notebooks/supervised/regression/linear/linear_regression_from_scratch.ipynb

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      "Coefficients: [ 1.37245527 -0.13972856  0.43861814]\n",
      "Intercept (Beta_0): 1.3724552745219012\n",
      "Coefficient of Feature 1 (Beta_1): -0.13972856261567002\n",
      "Coefficient of Feature 2 (Beta_2): 0.4386181369524983\n",
      "Prediction for features (1.50, 4): 2.9173349784083893\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "# Define the features (X) and target variable (y)\n",
    "features = np.array([[1, 0], [2, 3.50], [2.50, 4], [3.50, 4], [3, 1], [5, 1.50]])\n",
    "target = np.array([1.50, 2, 3.50, 2.50, 1, 1.50])\n",
    "\n",
    "# Add an intercept term to the features\n",
    "features_with_intercept = np.column_stack((np.ones(len(features)), features))\n",
    "\n",
    "# Calculate the coefficients (beta)\n",
    "coefficients = np.linalg.inv(features_with_intercept.T.dot(features_with_intercept)).dot(features_with_intercept.T).dot(target)\n",
    "\n",
    "# Print the coefficients\n",
    "print(\"Coefficients:\", coefficients)\n",
    "print(\"Intercept (Beta_0):\", coefficients[0])  # Intercept\n",
    "print(\"Coefficient of Feature 1 (Beta_1):\", coefficients[1])  # Coefficient for the first feature\n",
    "print(\"Coefficient of Feature 2 (Beta_2):\", coefficients[2])  # Coefficient for the second feature\n",
    "\n",
    "# Define a function to make predictions\n",
    "def predict(features, coefficients):\n",
    "    features_with_intercept = np.insert(features, 0, 1)  \n",
    "    return np.dot(features_with_intercept, coefficients)\n",
    "\n",
    "# Example prediction\n",
    "new_feature = np.array([1.50, 4])\n",
    "prediction = predict(new_feature, coefficients)\n",
    "print(\"Prediction for features (1.50, 4):\", prediction)\n"
   ]
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