Lab_6_Simple_Linear_Regression_Solution.ipynb

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      "name": "python3",
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      "name": "python"
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        "<a href=\"https://colab.research.google.com/github/Root-0/CSE317-Lab/blob/main/Lab_6_Simple_Linear_Regression_Solution.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aye6_J7499fJ"
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      "source": [
        "## **Problem Statement:**\n",
        "Suppose you want to predict the price of a book from the number of pages it has. You collected some data and it is stored in a csv file named bookprice.csv\n",
        "\n",
        "The n = 10 data points (a<sub>k</sub>, b<sub>k</sub>), where k = 1, 2, ..., 10  are given as below, on the right is the scatter plot of the data:\n",
        "\n",
        "<table>\n",
        "  <tr>\n",
        "    <td colspan=\"2\" align=\"center\">Data Points</td>\n",
        "    <td align=\"center\">Scatter Plot</td>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td align=\"center\">a</td>\n",
        "    <td align=\"center\">b</td>\n",
        "    <td rowspan=\"11\" align=\"center\">\n",
        "      <img 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\" alt=\"Scatter Plot\" />\n",
        "    </td>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td align=\"center\">166</td>\n",
        "    <td align=\"center\">54</td>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td align=\"center\">195</td>\n",
        "    <td align=\"center\">82</td>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td align=\"center\">200</td>\n",
        "    <td align=\"center\">72</td>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td align=\"center\">260</td>\n",
        "    <td align=\"center\">72</td>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td align=\"center\">265</td>\n",
        "    <td align=\"center\">90</td>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td align=\"center\">335</td>\n",
        "    <td align=\"center\">124</td>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td align=\"center\">370</td>\n",
        "    <td align=\"center\">94</td>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td align=\"center\">450</td>\n",
        "    <td align=\"center\">118</td>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td align=\"center\">517</td>\n",
        "    <td align=\"center\">152</td>\n",
        "  </tr>\n",
        "  <tr>\n",
        "    <td align=\"center\">552</td>\n",
        "    <td align=\"center\">132</td>\n",
        "  </tr>\n",
        "</table>\n",
        "\n",
        "\n",
        "What we want is to get the least square line that fits the data.\n",
        "\n",
        "That is, we want to find the coefficients $c_1$ and $c_2$ of a linear function $f(x) = c_1 + c_2 x$ such that, mean squared error $J = \\frac{1}{n} \\left\\|f(a)-b\\right\\|^2 $ is minimized.\n",
        "\n",
        "Now we know from the lecture that the values of $c_1$ and $c_2$ for which $J$ is minimum is given by,\n",
        "$$c_1 = avg(b) - avg(a)c_2 \\text{ and } c_2 = \\rho std(b)/std(a)$$\n",
        "\n",
        "You are to use the procedure below to find and plot the least square line for the above data.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L_m0EBogKK3S"
      },
      "source": [
        "## **Procedure:**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "crbxWmm56UA1"
      },
      "source": [
        "#### **1. Import necessary packages:**\n",
        "To read the data from csv file we will use a python package named **\"pandas\"**. To start working with pandas we first need to import it. We will also import other necessary packages that will be needed for this lab exercise."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "K4UgfP8N5-PL"
      },
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Mx72zbCvK-xa"
      },
      "source": [
        "#### **2. Upload and load dataset:**\n",
        "At first we have to upload the dataset to google colab to start working with it. Please download the **\"bookprice.csv\"** dataset from piazza resourse or [click here](https://piazza.com/class_profile/get_resource/ku1fdd7zhev3r2/ku7c2kiquo514q) to download it. Then click on files form sidebar, drag and drop your file to side bar to upload the dataset.\n",
        "\n",
        "Now, use `data = pd.read_csv(\"bookprice.csv\")` to load the data.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_v5J2XrWA85K"
      },
      "source": [
        "# Write appropriate code here\n",
        "data = pd.read_csv(\"bookprice.csv\")"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mCr8VqgRNz0w"
      },
      "source": [
        "#### **3. Seperate the data:**\n",
        "You can use simple indexing (**i.e.** `data['a']`) to seperate the data into a, b. By default this will return a panda dataset. To convet it to numpy array use `to_numpy()` method."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "fSg4SNysCtDV"
      },
      "source": [
        "# Write appropriate code here\n",
        "a = data['a']\n",
        "b = data['b']\n",
        "\n",
        "a = a.to_numpy()\n",
        "b = b.to_numpy()"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PABJcZetTvmG"
      },
      "source": [
        "#### **4. Plot the data:**\n",
        "Draw a scatter plot using `plt.scatter(a, b)`"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "l5jww1hNUKYj",
        "outputId": "813a13d6-6d46-41fd-f345-56c5630dd300"
      },
      "source": [
        "# Write appropriate code here\n",
        "plt.scatter(a, b)\n",
        "plt.xlabel('pages')\n",
        "plt.ylabel('price')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": "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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jPL1W0X6PYSi"
      },
      "source": [
        "#### **5. Find the value of $c_1$ and $c_2$:**\n",
        "1.   First compute the demean vectors $\\tilde{a}$ and $\\tilde{b}$\n",
        "2.   Use the demeaned vectors $\\tilde{a}$ and $\\tilde{b}$ to compute $\\rho$, $std(a)$, and $std(b)$\n",
        "3.   Use the equation given in problem statement to find the value of $c_1$ and $c_2$\n",
        "\n",
        "[**Note:** The values you should get are $c_1 = 31.2181$ and $c_2 = 0.2048$]"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "o93HQF9lRHTv",
        "outputId": "228b6cbf-bdaf-45ae-e9c3-9a533e54af4c"
      },
      "source": [
        "# Write appropriate code here\n",
        "avg_a = np.dot(np.ones(a.size), a)/a.size\n",
        "avg_b = np.dot(np.ones(b.size), b)/b.size\n",
        "print(avg_a, avg_b)\n",
        "\n",
        "a_tilde = a - avg_a\n",
        "b_tilde = b - avg_b\n",
        "\n",
        "std_a = np.sqrt(np.dot((a - avg_a), (a - avg_a))/(a.size-1))\n",
        "std_b = np.sqrt(np.dot((b - avg_b), (b - avg_b))/(b.size-1))\n",
        "print(std_a, std_b)\n",
        "\n",
        "rho = np.dot(a_tilde, b_tilde)/(np.sqrt(np.dot(a_tilde, a_tilde))*np.sqrt(np.dot(b_tilde, b_tilde)))\n",
        "print(rho)\n",
        "\n",
        "c_2 = (rho*std_b)/std_a\n",
        "c_1 = avg_b - avg_a*c_2\n",
        "\n",
        "print(c_1, c_2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "331.0 99.0\n",
            "138.00724618656804 31.201851796897497\n",
            "0.9057473931307639\n",
            "31.218126874117644 0.20477907288786212\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IkjPDxW3R8Cn"
      },
      "source": [
        "#### **6. Generate and fit data:**\n",
        "Use `np.linspace()` method to generate some data (page numbers) and plot the least square fit line (price) on the scatter plot. The graph of the fitted line should look like the following figure:\n",
        "\n",
        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)\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "YKj1EapcDXwB",
        "outputId": "5c5bdc1a-4e15-4fe0-da38-e305e00efd6b"
      },
      "source": [
        "# Write appropriate code here\n",
        "x = np.linspace(160, 555, 1000)\n",
        "y = c_1 + c_2*x\n",
        "\n",
        "plt.plot(a, b, 'o')\n",
        "plt.plot(x, y)\n",
        "plt.xlabel('pages')\n",
        "plt.ylabel('price')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gVefi7w5aDzn"
      },
      "source": [
        "#### **7. Using numpy function: polyfit():**\n",
        "Numpy has its own polynomial fit function called polyfit. Use `np.polyfit(a, b, 1)` to get the coffecients (make sure you understand the order of the coefficients produced).\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "id": "iXa1d62gagjY",
        "outputId": "23125ba5-791c-47e5-c7f1-8c71e380d441"
      },
      "source": [
        "# Write appropriate code here\n",
        "nc_2, nc_1 = np.polyfit(a, b, 1)\n",
        "\n",
        "x = np.linspace(160, 555, 1000)\n",
        "ny = nc_1 + nc_2*x\n",
        "\n",
        "plt.plot(a, b, 'o')\n",
        "plt.plot(x, ny)\n",
        "plt.xlabel('pages')\n",
        "plt.ylabel('price')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "x9UPrCd8bCW9"
      },
      "source": [
        "#### **8. Plot the quadratic polynomial:**\n",
        "The Last argument in the `np.polyfit()` function should be 1 if you want a fit a linear function. It can be some other number which will indicate the degree of the polynomial you want to fit. Plot the quadratic polynomial that fits the data.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3KiNXeFobvkm",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "outputId": "b7e423b7-6f56-44ff-ffe1-12e60d29da81"
      },
      "source": [
        "# Write appropriate code here\n",
        "nc_4, nc_3, nc_2, nc_1 = np.polyfit(a, b, 3)\n",
        "\n",
        "x = np.linspace(160, 555, 1000)\n",
        "ny = nc_1 + nc_2*x + nc_3*x**2 + nc_4*x**3\n",
        "\n",
        "plt.plot(a, b, 'o')\n",
        "plt.plot(x, ny)\n",
        "plt.xlabel('pages')\n",
        "plt.ylabel('price')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LGGMaVMVcDAf"
      },
      "source": [
        "#### **9. Goodness of fit: $r^2$ statistic:**\n",
        "A commonly used statistic that is related to the error, but is not the same as the error is the goodness-of-fit $r^2$ (r-squared) statistic. The $r^2$ statistic ranges from a value of $0$ for absolutely no relation between\n",
        "the data and the line to a value of $1$ which occurs only if all of the data fall exactly on the line, **i.e.**, no error. In some engineering disciplines, an equation fitted to data is acceptable only if $r^2 > 0.9$. Other\n",
        "engineering disciplines might find an $r^2$ low as $0.7$ acceptable for use.\n",
        "\n",
        "The $r^2$ statistic is computed as follows: \\\\\n",
        "\n",
        "$r^2 = 1 - SSE / SST$, where $SSE$ is the sum of squared errors: $(b - \\text{b_pred})^T(b - \\text{b_pred})$ and $SST = \\text{Total sum of squares : } (b - avg(b))^T(b - avg(b))$\n",
        "\n",
        "\n",
        "Find the **SSE** and **SST** values for the given data and the value of $r^2$ statistic.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "33729c-deQGW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1a215b51-c1e4-48eb-b32c-b285237f0090"
      },
      "source": [
        "# Write appropriate code here\n",
        "b_pred = c_1 + c_2*a\n",
        "\n",
        "SSE = np.dot((b-b_pred), (b-b_pred))\n",
        "SST = np.dot((b-avg_b), (b-avg_b))\n",
        "\n",
        "r_squared = 1 - SSE/SST\n",
        "\n",
        "print(r_squared)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "0.8203783401631748\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2zLJdD4KeJD8"
      },
      "source": [
        "#### **10. Displaying the equation on the graph:**\n",
        "1.   Create a string that contains the equation. You can insert a number to a string and formate as follow: `eqn = 'y = %.2f + %.2fx' %(c_1, c_2)`\n",
        "2.   Use `plt.text(Xcor, Ycor, 'string'`) to display the equation on the graph.\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 388
        },
        "id": "EbzZQ8Pkfq7p",
        "outputId": "bfbcbb22-3141-4f6d-8329-f358eac84f91"
      },
      "source": [
        "# Write appropriate code here\n",
        "eqn = 'y = %.2f + %.2fx' %(c_1, c_2)\n",
        "\n",
        "plt.subplots(figsize=(10,6))\n",
        "\n",
        "plt.plot(a, b, 'o')\n",
        "plt.text(400, 105, eqn, fontsize=10)\n",
        "plt.plot(x, y)\n",
        "plt.xlabel('pages')\n",
        "plt.ylabel('price')\n",
        "plt.title('Scatter Plot of Linear Regression')\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BL0H8sGCl57_"
      },
      "source": [
        "## **Exercise:**\n",
        "A healthy child’s systolic blood pressure p (in millimeters of mercury) and weight w (in pounds) are approximately related by the equation,\n",
        "\n",
        "$$p = \\beta_0 + \\beta_1 \\log(w)$$\n",
        "\n",
        "\n",
        "Use the following experimental data to estimate the systolic blood pressure of a healthy child weighing 100 pounds.\n",
        "\n",
        "<table>\n",
        "  <tr>\n",
        "    <td>w</td>\n",
        "    <td>44</td>\n",
        "    <td>61</td>\n",
        "    <td>81</td>\n",
        "    <td>113</td>\n",
        "    <td>131</td>\n",
        "  </tr>\n",
        "\n",
        "  <tr>\n",
        "    <td>p</td>\n",
        "    <td>91</td>\n",
        "    <td>98</td>\n",
        "    <td>103</td>\n",
        "    <td>110</td>\n",
        "    <td>112</td>\n",
        "  </tr>\n",
        "</table>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ahlLlK3lnEFt",
        "outputId": "a557cf15-dcdf-47f4-8817-65bd9728ed01",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 691
        }
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy import stats\n",
        "\n",
        "def analyze_blood_pressure(weights, pressures, target_weight=100):\n",
        "\n",
        "    log_weights = np.log(weights)\n",
        "\n",
        "    slope, intercept, r_value, p_value, std_err = stats.linregress(log_weights, pressures)\n",
        "\n",
        "    target_log_weight = np.log(target_weight)\n",
        "    predicted_pressure = slope * target_log_weight + intercept\n",
        "\n",
        "    plt.figure(figsize=(10, 6))\n",
        "\n",
        "    plt.scatter(weights, pressures, color='blue', label='Actual Data')\n",
        "\n",
        "    x_range = np.linspace(min(weights), max(weights), 100)\n",
        "    y_predicted = slope * np.log(x_range) + intercept\n",
        "    plt.plot(x_range, y_predicted, color='red', label='Regression Line')\n",
        "\n",
        "    plt.scatter([target_weight], [predicted_pressure], color='green',\n",
        "                s=100, label=f'Prediction ({target_weight} lbs)')\n",
        "\n",
        "    plt.xlabel('Weight (pounds)')\n",
        "    plt.ylabel('Systolic Blood Pressure (mmHg)')\n",
        "    plt.title('Blood Pressure vs. Weight with Logarithmic Regression')\n",
        "    plt.legend()\n",
        "    plt.grid(True)\n",
        "\n",
        "    return predicted_pressure, slope, intercept, r_value\n",
        "\n",
        "\n",
        "weights = np.array([44, 61, 81, 113, 131])\n",
        "pressures = np.array([91, 98, 103, 110, 112])\n",
        "\n",
        "prediction, beta1, beta0, r_value = analyze_blood_pressure(weights, pressures)\n",
        "\n",
        "print(f\"\\nRegression Results:\")\n",
        "print(f\"β₀ (intercept): {beta0:.3f}\")\n",
        "print(f\"β₁ (slope): {beta1:.3f}\")\n",
        "print(f\"R² value: {r_value**2:.3f}\")\n",
        "print(f\"\\nPredicted blood pressure for 100 lbs: {prediction:.1f} mmHg\")\n",
        "\n",
        "plt.show()"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "\n",
            "Regression Results:\n",
            "β₀ (intercept): 17.924\n",
            "β₁ (slope): 19.385\n",
            "R² value: 0.998\n",
            "\n",
            "Predicted blood pressure for 100 lbs: 107.2 mmHg\n"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1000x600 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    }
  ]
}