linear-regression.ipynb

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    "## <a class=\"anchor\" id=\"5\"></a>\n",
    "<div style=\"background-color: #2980b9; padding: 20px; border-radius: 10px; box-shadow: 0 6px 12px rgba(0, 0, 0, 0.1); text-align: center; margin-top: 20px;\">\n",
    "    <h2 style=\"color: #ecf0f1; font-size: 30px; font-weight: bold; margin: 0;\">\n",
    "       Linear Regression\n",
    "    </h2>\n",
    "</div>\n"
   ]
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    "## Table of Contents\n",
    "\n",
    "1. [Introduction to Linear Regression](#1)\n",
    "2. [History of Linear Regression](#2)\n",
    "3. [Importance in Machine Learning and Statistics](#3)\n",
    "4. [Assumptions of Linear Regression](#4)\n",
    "5. [Implementation of Linear Regression Using NumPy](#5)\n",
    "6. [Implementation of Linear Regression Using Scikit-Learn](#6)\n",
    "7. [Kaggle Challenges and Linear Regression](#7)\n"
   ]
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    "## <a class=\"anchor\" id=\"1\"></a>\n",
    "<div style=\"background-color: #e8f6f3; padding: 20px; border-radius: 12px; box-shadow: 0 6px 12px rgba(0, 0, 0, 0.1); text-align: center; margin-top: 20px;\">\n",
    "    <h2 style=\"color: #2c3e50; font-size: 25px; font-weight: bold; margin: 0;\">\n",
    "        Introduction to Linear Regression\n",
    "    </h2>\n",
    "</div>\n",
    "\n",
    "<p>Linear regression is a statistical method used to model the relationship between a dependent variable (target) and one or more independent variables (features). Simple linear regression involves a single feature and is used to predict the target based on the linear relationship. </p>\n",
    "\n",
    "\n",
    "## <a class=\"anchor\" id=\"2\"></a>\n",
    "<div style=\"background-color: #e8f6f3; padding: 20px; border-radius: 12px; box-shadow: 0 6px 12px rgba(0, 0, 0, 0.1); text-align: center; margin-top: 20px;\">\n",
    "    <h2 style=\"color: #2c3e50; font-size: 25px; font-weight: bold; margin: 0;\">\n",
    "        History of Linear Regression\n",
    "    </h2>\n",
    "</div>\n",
    "\n",
    "<p>Linear regression has its roots in the early 19th century. It was initially developed by Carl Friedrich Gauss, a German mathematician and later by Sir Francis Galton, a British statistician. The method was used to study the relationship between different variables such as the correlation between parents' heights and their children's heights.</p>\n",
    "\n",
    "## <a class=\"anchor\" id=\"3\"></a>\n",
    "<div style=\"background-color: #e8f6f3; padding: 20px; border-radius: 12px; box-shadow: 0 6px 12px rgba(0, 0, 0, 0.1); text-align: center; margin-top: 20px;\">\n",
    "    <h2 style=\"color: #2c3e50; font-size: 25px; font-weight: bold; margin: 0;\">\n",
    "        Importance in Machine Learning and Statistics\n",
    "    </h2>\n",
    "</div>\n",
    "\n",
    "<p>Linear regression is highly important in both machine learning and statistics because it's simple and helps us understand how different things relate to each other. In machine learning, it's a basic way to see how variables connect which is great for beginners and as a starting point for more complicated models. It's also good at handling big sets of data. In statistics, linear regression is key for testing ideas and figuring out how one thing affects another. The numbers in the model tell us how strong these connections are which helps people make decisions based on data.</p>\n",
    "\n",
    "## <a class=\"anchor\" id=\"4\"></a>\n",
    "<div style=\"background-color: #e8f6f3; padding: 20px; border-radius: 12px; box-shadow: 0 6px 12px rgba(0, 0, 0, 0.1); text-align: center; margin-top: 20px;\">\n",
    "    <h2 style=\"color: #2c3e50; font-size: 25px; font-weight: bold; margin: 0;\">\n",
    "        Assumptions of Linear Regression\n",
    "    </h2>\n",
    "</div>\n",
    "\n",
    "<ul>\n",
    "    <li>The relationship between the dependent and independent variables should be linear.</li>\n",
    "    <li>Observations should be independent.</li>\n",
    "    <li>The variance of the error terms should be constant.</li>\n",
    "    <li>The error terms should be normally distributed.</li>\n",
    "    <li>Independent variables should not be too highly correlated.</li>\n",
    "</ul>\n",
    "\n",
    "## <a class=\"anchor\" id=\"5\"></a>\n",
    "<div style=\"background-color: #e8f6f3; padding: 20px; border-radius: 12px; box-shadow: 0 6px 12px rgba(0, 0, 0, 0.1); text-align: center; margin-top: 20px;\">\n",
    "    <h2 style=\"color: #2c3e50; font-size: 25px; font-weight: bold; margin: 0;\">\n",
    "        Implementation of Linear Regression Using NumPy\n",
    "    </h2>\n",
    "</div>\n",
    "\n",
    "<p>Let's start by implementing linear regression from scratch using NumPy.</p>\n"
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    "## Step 1: Data Preparation¶\n",
    "\n",
    "We'll use a simple dataset for demonstration:\n",
    "\n",
    "    House sizes (1000 sqft): [1.0, 2.0, 3.0]\n",
    "    Prices (1000s of dollars): [300.0, 500.0, 700.0]\n"
   ]
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     "text": [
      "x_train = [1. 2. 3.]\n",
      "y_train = [300. 500. 700.]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x_train = np.array([1.0, 2.0, 3.0])\n",
    "y_train = np.array([300.0, 500.0, 700.0])\n",
    "\n",
    "print(f\"x_train = {x_train}\")\n",
    "print(f\"y_train = {y_train}\")"
   ]
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   "source": [
    "## Step 2: Exploratory Data Analysis\n",
    "\n",
    "Visualize the data to understand the relationship between size and price."
   ]
  },
  {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x_train, y_train, marker='x', c='r')\n",
    "plt.title(\"Housing Prices\")\n",
    "plt.xlabel('Size (1000 sqft)')\n",
    "plt.ylabel('Price (1000s of dollars)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "501c0aa8",
   "metadata": {
    "papermill": {
     "duration": 0.006029,
     "end_time": "2024-07-11T21:19:55.427748",
     "exception": false,
     "start_time": "2024-07-11T21:19:55.421719",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Step 3: Model Definition\n",
    "\n",
    "Define the hypothesis function and cost function. \n",
    "\n",
    "In linear regression, the hypothesis function predicts an output based on input data. It's like a rule or equation that the model uses to make predictions.\n",
    "\n",
    "The cost function measures how wrong the model's predictions are compared to the actual data. It quantifies the difference between predicted values and observed values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "64427648",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-07-11T21:19:55.441961Z",
     "iopub.status.busy": "2024-07-11T21:19:55.441575Z",
     "iopub.status.idle": "2024-07-11T21:19:55.447441Z",
     "shell.execute_reply": "2024-07-11T21:19:55.446351Z"
    },
    "papermill": {
     "duration": 0.015454,
     "end_time": "2024-07-11T21:19:55.449541",
     "exception": false,
     "start_time": "2024-07-11T21:19:55.434087",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def compute_cost(x, y, w, b):\n",
    "    m = x.shape[0]\n",
    "    cost = 0\n",
    "    for i in range(m):\n",
    "        f_wb = w * x[i] + b\n",
    "        cost += (f_wb - y[i]) ** 2\n",
    "    return cost / (2 * m)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd1f8995",
   "metadata": {
    "papermill": {
     "duration": 0.00598,
     "end_time": "2024-07-11T21:19:55.461699",
     "exception": false,
     "start_time": "2024-07-11T21:19:55.455719",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Step 4: Gradient Descent\n",
    "\n",
    "Gradient descent is an optimization algorithm used to minimize the cost function of a machine learning model. It works by iteratively adjusting the model's parameters in the direction that reduces the cost function the most. Think of the cost function as a bowl-shaped surface in a multi-dimensional space where each dimension represents a model parameter. The goal of gradient descent is to find the lowest point (global minimum) of this bowl which corresponds to the optimal values of the model parameters that best fit the data. By calculating the gradient (slope) of the cost function with respect to each parameter, gradient descent determines the direction and magnitude of parameter updates. It repeats this process iteratively until convergence gradually refining the model's predictions to improve accuracy.\n",
    "\n",
    "Implement the gradient descent algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "e04a5bbb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-07-11T21:19:55.475677Z",
     "iopub.status.busy": "2024-07-11T21:19:55.475276Z",
     "iopub.status.idle": "2024-07-11T21:19:55.481976Z",
     "shell.execute_reply": "2024-07-11T21:19:55.480934Z"
    },
    "papermill": {
     "duration": 0.016525,
     "end_time": "2024-07-11T21:19:55.484389",
     "exception": false,
     "start_time": "2024-07-11T21:19:55.467864",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def gradient_descent(x, y, w, b, alpha, num_iters):\n",
    "    m = x.shape[0]\n",
    "    for _ in range(num_iters):\n",
    "        dj_dw = 0\n",
    "        dj_db = 0\n",
    "        for i in range(m):\n",
    "            f_wb = w * x[i] + b\n",
    "            dj_dw += (f_wb - y[i]) * x[i]\n",
    "            dj_db += (f_wb - y[i])\n",
    "        w -= alpha * dj_dw / m\n",
    "        b -= alpha * dj_db / m\n",
    "    return w, b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "922e1720",
   "metadata": {
    "papermill": {
     "duration": 0.006006,
     "end_time": "2024-07-11T21:19:55.496663",
     "exception": false,
     "start_time": "2024-07-11T21:19:55.490657",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Step 5: Training the Model\n",
    "\n",
    "Train the model using gradient descent:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "893cb132",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-07-11T21:19:55.510709Z",
     "iopub.status.busy": "2024-07-11T21:19:55.510320Z",
     "iopub.status.idle": "2024-07-11T21:19:55.520897Z",
     "shell.execute_reply": "2024-07-11T21:19:55.519674Z"
    },
    "papermill": {
     "duration": 0.02064,
     "end_time": "2024-07-11T21:19:55.523474",
     "exception": false,
     "start_time": "2024-07-11T21:19:55.502834",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "w: 201.33075881026207, b: 96.97487242984855\n"
     ]
    }
   ],
   "source": [
    "w = 0\n",
    "b = 0\n",
    "alpha = 0.01\n",
    "num_iters = 1000\n",
    "\n",
    "w, b = gradient_descent(x_train, y_train, w, b, alpha, num_iters)\n",
    "print(f\"w: {w}, b: {b}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20fb2a80",
   "metadata": {
    "papermill": {
     "duration": 0.006629,
     "end_time": "2024-07-11T21:19:55.536493",
     "exception": false,
     "start_time": "2024-07-11T21:19:55.529864",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Step 6: Visualizing the Result\n",
    "\n",
    "Plot the data and the regression line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c3586488",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-07-11T21:19:55.552107Z",
     "iopub.status.busy": "2024-07-11T21:19:55.551681Z",
     "iopub.status.idle": "2024-07-11T21:19:55.865300Z",
     "shell.execute_reply": "2024-07-11T21:19:55.864211Z"
    },
    "papermill": {
     "duration": 0.323638,
     "end_time": "2024-07-11T21:19:55.867554",
     "exception": false,
     "start_time": "2024-07-11T21:19:55.543916",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x_train, y_train, marker='x', c='r', label='Training Data')\n",
    "plt.plot(x_train, w * x_train + b, label='Linear Regression')\n",
    "plt.title(\"Housing Prices\")\n",
    "plt.xlabel('Size (1000 sqft)')\n",
    "plt.ylabel('Price (1000s of dollars)')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "90c9dfdf",
   "metadata": {
    "papermill": {
     "duration": 0.006534,
     "end_time": "2024-07-11T21:19:55.880978",
     "exception": false,
     "start_time": "2024-07-11T21:19:55.874444",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## <a class=\"anchor\" id=\"6\"></a>\n",
    "<div style=\"background-color: #e8f6f3; padding: 20px; border-radius: 12px; box-shadow: 0 6px 12px rgba(0, 0, 0, 0.1); text-align: center; margin-top: 20px;\">\n",
    "    <h2 style=\"color: #2c3e50; font-size: 25px; font-weight: bold; margin: 0;\">\n",
    "        Implementation of Linear Regression Using Scikit-Learn\n",
    "    </h2>\n",
    "</div>\n",
    "\n",
    "\n",
    "<p>Now, let's implement linear regression using the scikit-learn library which simplifies the process.</p>\n",
    "\n",
    "## Step 1: Data Preparation\n",
    "\n",
    "We'll use the same dataset as before:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "ad618d95",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-07-11T21:19:55.896868Z",
     "iopub.status.busy": "2024-07-11T21:19:55.895944Z",
     "iopub.status.idle": "2024-07-11T21:19:57.210663Z",
     "shell.execute_reply": "2024-07-11T21:19:57.209496Z"
    },
    "papermill": {
     "duration": 1.325659,
     "end_time": "2024-07-11T21:19:57.213409",
     "exception": false,
     "start_time": "2024-07-11T21:19:55.887750",
     "status": "completed"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X = x_train.reshape(-1, 1)\n",
    "y = y_train\n",
    "\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e183939a",
   "metadata": {
    "papermill": {
     "duration": 0.006549,
     "end_time": "2024-07-11T21:19:57.227011",
     "exception": false,
     "start_time": "2024-07-11T21:19:57.220462",
     "status": "completed"
    },
    "tags": []
   },
   "source": [
    "## Step 2: Training the Model\n",
    "\n",
    "Train the model using scikit-learn's `LinearRegression` class:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a4cb0b11",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-07-11T21:19:57.242708Z",
     "iopub.status.busy": "2024-07-11T21:19:57.242296Z",
     "iopub.status.idle": "2024-07-11T21:19:57.351548Z",
     "shell.execute_reply": "2024-07-11T21:19:57.350465Z"
    },
    "papermill": {
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      ],
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       "LinearRegression()"
      ]
     },
     "execution_count": 8,
     "metadata": {},
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    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "model = LinearRegression()\n",
    "model.fit(X_train, y_train)"
   ]
  },
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   "source": [
    "## Step 3: Model Parameters\n",
    "\n",
    "Get the model parameters (slope and intercept):\n"
   ]
  },
  {
   "cell_type": "code",
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    {
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     "output_type": "stream",
     "text": [
      "w: 199.99999999999994, b: 100.00000000000011\n"
     ]
    }
   ],
   "source": [
    "print(f\"w: {model.coef_[0]}, b: {model.intercept_}\")"
   ]
  },
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   "cell_type": "markdown",
   "id": "d8c917c5",
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   "source": [
    "## 4. Model Evaluation\n",
    "\n",
    "Evaluate the model's performance using metrics such as mean squared error (MSE) and r-squared:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "35fdb358",
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     "text": [
      "Mean Squared Error: 6.462348535570529e-27\n",
      "R-squared: 1.0\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import mean_squared_error, r2_score\n",
    "\n",
    "y_pred = model.predict(X_train)\n",
    "mse = mean_squared_error(y_train, y_pred)\n",
    "r2 = r2_score(y_train, y_pred)\n",
    "\n",
    "print(f\"Mean Squared Error: {mse}\")\n",
    "print(f\"R-squared: {r2}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61238722",
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    "tags": []
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   "source": [
    "## 5. Making Predictions\n",
    "\n",
    "Use the trained model to make predictions for new data points:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "7909d684",
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   "outputs": [
    {
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     "text": [
      "Predicted price for a house with 1200 sqft: $340 thousand dollars\n"
     ]
    }
   ],
   "source": [
    "new_house_size = np.array([[1.2]])  # 1200 sqft\n",
    "predicted_price = model.predict(new_house_size)\n",
    "print(f\"Predicted price for a house with 1200 sqft: ${predicted_price[0]:.0f} thousand dollars\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b1e23c7",
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    "tags": []
   },
   "source": [
    "## <a class=\"anchor\" id=\"7\"></a>\n",
    "<div style=\"background-color: #e8f6f3; padding: 20px; border-radius: 12px; box-shadow: 0 6px 12px rgba(0, 0, 0, 0.1); text-align: center; margin-top: 20px;\">\n",
    "    <h2 style=\"color: #2c3e50; font-size: 25px; font-weight: bold; margin: 0;\">\n",
    "        Kaggle Challenges and Linear Regression\n",
    "    </h2>\n",
    "</div>\n",
    "\n",
    "<ul>\n",
    "    <li><a href=\"https://www.kaggle.com/c/house-prices-advanced-regression-techniques\">House Prices - Advanced Regression Techniques</a></li>\n",
    "    <li><a href=\"https://www.kaggle.com/c/competitive-data-science-predict-future-sales\">Predict Future Sales</a></li>\n",
    "    <li><a href=\"https://www.kaggle.com/c/new-york-city-taxi-fare-prediction\">New York City Taxi Fare Prediction</a></li>\n",
    "    <li><a href=\"https://www.kaggle.com/c/mercari-price-suggestion-challenge\">Mercari Price Suggestion Challenge</a></li>\n",
    "</ul>\n"
   ]
  }
 ],
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