left;\">AvgAHH</th><th style = \"text-align: left;\">AvgAHA</th><th style = \"text-align: left;\">B365CH</th><th style = \"text-align: left;\">B365CD</th><th style = \"text-align: left;\">B365CA</th><th style = \"text-align: left;\">BWCH</th><th style = \"text-align: left;\">BWCD</th><th style = \"text-align: left;\">BWCA</th><th style = \"text-align: left;\">IWCH</th><th style = \"text-align: left;\">IWCD</th><th style = \"text-align: left;\">IWCA</th><th style = \"text-align: left;\">PSCH</th><th style = \"text-align: left;\">PSCD</th><th style = \"text-align: left;\">PSCA</th><th style = \"text-align: left;\">WHCH</th><th style = \"text-align: left;\">WHCD</th><th style = \"text-align: left;\">WHCA</th><th style = \"text-align: left;\">VCCH</th><th style = \"text-align: left;\">VCCD</th><th style = \"text-align: left;\">VCCA</th><th style = \"text-align: left;\">MaxCH</th><th style = \"text-align: left;\">MaxCD</th><th style = \"text-align: left;\">MaxCA</th><th style = \"text-align: left;\">AvgCH</th><th style = \"text-align: left;\">AvgCD</th><th style = \"text-align: left;\">AvgCA</th><th style = \"text-align: left;\">B365C&gt;2.5</th><th style = \"text-align: left;\">B365C&lt;2.5</th><th style = \"text-align: left;\">PC&gt;2.5</th><th style = \"text-align: left;\">PC&lt;2.5</th><th style = \"text-align: left;\">MaxC&gt;2.5</th><th style = \"text-align: left;\">MaxC&lt;2.5</th><th style = \"text-align: left;\">AvgC&gt;2.5</th><th style = \"text-align: left;\">AvgC&lt;2.5</th><th style = \"text-align: left;\">AHCh</th><th style = \"text-align: left;\">B365CAHH</th><th style = \"text-align: left;\">B365CAHA</th><th style = \"text-align: right;\">&ctdot;</th></tr><tr class = \"subheader headerLastRow\"><th class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\"></th><th title = \"String3\" style = \"text-align: left;\">String3</th><th title = \"String15\" style = \"text-align: left;\">String15</th><th title = \"Dates.Time\" style = \"text-align: left;\">Time</th><th title = \"String31\" style = \"text-align: left;\">String31</th><th title = \"String31\" style = \"text-align: left;\">String31</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"String1\" style = \"text-align: left;\">String1</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"String1\" style = \"text-align: left;\">String1</th><th title = \"String15\" style = \"text-align: left;\">String15</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Int64\" style = \"text-align: left;\">Int64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Union{Missing, Float64}\" style = \"text-align: left;\">Float64?</th><th title = \"Union{Missing, Float64}\" style = \"text-align: left;\">Float64?</th><th title = \"Union{Missing, Float64}\" style = \"text-align: left;\">Float64?</th><th title = \"Union{Missing, Float64}\" style = \"text-align: left;\">Float64?</th><th title = \"Union{Missing, Float64}\" style = \"text-align: left;\">Float64?</th><th title = \"Union{Missing, Float64}\" style = \"text-align: left;\">Float64?</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Union{Missing, Float64}\" style = \"text-align: left;\">Float64?</th><th title = \"Union{Missing, Float64}\" style = \"text-align: left;\">Float64?</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Union{Missing, Float64}\" style = \"text-align: left;\">Float64?</th><th title = \"Union{Missing, Float64}\" style = \"text-align: left;\">Float64?</th><th title = \"Union{Missing, Float64}\" style = \"text-align: left;\">Float64?</th><th title = \"Union{Missing, Float64}\" style = \"text-align: left;\">Float64?</th><th title = \"Union{Missing, Float64}\" style = \"text-align: left;\">Float64?</th><th title = \"Union{Missing, Float64}\" style = \"text-align: left;\">Float64?</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Union{Missing, Float64}\" style = \"text-align: left;\">Float64?</th><th title = \"Union{Missing, Float64}\" style = \"text-align: left;\">Float64?</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: left;\">Float64</th><th title = \"Float64\" style = \"text-align: right;\">&ctdot;</th></tr></thead><tbody><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">1</td><td style = \"text-align: left;\">E0</td><td style = \"text-align: left;\">11/08/2023</td><td style = \"text-align: left;\">20:00:00</td><td style = \"text-align: left;\">Burnley</td><td style = \"text-align: left;\">Man City</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">3</td><td style = \"text-align: left;\">A</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: left;\">A</td><td style = \"text-align: left;\">C Pawson</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">17</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">5.5</td><td style = \"text-align: right;\">1.33</td><td style = \"text-align: right;\">8.75</td><td style = \"text-align: right;\">5.25</td><td style = \"text-align: right;\">1.34</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">5.5</td><td style = \"text-align: right;\">1.35</td><td style = \"text-align: right;\">8.58</td><td style = \"text-align: right;\">5.51</td><td style = \"text-align: right;\">1.37</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">5.0</td><td style = \"text-align: right;\">1.25</td><td style = \"text-align: right;\">9.5</td><td style = \"text-align: right;\">5.25</td><td style = \"text-align: right;\">1.33</td><td style = \"text-align: right;\">9.5</td><td style = \"text-align: right;\">5.68</td><td style = \"text-align: right;\">1.39</td><td style = \"text-align: right;\">9.02</td><td style = \"text-align: right;\">5.35</td><td style = \"text-align: right;\">1.35</td><td style = \"text-align: right;\">1.67</td><td style = \"text-align: right;\">2.2</td><td style = \"text-align: right;\">1.68</td><td style = \"text-align: right;\">2.29</td><td style = \"text-align: right;\">1.71</td><td style = \"text-align: right;\">2.4</td><td style = \"text-align: right;\">1.65</td><td style = \"text-align: right;\">2.27</td><td style = \"text-align: right;\">1.5</td><td style = \"text-align: right;\">1.86</td><td style = \"text-align: right;\">2.07</td><td style = \"text-align: right;\">1.86</td><td style = \"text-align: right;\">2.07</td><td style = \"text-align: right;\">1.93</td><td style = \"text-align: right;\">2.09</td><td style = \"text-align: right;\">1.85</td><td style = \"text-align: right;\">2.03</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">5.25</td><td style = \"text-align: right;\">1.33</td><td style = \"text-align: right;\">8.75</td><td style = \"text-align: right;\">5.25</td><td style = \"text-align: right;\">1.33</td><td style = \"text-align: right;\">8.5</td><td style = \"text-align: right;\">5.25</td><td style = \"text-align: right;\">1.35</td><td style = \"text-align: right;\">9.62</td><td style = \"text-align: right;\">5.81</td><td style = \"text-align: right;\">1.33</td><td style = \"text-align: right;\">7.5</td><td style = \"text-align: right;\">4.6</td><td style = \"text-align: right;\">1.29</td><td style = \"text-align: right;\">10.5</td><td style = \"text-align: right;\">5.25</td><td style = \"text-align: right;\">1.3</td><td style = \"text-align: right;\">10.5</td><td style = \"text-align: right;\">5.81</td><td style = \"text-align: right;\">1.36</td><td style = \"text-align: right;\">9.27</td><td style = \"text-align: right;\">5.45</td><td style = \"text-align: right;\">1.33</td><td style = \"text-align: right;\">1.67</td><td style = \"text-align: right;\">2.2</td><td style = \"text-align: right;\">1.65</td><td style = \"text-align: right;\">2.35</td><td style = \"text-align: right;\">1.73</td><td style = \"text-align: right;\">2.45</td><td style = \"text-align: right;\">1.64</td><td style = \"text-align: right;\">2.28</td><td style = \"text-align: right;\">1.5</td><td style = \"text-align: right;\">1.95</td><td style = \"text-align: right;\">1.98</td><td style = \"text-align: right;\">&ctdot;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">2</td><td style = \"text-align: left;\">E0</td><td style = \"text-align: left;\">12/08/2023</td><td style = \"text-align: left;\">12:30:00</td><td style = \"text-align: left;\">Arsenal</td><td style = \"text-align: left;\">Nott&apos;m Forest</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">H</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">H</td><td style = \"text-align: left;\">M Oliver</td><td style = \"text-align: right;\">15</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">7</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">8</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1.18</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">15.0</td><td style = \"text-align: right;\">1.17</td><td style = \"text-align: right;\">7.5</td><td style = \"text-align: right;\">15.5</td><td style = \"text-align: right;\">1.2</td><td style = \"text-align: right;\">7.25</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">1.18</td><td style = \"text-align: right;\">7.86</td><td style = \"text-align: right;\">15.67</td><td style = \"text-align: right;\">1.12</td><td style = \"text-align: right;\">6.5</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">1.14</td><td style = \"text-align: right;\">7.5</td><td style = \"text-align: right;\">17.0</td><td style = \"text-align: right;\">1.21</td><td style = \"text-align: right;\">8.5</td><td style = \"text-align: right;\">17.5</td><td style = \"text-align: right;\">1.18</td><td style = \"text-align: right;\">7.64</td><td style = \"text-align: right;\">15.67</td><td style = \"text-align: right;\">1.44</td><td style = \"text-align: right;\">2.75</td><td style = \"text-align: right;\">1.42</td><td style = \"text-align: right;\">2.93</td><td style = \"text-align: right;\">1.45</td><td style = \"text-align: right;\">2.98</td><td style = \"text-align: right;\">1.42</td><td style = \"text-align: right;\">2.85</td><td style = \"text-align: right;\">-2.0</td><td style = \"text-align: right;\">1.88</td><td style = \"text-align: right;\">2.02</td><td style = \"text-align: right;\">1.88</td><td style = \"text-align: right;\">2.01</td><td style = \"text-align: right;\">1.91</td><td style = \"text-align: right;\">2.06</td><td style = \"text-align: right;\">1.87</td><td style = \"text-align: right;\">1.99</td><td style = \"text-align: right;\">1.18</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">15.0</td><td style = \"text-align: right;\">1.18</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">14.5</td><td style = \"text-align: right;\">1.2</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">14.0</td><td style = \"text-align: right;\">1.19</td><td style = \"text-align: right;\">8.0</td><td style = \"text-align: right;\">16.0</td><td style = \"text-align: right;\">1.12</td><td style = \"text-align: right;\">6.5</td><td style = \"text-align: right;\">12.0</td><td style = \"text-align: right;\">1.22</td><td style = \"text-align: right;\">7.0</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">1.22</td><td style = \"text-align: right;\">8.4</td><td style = \"text-align: right;\">19.0</td><td style = \"text-align: right;\">1.19</td><td style = \"text-align: right;\">7.43</td><td style = \"text-align: right;\">15.98</td><td style = \"text-align: right;\">1.5</td><td style = \"text-align: right;\">2.63</td><td style = \"text-align: right;\">1.49</td><td style = \"text-align: right;\">2.65</td><td style = \"text-align: right;\">1.52</td><td style = \"text-align: right;\">2.79</td><td style = \"text-align: right;\">1.49</td><td style = \"text-align: right;\">2.63</td><td style = \"text-align: right;\">-2.0</td><td style = \"text-align: right;\">1.95</td><td style = \"text-align: right;\">1.98</td><td style = \"text-align: right;\">&ctdot;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">3</td><td style = \"text-align: left;\">E0</td><td style = \"text-align: left;\">12/08/2023</td><td style = \"text-align: left;\">15:00:00</td><td style = \"text-align: left;\">Bournemouth</td><td style = \"text-align: left;\">West Ham</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">D</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">D</td><td style = \"text-align: left;\">P Bankes</td><td style = \"text-align: right;\">14</td><td style = \"text-align: right;\">16</td><td style = \"text-align: right;\">5</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">14</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2.7</td><td style = \"text-align: right;\">3.4</td><td style = \"text-align: right;\">2.55</td><td style = \"text-align: right;\">2.65</td><td style = \"text-align: right;\">3.4</td><td style = \"text-align: right;\">2.55</td><td style = \"text-align: right;\">2.7</td><td style = \"text-align: right;\">3.45</td><td style = \"text-align: right;\">2.6</td><td style = \"text-align: right;\">2.7</td><td style = \"text-align: right;\">3.47</td><td style = \"text-align: right;\">2.71</td><td style = \"text-align: right;\">2.62</td><td style = \"text-align: right;\">3.2</td><td style = \"text-align: right;\">2.3</td><td style = \"text-align: right;\">2.63</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">2.63</td><td style = \"text-align: right;\">2.8</td><td style = \"text-align: right;\">3.62</td><td style = \"text-align: right;\">2.75</td><td style = \"text-align: right;\">2.69</td><td style = \"text-align: right;\">3.44</td><td style = \"text-align: right;\">2.64</td><td style = \"text-align: right;\">1.9</td><td style = \"text-align: right;\">2.0</td><td style = \"text-align: right;\">1.9</td><td style = \"text-align: right;\">1.99</td><td style = \"text-align: right;\">1.95</td><td style = \"text-align: right;\">2.03</td><td style = \"text-align: right;\">1.88</td><td style = \"text-align: right;\">1.94</td><td style = \"text-align: right;\">0.0</td><td style = \"text-align: right;\">1.95</td><td style = \"text-align: right;\">1.95</td><td style = \"text-align: right;\">1.95</td><td style = \"text-align: right;\">1.95</td><td style = \"text-align: right;\">1.98</td><td style = \"text-align: right;\">1.99</td><td style = \"text-align: right;\">1.94</td><td style = \"text-align: right;\">1.92</td><td style = \"text-align: right;\">2.63</td><td style = \"text-align: right;\">3.5</td><td style = \"text-align: right;\">2.6</td><td style = \"text-align: right;\">2.65</td><td style = \"text-align: right;\">3.5</td><td style = \"text-align: right;\">2.5</td><td style = \"text-align: right;\">2.6</td><td style = \"text-align: right;\">3.5</td><td style = \"text-align: right;\">2.6</td><td style = \"text-align: right;\">2.75</td><td style = \"text-align: right;\">3.6</td><td style = \"text-align: right;\">2.63</td><td style = \"text-align: right;\">2.5</td><td style = \"text-align: right;\">3.2</td><td style = \"text-align: right;\">2.45</td><td style = \"text-align: right;\">2.63</td><td style = \"text-align: right;\">3.5</td><td style = \"text-align: right;\">2.6</td><td style = \"text-align: right;\">2.88</td><td style = \"text-align: right;\">3.67</td><td style = \"text-align: right;\">2.7</td><td style = \"text-align: right;\">2.7</td><td style = \"text-align: right;\">3.53</td><td style = \"text-align: right;\">2.59</td><td style = \"text-align: right;\">1.73</td><td style = \"text-align: right;\">2.1</td><td style = \"text-align: right;\">1.76</td><td style = \"text-align: right;\">2.18</td><td style = \"text-align: right;\">1.83</td><td style = \"text-align: right;\">2.23</td><td style = \"text-align: right;\">1.74</td><td style = \"text-align: right;\">2.12</td><td style = \"text-align: right;\">0.0</td><td style = \"text-align: right;\">2.02</td><td style = \"text-align: right;\">1.91</td><td style = \"text-align: right;\">&ctdot;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">4</td><td style = \"text-align: left;\">E0</td><td style = \"text-align: left;\">12/08/2023</td><td style = \"text-align: left;\">15:00:00</td><td style = \"text-align: left;\">Brighton</td><td style = \"text-align: left;\">Luton</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">H</td><td style = \"text-align: right;\">1</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">H</td><td style = \"text-align: left;\">D Coote</td><td style = \"text-align: right;\">27</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">3</td><td style = \"text-align: right;\">11</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">7</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1.33</td><td style = \"text-align: right;\">5.5</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">1.32</td><td style = \"text-align: right;\">5.5</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">1.35</td><td style = \"text-align: right;\">5.25</td><td style = \"text-align: right;\">8.5</td><td style = \"text-align: right;\">1.33</td><td style = \"text-align: right;\">5.65</td><td style = \"text-align: right;\">9.61</td><td style = \"text-align: right;\">1.25</td><td style = \"text-align: right;\">4.6</td><td style = \"text-align: right;\">8.5</td><td style = \"text-align: right;\">1.29</td><td style = \"text-align: right;\">5.25</td><td style = \"text-align: right;\">10.0</td><td style = \"text-align: right;\">1.36</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">10.5</td><td style = \"text-align: right;\">1.33</td><td style = \"text-align: right;\">5.52</td><td style = \"text-align: right;\">9.61</td><td style = \"text-align: right;\">1.62</td><td style = \"text-align: right;\">2.3</td><td style = \"text-align: right;\">1.62</td><td style = \"text-align: right;\">2.4</td><td style = \"text-align: right;\">1.65</td><td style = \"text-align: right;\">2.45</td><td style = \"text-align: right;\">1.61</td><td style = \"text-align: right;\">2.34</td><td style = \"text-align: right;\">-1.5</td><td style = \"text-align: right;\">1.95</td><td style = \"text-align: right;\">1.95</td><td style = \"text-align: right;\">1.95</td><td style = \"text-align: right;\">1.95</td><td style = \"text-align: right;\">1.98</td><td style = \"text-align: right;\">2.0</td><td style = \"text-align: right;\">1.93</td><td style = \"text-align: right;\">1.93</td><td style = \"text-align: right;\">1.25</td><td style = \"text-align: right;\">6.5</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">1.26</td><td style = \"text-align: right;\">6.0</td><td style = \"text-align: right;\">11.0</td><td style = \"text-align: right;\">1.3</td><td style = \"text-align: right;\">5.5</td><td style = \"text-align: right;\">9.5</td><td style = \"text-align: right;\">1.27</td><td style = \"text-align: right;\">6.36</td><td style = \"text-align: right;\">11.36</td><td style = \"text-align: right;\">1.22</td><td style = \"text-align: right;\">5.5</td><td style = \"text-align: right;\">9.0</td><td style = \"text-align: right;\">1.25</td><td style = \"text-align: right;\">5.75</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">1.34</td><td style = \"text-align: right;\">6.59</td><td style = \"text-align: right;\">13.0</td><td style = \"text-align: right;\">1.28</td><td style = \"text-align: right;\">5.99</td><td style = \"text-align: right;\">10.91</td><td style = \"text-align: right;\">1.53</td><td style = \"text-align: right;\">2.5</td><td style = \"text-align: right;\">1.56</td><td style = \"text-align: right;\">2.54</td><td style = \"text-align: right;\">1.62</td><td style = \"text-align: right;\">2.66</td><td style = \"text-align: right;\">1.55</td><td style = \"text-align: right;\">2.48</td><td style = \"text-align: right;\">-1.75</td><td style = \"text-align: right;\">2.01</td><td style = \"text-align: right;\">1.92</td><td style = \"text-align: right;\">&ctdot;</td></tr><tr><td class = \"rowNumber\" style = \"font-weight: bold; text-align: right;\">5</td><td style = \"text-align: left;\">E0</td><td style = \"text-align: left;\">12/08/2023</td><td style = \"text-align: left;\">15:00:00</td><td style = \"text-align: left;\">Everton</td><td style = \"text-align: left;\">Fulham</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">1</td><td style = \"text-align: left;\">A</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: left;\">D</td><td style = \"text-align: left;\">S Attwell</td><td style = \"text-align: right;\">19</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">9</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">12</td><td style = \"text-align: right;\">6</td><td style = \"text-align: right;\">10</td><td style = \"text-align: right;\">4</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">0</td><td style = \"text-align: right;\">2.2</td><td style = \"text-align: right;\">3.4</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">2.2</td><td style = \"text-align: right;\">3.4</td><td style = \"text-align: right;\">3.25</td><td style = \"text-align: right;\">2.25</td><td style = \"text-align: right;\">3.4</td><td style = \"text-align: right;\">3.25</td><td style = \"text-align: right;\">2.27</td><td style = \"text-align: right;\">3.45</td><td style = \"text-align: right;\">3.35</td><td style = \"text-align: right;\">2.1</td><td style = \"text-align: right;\">3.2</td><td style = \"text-align: right;\">3.0</td><td style = \"text-align: right;\">2.2</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">3.25</td><td style = \"text-align: right;\">2.3</td><td style = \"text-align: right;\">3.57</td><td style = \"text-align: right;\">3.45</td><td style = \"text-align: right;\">2.24</td><td style = \"text-align: right;\">3.43</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">2.01</td><td style = \"text-align: right;\">1.89</td><td style = \"text-align: right;\">2.0</td><td style = \"text-align: right;\">1.89</td><td style = \"text-align: right;\">2.04</td><td style = \"text-align: right;\">1.92</td><td style = \"text-align: right;\">1.97</td><td style = \"text-align: right;\">1.86</td><td style = \"text-align: right;\">-0.25</td><td style = \"text-align: right;\">1.93</td><td style = \"text-align: right;\">1.97</td><td style = \"text-align: right;\">1.95</td><td style = \"text-align: right;\">1.95</td><td style = \"text-align: right;\">1.97</td><td style = \"text-align: right;\">2.0</td><td style = \"text-align: right;\">1.92</td><td style = \"text-align: right;\">1.93</td><td style = \"text-align: right;\">2.3</td><td style = \"text-align: right;\">3.2</td><td style = \"text-align: right;\">3.2</td><td style = \"text-align: right;\">2.35</td><td style = \"text-align: right;\">3.2</td><td style = \"text-align: right;\">3.1</td><td style = \"text-align: right;\">2.35</td><td style = \"text-align: right;\">3.25</td><td style = \"text-align: right;\">3.15</td><td style = \"text-align: right;\">2.39</td><td style = \"text-align: right;\">3.32</td><td style = \"text-align: right;\">3.3</td><td style = \"text-align: right;\">2.1</td><td style = \"text-align: right;\">3.2</td><td style = \"text-align: right;\">3.0</td><td style = \"text-align: right;\">2.38</td><td style = \"text-align: right;\">3.2</td><td style = \"text-align: right;\">3.2</td><td style = \"text-align: right;\">2.42</td><td style = \"text-align: right;\">3.42</td><td style = \"text-align: right;\">3.56</td><td style = \"text-align: right;\">2.32</td><td style = \"text-align: right;\">3.28</td><td style = \"text-align: right;\">3.27</td><td style = \"text-align: right;\">2.1</td><td style = \"text-align: right;\">1.73</td><td style = \"text-align: right;\">2.23</td><td style = \"text-align: right;\">1.72</td><td style = \"text-align: right;\">2.26</td><td style = \"text-align: right;\">1.81</td><td style = \"text-align: right;\">2.17</td><td style = \"text-align: right;\">1.71</td><td style = \"text-align: right;\">-0.25</td><td style = \"text-align: right;\">2.06</td><td style = \"text-align: right;\">1.87</td><td style = \"text-align: right;\">&ctdot;</td></tr></tbody></table></div>"
            ],
            "text/latex": "\\begin{tabular}{r|cccccccccccc}\n\t& Div & Date & Time & HomeTeam & AwayTeam & FTHG & FTAG & FTR & HTHG & HTAG & HTR & \\\\\n\t\\hline\n\t& String3 & String15 & Time & String31 & String31 & Int64 & Int64 & String1 & Int64 & Int64 & String1 & \\\\\n\t\\hline\n\t1 & E0 & 11/08/2023 & 20:00:00 & Burnley & Man City & 0 & 3 & A & 0 & 2 & A & $\\dots$ \\\\\n\t2 & E0 & 12/08/2023 & 12:30:00 & Arsenal & Nott'm Forest & 2 & 1 & H & 2 & 0 & H & $\\dots$ \\\\\n\t3 & E0 & 12/08/2023 & 15:00:00 & Bournemouth & West Ham & 1 & 1 & D & 0 & 0 & D & $\\dots$ \\\\\n\t4 & E0 & 12/08/2023 & 15:00:00 & Brighton & Luton & 4 & 1 & H & 1 & 0 & H & $\\dots$ \\\\\n\t5 & E0 & 12/08/2023 & 15:00:00 & Everton & Fulham & 0 & 1 & A & 0 & 0 & D & $\\dots$ \\\\\n\\end{tabular}\n"
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Measures of Central Tendency**\n",
        "\n",
        "Measures of central tendency are statistical metrics used to determine the centre or typical value of a dataset. These measures summarise a dataset with a single value that represents the entire distribution, making it easier to understand and interpret the data. The three most commonly used measures of central tendency are **mean**, **median**, and **mode**.\n",
        "\n",
        "---\n",
        "\n",
        "#### **1. Mean (Arithmetic Average)**\n",
        "The mean is the sum of all values in a dataset divided by the total number of values. It is the most widely used measure of central tendency, especially when the data is symmetrically distributed.\n",
        "\n",
        "**Formula**:\n",
        "\\[\n",
        "\\text{Mean} = \\frac{\\sum_{i=1}^n x_i}{n}\n",
        "\\]\n",
        "where \\(x_i\\) are the individual data points, and \\(n\\) is the total number of data points.\n",
        "\n",
        "**Example**:\n",
        "If the dataset is \\([10, 20, 30, 40, 50]\\), the mean is:\n",
        "\\[\n",
        "\\text{Mean} = \\frac{10 + 20 + 30 + 40 + 50}{5} = 30\n",
        "\\]\n",
        "\n",
        "**Pros**:\n",
        "- Easy to calculate.\n",
        "- Takes all values into account.\n",
        "\n",
        "**Cons**:\n",
        "- Sensitive to outliers (e.g., extremely high or low values).\n",
        "\n",
        "---\n",
        "\n",
        "#### **2. Median**\n",
        "The median is the middle value of a dataset when the data is arranged in ascending or descending order. If the number of data points is even, the median is the average of the two middle values.\n",
        "\n",
        "**Steps to Find the Median**:\n",
        "1. Arrange the data in ascending order.\n",
        "2. Identify the middle value (or average of the two middle values).\n",
        "\n",
        "**Example**:\n",
        "For the dataset \\([10, 20, 30, 40, 50]\\), the median is \\(30\\).  \n",
        "For the dataset \\([10, 20, 30, 40]\\), the median is:\n",
        "\\[\n",
        "\\text{Median} = \\frac{20 + 30}{2} = 25\n",
        "\\]\n",
        "\n",
        "**Pros**:\n",
        "- Not affected by outliers.\n",
        "- Suitable for skewed distributions.\n",
        "\n",
        "**Cons**:\n",
        "- Ignores the magnitude of values (only considers their order).\n",
        "\n",
        "---\n",
        "\n",
        "#### **3. Mode**\n",
        "The mode is the most frequently occurring value in a dataset. A dataset can have one mode (unimodal), more than one mode (multimodal), or no mode at all.\n",
        "\n",
        "**Example**:\n",
        "For the dataset \\([10, 20, 20, 30, 40]\\), the mode is \\(20\\).\n",
        "\n",
        "**Pros**:\n",
        "- Useful for categorical data.\n",
        "- Easy to identify in simple datasets.\n",
        "\n",
        "**Cons**:\n",
        "- May not be unique or well-defined for all datasets.\n",
        "\n",
        "---\n",
        "\n",
        "### **Comparison of Measures**\n",
        "| Measure  | When to Use                              | Advantages                     | Limitations                     |\n",
        "|----------|------------------------------------------|--------------------------------|---------------------------------|\n",
        "| **Mean** | For symmetric data with no outliers      | Easy to compute; widely used   | Affected by outliers            |\n",
        "| **Median**| For skewed data or data with outliers    | Robust to outliers             | Does not use all data points    |\n",
        "| **Mode** | For categorical or discrete data         | Easy to identify               | May not exist or be unique      |\n",
        "\n",
        "---\n",
        "\n",
        "### **Applications**\n",
        "- **Mean**: Calculating average scores, incomes, or prices.\n",
        "- **Median**: Analysing income distributions or property values where outliers exist.\n",
        "- **Mode**: Determining the most popular product, choice, or category.\n",
        "\n",
        "By understanding and applying these measures appropriately, you can summarise datasets effectively and derive insights that inform decisions."
      ],
      "metadata": {
        "id": "gOyo7xh4Jm5L"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Calculate the mean of the FTHG and FTAG column\n",
        "mean_fthg = mean(df.FTHG)\n",
        "mean_ftag = mean(df.FTAG)\n",
        "println(\"Average goal scored by Home Team in Full Time : \",mean_fthg)\n",
        "println(\"Average goal scored by Away Team in Full Time : \",mean_ftag)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ODjWFUcSIYsb",
        "outputId": "deced762-e16c-480d-92c5-dc4b20e9263a"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Average goal scored by Home Team in Full Time : 1.8\n",
            "Average goal scored by Away Team in Full Time : 1.4789473684210526\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Calculate the median of the FTHG and FTAG column\n",
        "median_fthg = median(df.FTHG)\n",
        "median_ftag = median(df.FTAG)\n",
        "println(\"Median goal scored by Home Team in Full Time : \",median_fthg)\n",
        "println(\"Median goal scored by Away Team in Full Time : \",median_ftag)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dfLTUBoKJImC",
        "outputId": "1b0e4db7-5c99-418f-89f9-47663dca6750"
      },
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Median goal scored by Home Team in Full Time : 2.0\n",
            "Median goal scored by Away Team in Full Time : 1.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### **Measures of Dispersion**\n",
        "\n",
        "Measures of dispersion describe the spread or variability of a dataset. While measures of central tendency like mean, median, and mode provide a summary of the dataset's central point, dispersion tells us how much the data values vary from the centre. Understanding dispersion is crucial for interpreting data variability and assessing consistency or risk.\n",
        "\n",
        "The common measures of dispersion are **range**, **interquartile range (IQR)**, **variance**, and **standard deviation**.\n",
        "\n",
        "---\n",
        "\n",
        "#### **1. Range**\n",
        "The range is the simplest measure of dispersion, calculated as the difference between the maximum and minimum values in a dataset.\n",
        "\n",
        "**Formula**:\n",
        "$$\n",
        "\\text{Range} = \\text{Maximum Value} - \\text{Minimum Value}\n",
        "$$\n",
        "\n",
        "**Example**:\n",
        "For the dataset \\([10, 20, 30, 40, 50]\\), the range is:\n",
        "$$\n",
        "\\text{Range} = 50 - 10 = 40\n",
        "$$\n",
        "\n",
        "**Pros**:\n",
        "- Easy to calculate and understand.\n",
        "\n",
        "**Cons**:\n",
        "- Sensitive to outliers.\n",
        "- Does not provide information about the distribution of data between extremes.\n",
        "\n",
        "---\n",
        "\n",
        "#### **2. Interquartile Range (IQR)**\n",
        "The interquartile range measures the spread of the middle 50% of the data, reducing the influence of outliers. It is calculated as the difference between the third quartile (\\(Q_3\\)) and the first quartile (\\(Q_1\\)).\n",
        "\n",
        "**Formula**:\n",
        "$$\n",
        "\\text{IQR} = Q_3 - Q_1\n",
        "$$\n",
        "\n",
        "**Steps**:\n",
        "1. Arrange the data in ascending order.\n",
        "2. Divide the data into four equal parts (quartiles).\n",
        "3. Subtract \\(Q_1\\) (25th percentile) from \\(Q_3\\) (75th percentile).\n",
        "\n",
        "**Example**:\n",
        "For the dataset \\([10, 20, 30, 40, 50]\\), \\(Q_1 = 20\\), \\(Q_3 = 40\\), so:\n",
        "$$\n",
        "\\text{IQR} = 40 - 20 = 20\n",
        "$$\n",
        "\n",
        "**Pros**:\n",
        "- Robust to outliers.\n",
        "- Focuses on the spread of the central data.\n",
        "\n",
        "**Cons**:\n",
        "- Does not account for the variability of extreme values.\n",
        "\n",
        "---\n",
        "\n",
        "#### **3. Variance**\n",
        "Variance quantifies the average squared deviation of each data point from the mean, providing a measure of data variability.\n",
        "\n",
        "**Formula**:\n",
        "$$\n",
        "\\text{Variance} (\\sigma^2) = \\frac{\\sum_{i=1}^n (x_i - \\bar{x})^2}{n}\n",
        "$$\n",
        "where \\(x_i\\) are the data points, \\(\\bar{x}\\) is the mean, and \\(n\\) is the number of data points.\n",
        "\n",
        "**Example**:\n",
        "For the dataset \\([10, 20, 30]\\), mean (\\(\\bar{x}\\)) is 20. Variance is:\n",
        "$$\n",
        "\\text{Variance} = \\frac{(10-20)^2 + (20-20)^2 + (30-20)^2}{3} = \\frac{100 + 0 + 100}{3} = 66.67\n",
        "$$\n",
        "\n",
        "**Pros**:\n",
        "- Uses all data points.\n",
        "- Important for inferential statistics and modelling.\n",
        "\n",
        "**Cons**:\n",
        "- Units are squared, which can be less interpretable.\n",
        "\n",
        "---\n",
        "\n",
        "#### **4. Standard Deviation**\n",
        "The standard deviation is the square root of the variance, bringing the units back to the same scale as the data.\n",
        "\n",
        "**Formula**:\n",
        "$$\n",
        "\\text{Standard Deviation} (\\sigma) = \\sqrt{\\text{Variance}}\n",
        "$$\n",
        "\n",
        "**Example**:\n",
        "Using the previous variance example (\\(66.67\\)):\n",
        "$$\n",
        "\\text{Standard Deviation} = \\sqrt{66.67} \\approx 8.16\n",
        "$$\n",
        "\n",
        "**Pros**:\n",
        "- Easy to interpret compared to variance.\n",
        "- Widely used in data analysis and probability.\n",
        "\n",
        "**Cons**:\n",
        "- Sensitive to outliers.\n",
        "\n",
        "---\n",
        "\n",
        "### **Comparison of Measures**\n",
        "| Measure         | When to Use                              | Advantages                     | Limitations                     |\n",
        "|------------------|------------------------------------------|--------------------------------|---------------------------------|\n",
        "| **Range**        | Quick assessment of variability          | Easy to calculate              | Ignores data distribution       |\n",
        "| **IQR**          | For datasets with outliers               | Robust to outliers             | Does not use all data points    |\n",
        "| **Variance**     | For statistical and theoretical models   | Uses all data points           | Units are squared               |\n",
        "| **Standard Deviation** | Interpreting spread in original units | Widely used; easy to interpret | Sensitive to outliers           |\n",
        "\n",
        "---\n",
        "\n",
        "### **Applications**\n",
        "- **Range**: Measuring the spread of prices in a market.\n",
        "- **IQR**: Identifying variability in median house prices.\n",
        "- **Variance/Standard Deviation**: Assessing risk in finance or consistency in manufacturing processes.\n",
        "\n",
        "By analysing measures of dispersion, you gain deeper insights into data variability, allowing better understanding and more informed decision-making."
      ],
      "metadata": {
        "id": "zSFsxrQoNixF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Use descriptive variable names to avoid conflicts with Julia's built-in functions\n",
        "max_val = maximum(df.FTHG)\n",
        "min_val = minimum(df.FTHG)\n",
        "println(\"Maximum goal scored by Home Team: \", max_val)\n",
        "println(\"Minimum goal scored by Home Team: \", min_val)\n",
        "println(\"Range of FTHG: \", max_val - min_val)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "c3vBH6cKKBZe",
        "outputId": "e8e67acf-aee0-4192-8f64-92f62b3aa89e"
      },
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Maximum goal scored by Home Team: 6\n",
            "Minimum goal scored by Home Team: 0\n",
            "Range of FTHG: 6\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Calculate quantiles\n",
        "quantiles = quantile(df.FTHG, [0.25, 0.5, 0.75]) # 25th, 50th (median), and 75th percentiles\n",
        "println(\"Quantiles of home team's goal scored distribution : \", quantiles)\n",
        "println(\"IQR of home team's goal scored distribution : \", quantiles[3]-quantiles[1])\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ho5Gk5C-ORzu",
        "outputId": "4f103ac3-9293-4b7a-a561-0dfe4bad6d5a"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Quantiles of home team's goal scored distribution : [1.0, 2.0, 3.0]\n",
            "IQR of home team's goal scored distribution : 2.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "println(\"Variance of goal scored by Home Team : \", var(df.FTHG))\n",
        "println(\"Variance of goal scored by Away Team : \", var(df.FTAG))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "93bCDupMQ75Z",
        "outputId": "d099a663-f319-4214-9edb-5dd3a140e0c1"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Variance of goal scored by Home Team : 1.8649076517150394\n",
            "Variance of goal scored by Away Team : 1.6328009998611304\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "println(\"Standard deviation of goal scored by Home Team : \", var(df.FTHG))\n",
        "println(\"Standard deviation of goal scored by Away Team : \", var(df.FTAG))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KerAqw0cRWtR",
        "outputId": "4e17ec96-5c48-48df-ddf1-718de3b89d66"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Standard deviation of goal scored by Home Team : 1.8649076517150394\n",
            "Standard deviation of goal scored by Away Team : 1.6328009998611304\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Count frequencies for FTHG and FTAG\n",
        "fthg_counts = combine(groupby(DataFrame(value=df.FTHG), :value), nrow => :count)\n",
        "ftag_counts = combine(groupby(DataFrame(value=df.FTAG), :value), nrow => :count)\n",
        "println(\"Frequency Table of Goals scored by Home Team : \",fthg_counts)\n",
        "println(\"Frequency Table of Goals scored by Away Team : \",ftag_counts)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "py4UJuA0bQZS",
        "outputId": "bf62eef3-6263-4def-e099-a31f00d0d994"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Frequency Table of Goals scored by Home Team : \u001b[1m7×2 DataFrame\u001b[0m\n",
            "\u001b[1m Row \u001b[0m│\u001b[1m value \u001b[0m\u001b[1m count \u001b[0m\n",
            "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\n",
            "─────┼──────────────\n",
            "   1 │     0     68\n",
            "   2 │     1    109\n",
            "   3 │     2     97\n",
            "   4 │     3     63\n",
            "   5 │     4     26\n",
            "   6 │     5     14\n",
            "   7 │     6      3\n",
            "Frequency Table of Goals scored by Away Team : \u001b[1m8×2 DataFrame\u001b[0m\n",
            "\u001b[1m Row \u001b[0m│\u001b[1m value \u001b[0m\u001b[1m count \u001b[0m\n",
            "     │\u001b[90m Int64 \u001b[0m\u001b[90m Int64 \u001b[0m\n",
            "─────┼──────────────\n",
            "   1 │     0     89\n",
            "   2 │     1    131\n",
            "   3 │     2     90\n",
            "   4 │     3     42\n",
            "   5 │     4     20\n",
            "   6 │     5      5\n",
            "   7 │     6      2\n",
            "   8 │     8      1\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Visualisation"
      ],
      "metadata": {
        "id": "Mg6eHZjrRy94"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Create side-by-side bar plots\n",
        "p1 = bar(fthg_counts.value, fthg_counts.count, title=\" Home Team\"\n",
        "            , xlabel=\"Number of Goals\", ylabel=\"Frequency\", legend=false)\n",
        "p2 = bar(ftag_counts.value, ftag_counts.count, title=\" Away Team\"\n",
        "             , xlabel=\"Number of Goals\", ylabel=\"Frequency\", legend=false\n",
        "             , colour = \"orange\")\n",
        "\n",
        "# Create a scatter plot\n",
        "p3 = scatter(\n",
        "        df.FTHG, df.FTAG,\n",
        "        title = \"Home  vs Away \",\n",
        "        xlabel = \"Goals by Home (FTHG)\",\n",
        "        ylabel = \"Goals by Away (FTAG)\",\n",
        "        legend = false,\n",
        "        markersize = 5,\n",
        "        colour = \"red\"\n",
        "    )\n",
        "\n",
        "p4 = scatter(\n",
        "        df.B365H, df.FTHG,\n",
        "        title=\"Odds vs Goal\",\n",
        "        xlabel=\"Odds of Home by Bet365\",\n",
        "        ylabel=\"Goals by Home (FTHG)\",\n",
        "        legend=false,\n",
        "        markersize=5,\n",
        "        color=\"blue\"\n",
        "    )\n",
        "\n",
        "# Display the plots in a 2x2 layout\n",
        "plot(p1, p2, p3, p4, layout=(2, 2))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 421
        },
        "id": "89d-ceorRvau",
        "outputId": "f934b89b-9c9b-4036-95c6-57f1406868ff"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "image/png": 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          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Calculate the correlation between B365H and FTHG\n",
        "correlation_value = cor(df.B365H, df.FTHG)\n",
        "println(\"Correlation between Bet365 Home Odds and Home Goals: \", correlation_value)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Gag3hG-nbPSO",
        "outputId": "191e1b7e-ed71-4003-81c7-226c3bec7ef2"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Correlation between Bet365 Home Odds and Home Goals: -0.3162673821156749\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Poisson Regression in the Context of Goal Scored by Home Team and Bet365 Odds\n",
        "\n",
        "Poisson regression is a type of generalised linear model (GLM) designed for modelling count data and rates of occurrence of events. The model assumes that the response variable $ Y $ follows a Poisson distribution, characterised by the probability mass function:\n",
        "$$\n",
        "P(Y = k) = \\frac{\\lambda^k e^{-\\lambda}}{k!}, \\quad k = 0, 1, 2, \\dots\n",
        "$$\n",
        "where $ \\lambda $ is the expected value (mean) of $ Y $ and also its variance. Poisson regression is particularly suited for situations where the outcome variable represents counts or frequencies.\n",
        "\n",
        "In the context of football, the number of goals scored by the home team (FTHG) in a match can be modelled using Poisson regression. The Bet365 odds for the home team ($ X $, B365H) serve as a predictor variable. The regression model establishes a relationship between the predictor and the expected count of goals ($ \\lambda $).\n",
        "\n",
        "The mathematical formulation of the Poisson regression model is:\n",
        "\n",
        "$$\n",
        "\\log(\\lambda) = \\beta_0 + \\beta_1 X\n",
        "$$\n",
        "\n",
        "where:\n",
        "\n",
        "- $ \\lambda $ is the expected count of goals (\\( \\mathbb{E}[Y] \\)).\n",
        "\n",
        "- $ \\beta_0 $ is the intercept, representing the baseline log-rate of goals when \\( X \\) (B365H odds) is zero.\n",
        "\n",
        "- $ \\beta_1 $ quantifies the change in the log-rate of goals for a unit change in \\( X \\).\n",
        "\n",
        "The logarithmic link function $ \\log(\\lambda) $ ensures that the predicted count remains non-negative. For example, if $ \\beta_1 $ is negative, it suggests that lower odds (better predicted chances of a home win) are associated with a higher expected number of goals scored by the home team.\n",
        "\n",
        "By applying Poisson regression, analysts can explore how betting market expectations, represented by B365H odds, align with or influence actual match outcomes, such as goal counts. This model provides a structured approach to uncovering the relationships between event counts and predictor variables in a football context."
      ],
      "metadata": {
        "id": "nyRTEzPheuDY"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "modl = fit(@formula(FTHG~B365H),df,PoissonRegression())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "F88sJHnIf32G",
        "outputId": "3a2b2d41-1264-4f06-d18e-912b0e9b2c5c"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Model Class: Poisson Regression\n",
              "Likelihood Mode: Poison\n",
              "Link Function: Log\n",
              "Computing Method: Optimization\n",
              "─────────────────────────────────────────────────────────────────────────\n",
              "                 Coef.  Std. Error      z  Pr(>|z|)  Lower 95%  Upper 95%\n",
              "─────────────────────────────────────────────────────────────────────────\n",
              "(Intercept)   1.03728    0.0754994  13.74    <1e-42   0.889305   1.18526\n",
              "B365H        -0.173252   0.0274976  -6.30    <1e-09  -0.227146  -0.119358\n",
              "─────────────────────────────────────────────────────────────────────────\n"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "b = coef(modl)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "hJmJXLStgPcr",
        "outputId": "290076e8-4e1d-4de7-fd12-bac1dcdfb55f"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2-element Vector{Float64}:\n",
              "  1.0372808760079697\n",
              " -0.17325191704402648"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "x0 = [1, 3 , 6]\n",
        "lambda_hat = exp.(b[1] .+ b[2]*x0)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "o8IqMu7jgfjM",
        "outputId": "dded3369-4c14-40e6-e8a4-30e1c2e1f7af"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3-element Vector{Float64}:\n",
              " 2.372700976965593\n",
              " 1.6778699882791348\n",
              " 0.9977718597417706"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Calculate the CDF for each Poisson distribution at k = 3\n",
        "cdf_values = [cdf(Poisson(λ), 3) for λ in lambda_hat]\n",
        "\n",
        "prob_more_3_goals = 1 .- cdf_values\n",
        "\n",
        "println(\"Prob that Home Team will score more tha 3 goals: \", prob_more_3_goals)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nTpnzWX5hUiz",
        "outputId": "89209eed-91dc-4d1a-e2dd-7a6097aff3d0"
      },
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Prob that Home Team will score more tha 3 goals: [0.2155910021981431, 0.0899071958659835, 0.0188518466602855]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "res = DataFrame(\n",
        "    B365H_Odds = x0,\n",
        "    lambda_hat = lambda_hat,\n",
        "    prob_more_3_goals = prob_more_3_goals\n",
        ")\n",
        "\n",
        "println(res)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ukzOaU2NkOKW",
        "outputId": "c1ab69a8-773c-4fb1-fed4-893984e408a4"
      },
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\u001b[1m3×3 DataFrame\u001b[0m\n",
            "\u001b[1m Row \u001b[0m│\u001b[1m B365H_Odds \u001b[0m\u001b[1m lambda_hat \u001b[0m\u001b[1m prob_more_3_goals \u001b[0m\n",
            "     │\u001b[90m Int64      \u001b[0m\u001b[90m Float64    \u001b[0m\u001b[90m Float64           \u001b[0m\n",
            "─────┼───────────────────────────────────────────\n",
            "   1 │          1    2.3727            0.215591\n",
            "   2 │          3    1.67787           0.0899072\n",
            "   3 │          6    0.997772          0.0188518\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "FTHG_hat= predict(modl,df)\n",
        "R2_mod1 = cor(FTHG_hat,df.FTHG)^2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yiQnlIDWpKPw",
        "outputId": "7bd5e20d-a72f-483c-cb9d-2cbdab46e444"
      },
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.1457371388225332"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "modl2 = fit(@formula(FTHG~B365H+B365A),df,PoissonRegression())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oIzRpxRImXRY",
        "outputId": "9ab1707c-6569-45c6-aca9-f69b842bb3a7"
      },
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Model Class: Poisson Regression\n",
              "Likelihood Mode: Poison\n",
              "Link Function: Log\n",
              "Computing Method: Optimization\n",
              "─────────────────────────────────────────────────────────────────────────────\n",
              "                  Coef.  Std. Error      z  Pr(>|z|)    Lower 95%   Upper 95%\n",
              "─────────────────────────────────────────────────────────────────────────────\n",
              "(Intercept)   0.78843    0.115006     6.86    <1e-11   0.563023     1.01384\n",
              "B365H        -0.128494   0.0300981   -4.27    <1e-04  -0.187485    -0.0695024\n",
              "B365A         0.0265285  0.00937552   2.83    0.0047   0.00815284   0.0449042\n",
              "─────────────────────────────────────────────────────────────────────────────\n"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "FTHG_hat= predict(modl2,df)\n",
        "R2_mod2 = cor(FTHG_hat,df.FTHG)^2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "IL-n4pXTpD4t",
        "outputId": "6d9e7d0f-ae6a-4a02-9b0c-6df17e035af0"
      },
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.1584919687523394"
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "modl3 = fit(@formula(FTHG~B365H+HST),df,PoissonRegression())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "w_tqac7Umzh_",
        "outputId": "a0649da9-0617-41a3-a9cf-d595d22cf5e8"
      },
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Model Class: Poisson Regression\n",
              "Likelihood Mode: Poison\n",
              "Link Function: Log\n",
              "Computing Method: Optimization\n",
              "────────────────────────────────────────────────────────────────────────────\n",
              "                  Coef.  Std. Error      z  Pr(>|z|)   Lower 95%   Upper 95%\n",
              "────────────────────────────────────────────────────────────────────────────\n",
              "(Intercept)   0.063115    0.133226    0.47    0.6357  -0.198003    0.324233\n",
              "B365H        -0.0755733   0.0270325  -2.80    0.0052  -0.128556   -0.0225906\n",
              "HST           0.119134    0.0129982   9.17    <1e-19   0.0936581   0.14461\n",
              "────────────────────────────────────────────────────────────────────────────\n"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "FTHG_hat= predict(modl3,df)\n",
        "R2_mod3 = cor(FTHG_hat,df.FTHG)^2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "4ApGpLZDoqBI",
        "outputId": "8869d476-612c-4388-8bb5-029aa68e995f"
      },
      "execution_count": 26,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.3143933647981"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Bayesian Poisson Regression"
      ],
      "metadata": {
        "id": "rt1Uhcn-r4nj"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "modl4 = fit(@formula(FTHG~B365H+HST),df,PoissonRegression(),Prior_Ridge())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wdA0hZBFn6wF",
        "outputId": "4ecfddd4-0b60-40d4-e5b3-a6a5c069e4c1"
      },
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "\u001b[36m\u001b[1m┌ \u001b[22m\u001b[39m\u001b[36m\u001b[1mInfo: \u001b[22m\u001b[39mFound initial step size\n",
            "\u001b[36m\u001b[1m└ \u001b[22m\u001b[39m  ϵ = 0.00625\n",
            "\u001b[32mSampling: 100%|█████████████████████████████████████████████████████████████| Time: 0:00:03\u001b[39m\n"
          ]
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Formula: FTHG ~ 1 + B365H + HST\n",
              "Link: CRRao.Identity(CRRao.Identity_Link)\n",
              "Chain: Chains MCMC chain (1000×16×1 Array{Float64, 3}):\n",
              "\n",
              "Iterations        = 501:1:1500\n",
              "Number of chains  = 1\n",
              "Samples per chain = 1000\n",
              "Wall duration     = 22.33 seconds\n",
              "Compute duration  = 22.33 seconds\n",
              "parameters        = λ, β[1], β[2], β[3]\n",
              "internals         = lp, n_steps, is_accept, acceptance_rate, log_density, hamiltonian_energy, hamiltonian_energy_error, max_hamiltonian_energy_error, tree_depth, numerical_error, step_size, nom_step_size\n",
              "\n",
              "Summary Statistics\n",
              " \u001b[1m parameters \u001b[0m \u001b[1m    mean \u001b[0m \u001b[1m     std \u001b[0m \u001b[1m    mcse \u001b[0m \u001b[1m ess_bulk \u001b[0m \u001b[1m ess_tail \u001b[0m \u001b[1m    rhat \u001b[0m \u001b[1m ess_per_sec \u001b[0m\n",
              " \u001b[90m     Symbol \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m  Float64 \u001b[0m \u001b[90m  Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m     Float64 \u001b[0m\n",
              "\n",
              "           λ    0.1477    0.1192    0.0069   349.3954   349.3958    1.0110       15.6497\n",
              "        β[1]    0.0347    0.0862    0.0043   418.1588   404.8596    1.0043       18.7297\n",
              "        β[2]   -0.0685    0.0220    0.0011   428.2123   493.9941    1.0079       19.1800\n",
              "        β[3]    0.1201    0.0098    0.0004   569.2947   409.8112    1.0038       25.4992\n",
              "\n",
              "Quantiles\n",
              " \u001b[1m parameters \u001b[0m \u001b[1m    2.5% \u001b[0m \u001b[1m   25.0% \u001b[0m \u001b[1m   50.0% \u001b[0m \u001b[1m   75.0% \u001b[0m \u001b[1m   97.5% \u001b[0m\n",
              " \u001b[90m     Symbol \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m Float64 \u001b[0m \u001b[90m Float64 \u001b[0m\n",
              "\n",
              "           λ    0.0571    0.0909    0.1195    0.1643    0.3928\n",
              "        β[1]   -0.1340   -0.0158    0.0340    0.0878    0.2240\n",
              "        β[2]   -0.1122   -0.0838   -0.0686   -0.0527   -0.0275\n",
              "        β[3]    0.1016    0.1139    0.1202    0.1263    0.1387\n"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "FTHG_hat = predict(modl4,df)\n",
        "R2_mod4 = cor(FTHG_hat,df.FTHG)^2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "v8gPknKboeWx",
        "outputId": "847fca79-c984-42f3-e1d4-f2b9ec21d682"
      },
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.3133798062366485"
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "[R2_mod1,R2_mod2,R2_mod3,R2_mod4]"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "I2Mmt0S3pdca",
        "outputId": "fa93f634-2290-4c26-987a-d307b1352422"
      },
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "4-element Vector{Float64}:\n",
              " 0.1457371388225332\n",
              " 0.1584919687523394\n",
              " 0.3143933647981\n",
              " 0.3133798062366485"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# **Wrap-Up**\n",
        "\n",
        "In this session, we explored various aspects of data analysis and modelling using Julia, focusing on practical applications in statistics. Key highlights included:\n",
        "\n",
        "1. **Data Manipulation**:\n",
        "   - We learned to import and preprocess data using `CSV.jl` and `DataFrames.jl`.\n",
        "   - Frequency calculations and creating visualisations like bar plots and scatter plots provided insights into the data.\n",
        "\n",
        "2. **Statistical Measures**:\n",
        "   - Calculated measures of central tendency (mean, median, mode) and dispersion (variance, standard deviation, range).\n",
        "   - Computed quantiles to understand data distribution better.\n",
        "\n",
        "3. **Modelling and Inference**:\n",
        "   - Applied regression models, including Poisson regression, to establish relationships between variables such as home goals and Bet365 odds.\n",
        "   - Discussed the mathematical basis of Poisson regression and how it is used to predict count data.\n",
        "\n",
        "4. **Visualisation**:\n",
        "   - Created meaningful visualisations like bar plots, histograms, and scatter plots to summarise and interpret data relationships.\n",
        "\n",
        "5. **Correlation**:\n",
        "   - Explored relationships between numerical variables using correlation, showcasing the connection between betting odds and match outcomes.\n",
        "\n",
        "By leveraging Julia's robust ecosystem of packages, we efficiently performed complex data analysis and statistical modelling tasks. Julia’s high performance and ease of use make it an excellent choice for real-world data analysis, especially for large datasets and computationally intensive tasks.\n",
        "\n",
        "Feel free to continue exploring Julia for more advanced statistical analyses, machine learning, and custom visualisations. Thank you for your attention, and happy coding! 🎉"
      ],
      "metadata": {
        "id": "aTjIP8iIqkjv"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Q&A"
      ],
      "metadata": {
        "id": "gavE-iZOqzV1"
      }
    }
  ]
}