polynomial linear regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:01:41.942688648Z",
     "start_time": "2023-05-13T14:01:41.860147103Z"
    }
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import PolynomialFeatures, StandardScaler\n",
    "from sklearn.linear_model import LinearRegression, SGDRegressor\n",
    "from sklearn.metrics import r2_score\n",
    "from sklearn.pipeline import Pipeline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "outputs": [],
   "source": [
    "X = 6 * np.random.rand(200, 1) - 3\n",
    "y = 0.8 * X**2 + 0.9 * X + 2 + np.random.randn(200, 1)\n",
    "\n",
    "# y = 0.8x^2 + 0.9x + 2"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:01:43.178140075Z",
     "start_time": "2023-05-13T14:01:43.079988503Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X,y,'b.')\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:01:44.463916271Z",
     "start_time": "2023-05-13T14:01:44.188107517Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "outputs": [],
   "source": [
    "X_train,X_test,y_train,y_test=train_test_split(X,y,test_size=0.2,random_state=2)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:01:45.496808303Z",
     "start_time": "2023-05-13T14:01:45.430339286Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Applying linear regression"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "outputs": [
    {
     "data": {
      "text/plain": "0.33767133071319233"
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr=LinearRegression()\n",
    "model=lr.fit(X_train,y_train)\n",
    "y_pred=model.predict(X_test)\n",
    "r2_score(y_test,y_pred)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:01:46.972931275Z",
     "start_time": "2023-05-13T14:01:46.941638892Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_train,lr.predict(X_train),color='r')\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:01:48.474609908Z",
     "start_time": "2023-05-13T14:01:48.212781579Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Applying polynomial regression"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "outputs": [],
   "source": [
    "poly=PolynomialFeatures(degree=2)\n",
    "X_train_poly=poly.fit_transform(X_train)\n",
    "X_test_poly=poly.transform(X_test)\n"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:01:50.281957497Z",
     "start_time": "2023-05-13T14:01:50.245416558Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.25280355]\n",
      "[1.         1.25280355 1.56951672]\n"
     ]
    }
   ],
   "source": [
    "print(X_train[0])\n",
    "print(X_train_poly[0])"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:01:51.259899176Z",
     "start_time": "2023-05-13T14:01:51.183095009Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "outputs": [
    {
     "data": {
      "text/plain": "0.891029485166235"
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr=LinearRegression()\n",
    "model=lr.fit(X_train_poly,y_train)\n",
    "y_pred=model.predict(X_test_poly)\n",
    "r2_score(y_test,y_pred)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:01:52.030935421Z",
     "start_time": "2023-05-13T14:01:51.959554058Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_train_poly,lr.predict(X_train_poly),color='r')\n",
    "plt.plot(X, y, \"b.\")\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"Y\")\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:01:53.157948034Z",
     "start_time": "2023-05-13T14:01:52.911617765Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "outputs": [],
   "source": [
    "X_new=np.linspace(-3, 3, 200).reshape(200, 1)\n",
    "X_new_poly = poly.transform(X_new)\n",
    "y_new = lr.predict(X_new_poly)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:01:53.957138582Z",
     "start_time": "2023-05-13T14:01:53.892511390Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(X_new, y_new, \"r-\", linewidth=2, label=\"Predictions\")\n",
    "plt.plot(X_train, y_train, \"b.\",label='Training points')\n",
    "plt.plot(X_test, y_test, \"g.\",label='Testing points')\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:01:55.703441891Z",
     "start_time": "2023-05-13T14:01:55.364472996Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Function for checking optimizied degree value"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "outputs": [],
   "source": [
    "def polynomial_regression(degree):\n",
    "    X_new=np.linspace(-3, 3, 100).reshape(100, 1)\n",
    "    X_new_poly = poly.transform(X_new)\n",
    "\n",
    "    polybig_features = PolynomialFeatures(degree=degree, include_bias=False)\n",
    "    std_scaler = StandardScaler()\n",
    "    lin_reg = LinearRegression()\n",
    "    polynomial_regression = Pipeline([\n",
    "        (\"poly_features\", polybig_features),\n",
    "        (\"std_scaler\", std_scaler),\n",
    "        (\"lin_reg\", lin_reg),\n",
    "    ])\n",
    "    polynomial_regression.fit(X, y)\n",
    "    y_newbig = polynomial_regression.predict(X_new)\n",
    "    plt.plot(X_new, y_newbig,'r', label=\"Degree \" + str(degree), linewidth=2)\n",
    "\n",
    "    plt.plot(X_train, y_train, \"b.\", linewidth=3)\n",
    "    plt.plot(X_test, y_test, \"g.\", linewidth=3)\n",
    "    plt.legend(loc=\"upper left\")\n",
    "    plt.xlabel(\"X\")\n",
    "    plt.ylabel(\"y\")\n",
    "    plt.axis([-3, 3, 0, 10])\n",
    "    plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:01:57.493016003Z",
     "start_time": "2023-05-13T14:01:57.453748771Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "outputs": [
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "polynomial_regression(10)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:02:36.641585858Z",
     "start_time": "2023-05-13T14:02:36.343056628Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "# Applying gradient descent"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/zuhaib/anaconda3/lib/python3.10/site-packages/sklearn/utils/validation.py:1143: DataConversionWarning: A column-vector y was passed when a 1d array was expected. Please change the shape of y to (n_samples, ), for example using ravel().\n",
      "  y = column_or_1d(y, warn=True)\n"
     ]
    },
    {
     "data": {
      "text/plain": "<Figure size 640x480 with 1 Axes>",
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Applying Gradient Descent\n",
    "\n",
    "poly = PolynomialFeatures(degree=2)\n",
    "\n",
    "X_train_trans = poly.fit_transform(X_train)\n",
    "X_test_trans = poly.transform(X_test)\n",
    "\n",
    "sgd = SGDRegressor(max_iter=100)\n",
    "sgd.fit(X_train_trans,y_train)\n",
    "\n",
    "X_new=np.linspace(-2.9, 2.8, 200).reshape(200, 1)\n",
    "X_new_poly = poly.transform(X_new)\n",
    "y_new = sgd.predict(X_new_poly)\n",
    "\n",
    "y_pred = sgd.predict(X_test_trans)\n",
    "\n",
    "plt.plot(X_new, y_new, \"r-\", linewidth=2, label=\"Predictions \" + str(round(r2_score(y_test,y_pred),2)))\n",
    "plt.plot(X_train, y_train, \"b.\",label='Training points')\n",
    "plt.plot(X_test, y_test, \"g.\",label='Testing points')\n",
    "plt.xlabel(\"X\")\n",
    "plt.ylabel(\"y\")\n",
    "plt.legend()\n",
    "plt.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:00:15.339377394Z",
     "start_time": "2023-05-13T14:00:15.126214401Z"
    }
   }
  },
  {
   "cell_type": "markdown",
   "source": [
    "# 3D Polynomial Regression"
   ],
   "metadata": {
    "collapsed": false
   }
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "outputs": [],
   "source": [
    "# 3D polynomial regression\n",
    "x = 7 * np.random.rand(100, 1) - 2.8\n",
    "y = 7 * np.random.rand(100, 1) - 2.8\n",
    "\n",
    "z = x**2 + y**2 + 0.2*x + 0.2*y + 0.1*x*y +2 + np.random.randn(100, 1)\n",
    "# z = x^2 + y^2 + 0.2x + 0.2y + 0.1xy + 2"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:04:52.211698021Z",
     "start_time": "2023-05-13T14:04:52.128622598Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
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         "hovertemplate": "x=%{x}<br>y=%{y}<br>z=%{z}<extra></extra>",
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         "marker": {
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          "symbol": "circle"
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         "mode": "markers",
         "name": "",
         "scene": "scene",
         "showlegend": false,
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import plotly.express as px\n",
    "df = px.data.iris()\n",
    "fig = px.scatter_3d(df, x=x.ravel(), y=y.ravel(), z=z.ravel())\n",
    "fig.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:04:53.231241272Z",
     "start_time": "2023-05-13T14:04:53.112080230Z"
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   }
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "outputs": [],
   "source": [
    "lr = LinearRegression()\n",
    "lr.fit(np.array([x,y]).reshape(100,2),z)\n",
    "\n",
    "x_input = np.linspace(x.min(), x.max(), 10)\n",
    "y_input = np.linspace(y.min(), y.max(), 10)\n",
    "xGrid, yGrid = np.meshgrid(x_input,y_input)\n",
    "\n",
    "final = np.vstack((xGrid.ravel().reshape(1,100),yGrid.ravel().reshape(1,100))).T\n",
    "\n",
    "z_final = lr.predict(final).reshape(10,10)\n",
    "\n"
   ],
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    "ExecuteTime": {
     "end_time": "2023-05-13T14:04:54.300276188Z",
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import plotly.graph_objects as go\n",
    "\n",
    "fig = px.scatter_3d(df, x=x.ravel(), y=y.ravel(), z=z.ravel())\n",
    "\n",
    "fig.add_trace(go.Surface(x = x_input, y = y_input, z =z_final ))\n",
    "\n",
    "fig.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:04:55.612134507Z",
     "start_time": "2023-05-13T14:04:55.507706094Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "outputs": [
    {
     "data": {
      "text/plain": "(100, 2)"
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_multi = np.array([x,y]).reshape(100,2)\n",
    "X_multi.shape"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:04:56.726674285Z",
     "start_time": "2023-05-13T14:04:56.683626771Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "outputs": [],
   "source": [
    "poly = PolynomialFeatures(degree=10)\n",
    "X_multi_trans = poly.fit_transform(X_multi)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:05:25.064308309Z",
     "start_time": "2023-05-13T14:05:25.016823351Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Powers\n",
      " [[ 0  0]\n",
      " [ 1  0]\n",
      " [ 0  1]\n",
      " [ 2  0]\n",
      " [ 1  1]\n",
      " [ 0  2]\n",
      " [ 3  0]\n",
      " [ 2  1]\n",
      " [ 1  2]\n",
      " [ 0  3]\n",
      " [ 4  0]\n",
      " [ 3  1]\n",
      " [ 2  2]\n",
      " [ 1  3]\n",
      " [ 0  4]\n",
      " [ 5  0]\n",
      " [ 4  1]\n",
      " [ 3  2]\n",
      " [ 2  3]\n",
      " [ 1  4]\n",
      " [ 0  5]\n",
      " [ 6  0]\n",
      " [ 5  1]\n",
      " [ 4  2]\n",
      " [ 3  3]\n",
      " [ 2  4]\n",
      " [ 1  5]\n",
      " [ 0  6]\n",
      " [ 7  0]\n",
      " [ 6  1]\n",
      " [ 5  2]\n",
      " [ 4  3]\n",
      " [ 3  4]\n",
      " [ 2  5]\n",
      " [ 1  6]\n",
      " [ 0  7]\n",
      " [ 8  0]\n",
      " [ 7  1]\n",
      " [ 6  2]\n",
      " [ 5  3]\n",
      " [ 4  4]\n",
      " [ 3  5]\n",
      " [ 2  6]\n",
      " [ 1  7]\n",
      " [ 0  8]\n",
      " [ 9  0]\n",
      " [ 8  1]\n",
      " [ 7  2]\n",
      " [ 6  3]\n",
      " [ 5  4]\n",
      " [ 4  5]\n",
      " [ 3  6]\n",
      " [ 2  7]\n",
      " [ 1  8]\n",
      " [ 0  9]\n",
      " [10  0]\n",
      " [ 9  1]\n",
      " [ 8  2]\n",
      " [ 7  3]\n",
      " [ 6  4]\n",
      " [ 5  5]\n",
      " [ 4  6]\n",
      " [ 3  7]\n",
      " [ 2  8]\n",
      " [ 1  9]\n",
      " [ 0 10]]\n"
     ]
    }
   ],
   "source": [
    "\n",
    "print(\"Powers\\n\",poly.powers_)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:05:26.736248386Z",
     "start_time": "2023-05-13T14:05:26.021620414Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "outputs": [],
   "source": [
    "lr = LinearRegression()\n",
    "lr.fit(X_multi_trans,z)\n",
    "X_test_multi = poly.transform(final)\n",
    "z_final = lr.predict(X_multi_trans).reshape(10,10)"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:05:27.527148856Z",
     "start_time": "2023-05-13T14:05:26.820747012Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "outputs": [
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     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = px.scatter_3d(x=x.ravel(), y=y.ravel(), z=z.ravel())\n",
    "\n",
    "fig.add_trace(go.Surface(x = x_input, y = y_input, z =z_final))\n",
    "\n",
    "fig.update_layout(scene = dict(zaxis = dict(range=[0,35])))\n",
    "\n",
    "fig.show()"
   ],
   "metadata": {
    "collapsed": false,
    "ExecuteTime": {
     "end_time": "2023-05-13T14:05:29.022216567Z",
     "start_time": "2023-05-13T14:05:28.236081081Z"
    }
   }
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "outputs": [],
   "source": [],
   "metadata": {
    "collapsed": false
   }
  }
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