Correlation_and_scatter_plots_.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "\n",
        "def calculate_correlation(x, y):\n",
        "    \"\"\"\n",
        "    Calculate the correlation coefficient between two variables.\n",
        "    \"\"\"\n",
        "    mean_x = np.mean(x)\n",
        "    mean_y = np.mean(y)\n",
        "    numerator = np.sum((x - mean_x) * (y - mean_y))\n",
        "    denominator = np.sqrt(np.sum((x - mean_x) ** 2) * np.sum((y - mean_y) ** 2))\n",
        "    correlation = numerator / denominator\n",
        "    return correlation\n",
        "\n",
        "def main():\n",
        "    # Example data\n",
        "    x = np.array([1, 2, 3, 4, 5])\n",
        "    y = np.array([2, 3, 4, 5, 6])\n",
        "\n",
        "    # Calculate correlation coefficient\n",
        "    correlation = calculate_correlation(x, y)\n",
        "    print(f\"Correlation coefficient: {correlation}\")\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    main()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "1LM2F0jaZnOn",
        "outputId": "d4b06ea0-62d8-473d-94a7-b1a9f7134073"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Correlation coefficient: 1.0\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def plot_scatter(x, y):\n",
        "    \"\"\"\n",
        "    Create a scatter plot to visualize the relationship between two variables.\n",
        "    \"\"\"\n",
        "    plt.scatter(x, y, alpha=0.7)\n",
        "    plt.xlabel('X')\n",
        "    plt.ylabel('Y')\n",
        "    plt.title('Scatter Plot')\n",
        "    plt.grid(True)\n",
        "    plt.show()\n",
        "\n",
        "def main():\n",
        "    # Example data\n",
        "    x = np.array([1, 2, 3, 4, 5])\n",
        "    y = np.array([2, 3, 4, 5, 6])\n",
        "\n",
        "    # Plot scatter plot\n",
        "    plot_scatter(x, y)\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    main()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "id": "SLHZrhfnZphy",
        "outputId": "2583256a-8f27-4ee1-e5a7-d16908476ac4"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 489
        },
        "id": "DBPuFysDZKB6",
        "outputId": "97572f7c-0347-4627-87ec-5f6ae18c45d5"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Correlation coefficient: 1.0\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "def calculate_correlation(x, y):\n",
        "    \"\"\"\n",
        "    Calculate the correlation coefficient between two variables.\n",
        "    \"\"\"\n",
        "    mean_x = np.mean(x)\n",
        "    mean_y = np.mean(y)\n",
        "    numerator = np.sum((x - mean_x) * (y - mean_y))\n",
        "    denominator = np.sqrt(np.sum((x - mean_x) ** 2) * np.sum((y - mean_y) ** 2))\n",
        "    correlation = numerator / denominator\n",
        "    return correlation\n",
        "\n",
        "def plot_scatter(x, y):\n",
        "    \"\"\"\n",
        "    Create a scatter plot to visualize the relationship between two variables.\n",
        "    \"\"\"\n",
        "    plt.scatter(x, y)\n",
        "    plt.xlabel('X')\n",
        "    plt.ylabel('Y')\n",
        "    plt.title('Scatter Plot')\n",
        "    plt.grid(True)\n",
        "    plt.show()\n",
        "\n",
        "def main():\n",
        "    # Example data\n",
        "    x = np.array([1, 2, 3, 4, 5])\n",
        "    y = np.array([2, 3, 4, 5, 6])\n",
        "\n",
        "    # Calculate correlation coefficient\n",
        "    correlation = calculate_correlation(x, y)\n",
        "    print(f\"Correlation coefficient: {correlation}\")\n",
        "\n",
        "    # Plot scatter plot\n",
        "    plot_scatter(x, y)\n",
        "\n",
        "if __name__ == \"__main__\":\n",
        "    main()"
      ]
    }
  ]
}