Abalone _Age.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Abalone's age prediction using Regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.model_selection import train_test_split\n",
    "from math import sqrt\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.linear_model import LinearRegression \n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "import pickle"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using 'abalone.csv' file :-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Length</th>\n",
       "      <th>Diameter</th>\n",
       "      <th>Height</th>\n",
       "      <th>Whole weight</th>\n",
       "      <th>Shucked weight</th>\n",
       "      <th>Viscera weight</th>\n",
       "      <th>Shell weight</th>\n",
       "      <th>Rings</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.455</td>\n",
       "      <td>0.365</td>\n",
       "      <td>0.095</td>\n",
       "      <td>0.5140</td>\n",
       "      <td>0.2245</td>\n",
       "      <td>0.1010</td>\n",
       "      <td>0.150</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.350</td>\n",
       "      <td>0.265</td>\n",
       "      <td>0.090</td>\n",
       "      <td>0.2255</td>\n",
       "      <td>0.0995</td>\n",
       "      <td>0.0485</td>\n",
       "      <td>0.070</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.530</td>\n",
       "      <td>0.420</td>\n",
       "      <td>0.135</td>\n",
       "      <td>0.6770</td>\n",
       "      <td>0.2565</td>\n",
       "      <td>0.1415</td>\n",
       "      <td>0.210</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.440</td>\n",
       "      <td>0.365</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.5160</td>\n",
       "      <td>0.2155</td>\n",
       "      <td>0.1140</td>\n",
       "      <td>0.155</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.330</td>\n",
       "      <td>0.255</td>\n",
       "      <td>0.080</td>\n",
       "      <td>0.2050</td>\n",
       "      <td>0.0895</td>\n",
       "      <td>0.0395</td>\n",
       "      <td>0.055</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Length  Diameter  Height  Whole weight  Shucked weight  Viscera weight  \\\n",
       "0   0.455     0.365   0.095        0.5140          0.2245          0.1010   \n",
       "1   0.350     0.265   0.090        0.2255          0.0995          0.0485   \n",
       "2   0.530     0.420   0.135        0.6770          0.2565          0.1415   \n",
       "3   0.440     0.365   0.125        0.5160          0.2155          0.1140   \n",
       "4   0.330     0.255   0.080        0.2050          0.0895          0.0395   \n",
       "\n",
       "   Shell weight  Rings  \n",
       "0         0.150     15  \n",
       "1         0.070      7  \n",
       "2         0.210      9  \n",
       "3         0.155     10  \n",
       "4         0.055      7  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('abalone.csv')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Splitting the data into test and train"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "[X_train, X_test] =train_test_split(df, test_size=0.30, random_state=42, shuffle = True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Saving the training and testing data in CSV files"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train.to_csv(\"abalone-train.csv\",index = False)\n",
    "X_test.to_csv(\"abalone-test.csv\",index = False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finding the attribute which has the highest Pearson correlation coefficient with the target attribute \n",
    "Rings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Length            0.556720\n",
      "Diameter          0.574660\n",
      "Height            0.557467\n",
      "Whole weight      0.540390\n",
      "Shucked weight    0.420884\n",
      "Viscera weight    0.503819\n",
      "Shell weight      0.627574\n",
      "Rings             1.000000\n",
      "Name: Rings, dtype: float64\n"
     ]
    }
   ],
   "source": [
    "corr = df.corr(method = 'pearson')\n",
    "print(corr['Rings'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Function for simple linear (straight-line) regression model to predict \n",
    "rings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def linear_fit(data):\n",
    "    regressor = LinearRegression()\n",
    "    shell_weight = np.array(data['Shell weight'])\n",
    "    shell_weight = shell_weight.reshape(-1,1)\n",
    "    Rings = np.array(data['Rings'])\n",
    "    Rings = Rings.reshape(-1,1)\n",
    "    regressor.fit(shell_weight, Rings)\n",
    "    y_pred = regressor.predict(shell_weight)\n",
    "    return y_pred"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Best fit line between 'Shell weight' and 'Rings'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Best Fit\")\n",
    "plt.xlabel(\"Shell weight\")\n",
    "plt.ylabel(\"Rings\")\n",
    "plt.plot(X_train['Shell weight'], linear_fit(X_train))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The prediction accuracy on the training and data using root mean squared error"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE Error for Linear Regression, Train data is : 2.53\n",
      "RMSE Error for Linear Regression, Test data is : 2.47\n"
     ]
    }
   ],
   "source": [
    "error_train = sqrt(mean_squared_error(X_train['Rings'], linear_fit(X_train))) #computing the error in train data\n",
    "error_test = sqrt(mean_squared_error(X_test['Rings'],linear_fit(X_test)))#computing the error in test data\n",
    "print(\"RMSE Error for Linear Regression, Train data is : %.2f\"%(error_train))\n",
    "print(\"RMSE Error for Linear Regression, Test data is : %.2f\"%(error_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " The scatter plot of actual Rings (x-axis) vs predicted Rings (y-axis) on the test data :-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Scatter Plot\") \n",
    "plt.xlabel(\"Rings(Actual)\")\n",
    "plt.ylabel(\"Rings(Predicted)\")\n",
    "plt.scatter(X_test['Rings'], linear_fit(X_test))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multivariate Linear Regression Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Function for Multivariate linear regression model to predict rings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def multiple_fit(data):\n",
    "    regressor = LinearRegression()\n",
    "    input_var = np.array(data.iloc[:,:-1])\n",
    "    target = np.array(data.iloc[:,-1])\n",
    "    regressor.fit(input_var,target)\n",
    "    pred = regressor.predict(input_var)\n",
    "    return pred"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The prediction accuracy on the training and data using root mean squared error :-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE Error for Multiple Regression, Train data is : 2.22\n",
      "RMSE Error for Multiple Regression, Test data is : 2.21\n"
     ]
    }
   ],
   "source": [
    "multiple_error_train = sqrt(mean_squared_error(X_train['Rings'], multiple_fit(X_train))) #computing the error in train data\n",
    "multiple_error_test = sqrt(mean_squared_error(X_test['Rings'],multiple_fit(X_test)))#computing the error in test data\n",
    "print(\"RMSE Error for Multiple Regression, Train data is : %.2f\"%(multiple_error_train))\n",
    "print(\"RMSE Error for Multiple Regression, Test data is : %.2f\"%(multiple_error_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The scatter plot of actual Rings (x-axis) vs predicted Rings (y-axis) on the test data :-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title(\"Scatter Plot for multivariate regression\")\n",
    "plt.xlabel(\"Rings(Actual)\")\n",
    "plt.ylabel(\"Rings(Predicted)\")\n",
    "plt.scatter(X_test['Rings'], multiple_fit(X_test))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simple Nonlinear Regression Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Simple nonlinear regression model using polynomial curve fitting \n",
    "to predict Rings :-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def poly_pred(data):#Function for prediction of data\n",
    "    l = []\n",
    "    for i in [2,3,4,5]:\n",
    "        polynomial_features = PolynomialFeatures(degree = i)\n",
    "        shell_weight = np.array(data['Shell weight'])\n",
    "        shell_weight = shell_weight.reshape(-1,1)\n",
    "        Rings = np.array(data['Rings'])\n",
    "        Rings = Rings.reshape(-1,1)\n",
    "        x_poly = polynomial_features.fit_transform(shell_weight)\n",
    "        regressor = LinearRegression()\n",
    "        regressor.fit(x_poly, Rings)\n",
    "        y_pred = regressor.predict(x_poly)\n",
    "        error = sqrt(mean_squared_error(data['Rings'], y_pred))\n",
    "        l.append(error)\n",
    "    ls = [round(x,3) for x in l]\n",
    "    return [ls,y_pred]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prediction accuracy on the training and test data for the different values of degree of \n",
    "the polynomial (p = 2, 3, 4, 5) using root mean squared error (RMSE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "RMSE for Training data :-\n",
      "RMSE Error for p = 2 is 2.50\n",
      "RMSE Error for p = 3 is 2.48\n",
      "RMSE Error for p = 4 is 2.47\n",
      "RMSE Error for p = 5 is 2.47\n",
      "\n",
      "RMSE for Test data :-\n",
      "RMSE Error for p = 2 is 2.43\n",
      "RMSE Error for p = 3 is 2.41\n",
      "RMSE Error for p = 4 is 2.41\n",
      "RMSE Error for p = 5 is 2.41\n"
     ]
    }
   ],
   "source": [
    "p = [2,3,4,5]\n",
    "print(\"\\nRMSE for Training data :-\")\n",
    "for i in range(len(p)):\n",
    "    print(\"RMSE Error for p = %d is %.2f\"%(p[i],poly_pred(X_train)[0][i]))\n",
    "print(\"\\nRMSE for Test data :-\")\n",
    "for i in range(len(p)):\n",
    "    print(\"RMSE Error for p = %d is %.2f\"%(p[i],poly_pred(X_test)[0][i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the RMSE vs degree of polynomial graph :-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZmVVU2xFIftj9T4DZEfGDJmXWBx6PiMjP4l6D9HhXG2x8dFcft2193Larpc4urJ1Jz3W+V9KsPO4EYCxAREwF9geOlLSc9ED3A8MPKDEzGxRqSyARcQvQMr1HxBRgSl0xmJlZffxLdDMzq8QJxMzMKnECMTOzSpxAzMysEicQMzOrxAnEzMwqcQIxM7NKnEDMzKwSJxAzM6vECcTMzCpxAjEzs0qcQMzMrBInEDMzq8QJxMzMKnECMTOzSpxAzMysEicQMzOrxAnEzMwqcQIxM7NKnEDMzKwSJxAzM6vECcTMzCpxAjEzs0qcQMzMrBInEDMzq8QJxMzMKnECMTOzSpxAzMysEicQMzOrxAnEzMwqcQIxM7NKnEDMzKwSJxAzM6uktgQiaYyk6yXNlnS/pKMblJGkUyXNkXSPpG3risfMzPrW0BrrXg4cGxEzJY0AZki6NiIeKJTZA9g0/+0AnJ7/m5lZl6vtCCQiFkTEzPx6CTAbGF0qNgk4N5LbgPUkbVBXTGZm1nf65RyIpPHAO4DbS5NGA3MLw/NYNckgabKk6ZKmL1y4sLY4zcysc7UnEEmvBi4HjomIxeXJDWaJVUZEnBEREyJiwqhRo+oI08zMeqnWBCJpGCl5XBARP2tQZB4wpjC8ETC/zpjMzKxv1HkVloCfALMj4gdNil0JfCpfjbUjsCgiFtQVk5mZ9Z06r8LaGfgkcK+kWXncCcBYgIiYCkwD9gTmAH8BDq0xHjMz60O1JZCIuIXG5ziKZQL4XF0xmJlZffxLdDMzq8QJxMzMKnECMTOzSpxAzMysEicQMzOrxAnEzMwqcQIxM7NKnEDMzKwSJxAzM6vECcTMzCpxAjEzs0qcQMzMrBInEDMzq8QJxMzMKnECMTOzSpxAzMysEicQMzOrxAnEzMwqcQIxM7NKnEDMzKwSJxAzM6vECcTMzCpxAjEzs0qcQMzMrBInEDMzq8QJxMzMKnECMTOzSpxAzMysEicQMzOrxAnEzMwqcQIxM7NKnEDMzKyS2hKIpLMkPSHpvibTJ0paJGlW/juxrljMzKzvDa2x7rOBKcC5LcrcHBF71xiDmZnVpLYjkIi4CXi6rvrNzGxgDfQ5kJ0k3S3paklbNCskabKk6ZKmL1y4sD/jMzOzJgYygcwExkXE1sBpwBXNCkbEGRExISImjBo1qr/iMzOzFgYsgUTE4ohYml9PA4ZJGjlQ8ZiZWe8MWAKRtL4k5dfb51ieGqh4zMysd2q7CkvSRcBEYKSkecDXgWEAETEV2B84UtJyYBlwYEREXfGYmVnfaplAJL0vIq7LrzeOiD8Wpu0XET9rNm9EHNSq7oiYQrrM18zMBqF2XVjfL7y+vDTtq30ci5mZDSLtEoiavG40bGZmryDtEkg0ed1o2MzMXkHanUR/k6QrSUcbPa/JwxvXGpmZmXW1dglkUuH190vTysNmZvYK0jKBRMSNxWFJw4C3A49GxBN1BmZmZt2t5TkQSVN77lElaV3gbtLdde+S1PIyXTMze3lrdxJ9l4i4P78+FHg4IrYEtgOOrzUyMzPrau0SyAuF1x8g3/AwIh6rKyAzMxsc2iWQZyXtLekdwM7ArwAkDQWG1x2cmZl1r3ZXYX0WOBVYHzimcOTxfuCXdQZmZmbdrd1VWA8DuzcYfw1wTV1BmZlZ92t3M8VTW02PiC/0bThmZjZYtOvCOgK4D7gUmI/vf2VmZlm7BLIB8FHgAGA5cAlweUQ8U3dgZmbW3VpehRURT0XE1Ih4L3AIsB5wv6RP9kNsZmbWxTp6IqGkbYGDSL8FuRqYUWdQZmbW/dqdRD8Z2BuYDVwMfCUilvdHYGZm1t3aHYF8DfgDsHX++5YkSCfTIyK2qjc8MzPrVu0SiJ/5YWZmDbX7IeGfGo2XNAQ4EGg43czMXv7a3c79NZK+ImmKpA8q+TypW+tj/ROimZl1o3ZdWOcBzwC3AocDXwLWBCZFxKx6QzMzs27W9pno+fkfSDoTeBIYGxFLao/MzMy6Wrvbuf+t50VErAD+6ORhZmbQ/ghka0mL82sBw/Nwz2W8r6k1OjMz61rtrsIa0l+BmJnZ4NKuC8vMzKwhJxAzM6vECcTMzCpxAjEzs0qcQMzMrBInEDMzq6S2BCLpLElPSLqvyXRJOlXSHEn35IdWmZnZIFHnEcjZwO4tpu8BbJr/JgOn1xiLmZn1sdoSSETcBDzdosgk4NxIbgPWk7RBXfGYmVnfGshzIKOBuYXheXncKiRNljRd0vSFCxf2S3BmZtbaQCYQNRgXjQpGxBkRMSEiJowaNarmsMzMrBMDmUDmAWMKwxsB8wcoFjMz66WBTCBXAp/KV2PtCCyKiAUDGI+ZmfVCu9u5VybpImAiMFLSPODrwDCAiJgKTAP2BOYAfwEOrSsWMzPre7UlkIg4qM30AD5X1/LNzKxe/iW6mZlV4gRiZmaVOIGYmVklTiBmZlaJE4iZmVXiBGJmZpU4gZiZWSVOIGZmVokTiJmZVeIEYmZmlTiBmJlZJU4gZmZWiROImZlV4gRiZmaVOIGYmVklTiBmZlaJE4iZmVXiBGJmZpU4gZiZWSVOIGZmVokTiJmZVeIEYmZmlTiBmJlZJU4gZmZWiROImZlV4gRiZmaVOIGYmVklTiBmZlaJE4iZmVXiBGJmZpU4gZiZWSVOIGZmVkmtCUTS7pIekjRH0pcbTJ8oaZGkWfnvxDrjMTOzvjO0roolDQH+A/gAMA+4U9KVEfFAqejNEbF3XXGYmVk96jwC2R6YExF/iIgXgIuBSTUuz8zM+lGdCWQ0MLcwPC+PK9tJ0t2Srpa0RaOKJE2WNF3S9IULF9YRq5mZ9VKdCUQNxkVpeCYwLiK2Bk4DrmhUUUScERETImLCqFGj+jZKMzOrpM4EMg8YUxjeCJhfLBARiyNiaX49DRgmaWSNMZmZWR+pM4HcCWwqaWNJawIHAlcWC0haX5Ly6+1zPE/VGJOZmfWR2q7Ciojlko4CrgGGAGdFxP2SjsjTpwL7A0dKWg4sAw6MiHI3l5mZdaHaEgi81C01rTRuauH1FGBKnTGYmVk9/Et0MzOrxAnEzMwqcQIxM7NKnEDMzKwSJxAzM6vECcTMzCpxAjEzs0qcQMzMrBInEDMzq8QJxMzMKnECMTOzSpxAzMysEicQMzOrxAnEzMwqcQIxM7NKnEDMzKwSJxAzM6vECcTMzCpxAjEzs0qcQMzMrBInEDMzq8QJxMzMKnECMTOzSpxAzMysEicQMzOrxAnEzMwqcQIxM7NKnEDMzKwSJxAzM6vECcTMzCpxAjEzs0qcQMzMrBInEDMzq6TWBCJpd0kPSZoj6csNpkvSqXn6PZK2rTMeMzPrO7UlEElDgP8A9gA2Bw6StHmp2B7ApvlvMnB6XfGYmVnfqvMIZHtgTkT8ISJeAC4GJpXKTALOjeQ2YD1JG9QYk5mZ9ZGhNdY9GphbGJ4H7NBBmdHAgmIhSZNJRygASyU91LehrraRwJN9Xus/qM+rzOqJtx5u2/q4bevTjW07rq/C6FFnAmm0plGhDBFxBnBGXwRVB0nTI2LCQMfRqcEU72CKFQZXvIMpVhhc8Q6mWFdHnV1Y84AxheGNgPkVypiZWReqM4HcCWwqaWNJawIHAleWylwJfCpfjbUjsCgiFpQrMjOz7lNbF1ZELJd0FHANMAQ4KyLul3REnj4VmAbsCcwB/gIcWlc8Neva7rUmBlO8gylWGFzxDqZYYXDFO5hirUwRq5xyMDMza8u/RDczs0qcQMzMrBInkA5JGiPpekmzJd0v6egGZbri1iwdxjpR0iJJs/LfiQMRa45lbUl3SLo7x3tygzLd0radxNo1bVuIaYikuyRd1WBaV7RtIZ5WsXZV20p6RNK9OZbpDaZ3Vdv2tTp/B/Jysxw4NiJmShoBzJB0bUQ8UChTvDXLDqRbs5R/PNkfOokV4OaI2HsA4iv7K/C+iFgqaRhwi6Sr890JenRL23YSK3RP2/Y4GpgNvKbBtG5p2x6tYoXua9v3RkSzHw12W9v2KR+BdCgiFkTEzPx6CWkDH10q1hW3Zukw1q6R22tpHhyW/8pXd3RL23YSa1eRtBGwF3BmkyJd0bbQUayDTde0bR2cQCqQNB54B3B7aVKzW7MMmBaxAuyUu2KulrRF/0a2stxtMQt4Arg2Irq2bTuIFbqobYFTgOOBF5tM75q2pX2s0F1tG8CvJc1QuuVSWTe1bZ9zAuklSa8GLgeOiYjF5ckNZhmwb6dtYp0JjIuIrYHTgCv6ObyVRMSKiNiGdDeC7SW9vVSka9q2g1i7pm0l7Q08EREzWhVrMK7f27bDWLumbbOdI2JbUlfV5yS9pzS9K9q2Lk4gvZD7vC8HLoiInzUo0jW3ZmkXa0Qs7umKiYhpwDBJI/s5zFVExLPADcDupUld07Y9msXaZW27M/BhSY+Q7oj9Pknnl8p0S9u2jbXL2paImJ//PwH8nHQX8qJuadtaOIF0SJKAnwCzI+IHTYp1xa1ZOolV0vq5HJK2J20LT/VflCvFMkrSevn1cGA34MFSsW5p27axdlPbRsRXImKjiBhPup3QdRHxiVKxrmjbTmLtpraV9Kp8kQqSXgV8ELivVKwr2rYuvgqrczsDnwTuzf3fACcAY6Hrbs3SSaz7A0dKWg4sAw6MgbstwQbAOUoPIVsDuDQirlJ33vamk1i7qW0b6tK2baiL2/aNwM9zPhsKXBgRvxpMbbu6fCsTMzOrxF1YZmZWiROImZlV4gRiZmaVOIGYmVklTiBmZlaJE4gNGEkr8l1M78+3pviipK7eJvPvQG5XulvsLqtZ10mSjuur2Hq57DMlbd6mzA2SJvRXTDb4+HcgNpCW5VuCIOkNwIXAusDXV7diSUMiYsXq1tPA+4EHI+LgGuruNxFx+EDHYINfV3/bs1eOfCuIycBR+Ve7QyR9T9KdSs9R+CyApDUk/Wc+arlK0jRJ++dpj0g6UdItwEclfVDSrZJmSros3xsMSdtJujHfAO8aNbg7qqRxkn6Tl/0bSWMlbQN8F9gzHzkNL83ziKTvKD0v5A5JmzSrqzTfmyXNLAxvKmlGoc6T8zrcK+mtefzrJF2R67xN0lZ5/EmSzpH06zzvfpK+m+f9ldItblY6upB0uqTpavJ8E7NmnECsa0TEH0jb5BuAw0i3fXgn8E7gM5I2BvYDxgNbAocDO5WqeT4i3g38D/BVYLd8s7vpwBfzDvQ0YP+I2A44C/hmg3CmkG7DvRVwAXBqRMwCTgQuiYhtImJZg/kWR8T2ef5TmtVVWu/fA4tygoL0a+WzC0WezOtwOtDT5XUycFeu8wTg3EL5N5NuiT4JOB+4PiK2JP1ye68GMf9zREwAtgJ27UlGZu24C8u6Tc/dSz8IbNVzdEHq2toUeDdwWUS8CDwm6frS/Jfk/zsCmwO/zbeaWBO4FXgL8Hbg2jx+CNDo3kQ7kZIVwHmkI49OXFT4/8Ne1HUmcKikLwIHsPJN+XpuhjmjUM+7gY8ARMR1kl4vad087eqI+Juke0nr96s8/l5S8i37mNKtyIeSbtWyOXBP+1W1VzonEOsakt4ErCA9Z0PA5yPimlKZRt+gi57rKUp6VsdBpfm3BO6PiPKRSzud3vMnmrxuV9flpHM/1wEzIqJ4g8C/5v8r+PtnttVtwv8KEBEvSvpb4V5RL1L6zOejuuOAd0bEM5LOBtZuErfZStyFZV1B0ihgKjAl7/CuId00r6fPfjOlO57eAnwknwt5IzCxSZW3ATsXzkOsI2kz4CFglKSd8vhhavxQot+R7ggL8A95uZ04oPD/1k7riojnSet8OvDTDpZzU64LSRNJ3VzlZ7504jWkpLsot+ceFeqwVygfgdhAGq50t+BhpOe4nwf03H7+TFJ3y0ylvqaFwL6kb+rvJ902+2HSkxYXlSuOiIWSDgEukrRWHv3ViHg4d4udmrt8hpLOVdxfquILwFmSvpSX3eldVNeSdDvpy1nP0U+ndV1A6qL6dQfLOQn4qaR7SHd5rXRVWETcLeku0vr/AfhtlXrslcl347VBR9KrI2KppNcDd5CeCvdYF8T1CDAhIp6sOP9xwLoR8bU+DcysJj4CscHoKqWHOq0J/Gs3JI/VJennpKun3jfQsZh1ykcgZmZWiU+im5lZJU4gZmZWiROImZlV4gRiZmaVOIGYmVkl/wsskvH37/mYTAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot2(data,x,y): #function for plotting RMSE vs degree of polynomial\n",
    "    plt.title('Bar graph of RMSE vs degree of polynomial for %s'%(data))\n",
    "    plt.xlabel('Degree of polynomial')\n",
    "    plt.ylabel('RMSE')\n",
    "    plt.bar(x, y, color = 'orange', width = .50)\n",
    "    plt.show()\n",
    "    \n",
    "plot2('Traning Data',[2,3,4,5],poly_pred(X_train)[0])\n",
    "plot2('Test Data',[2,3,4,5],poly_pred(X_test)[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the best fit curve using the best fit model on the training data :-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Best Fit Polynomial') #plotting scatter plot for best fit polynomial\n",
    "plt.xlabel('Shell weight')\n",
    "plt.ylabel(\"Predicted Rings\")\n",
    "plt.scatter(X_train['Shell weight'],poly_pred(X_train)[1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the scatter plot of the actual number of Rings (x-axis) vs the predicted number of \n",
    "Rings (y-axis) on the test data for the best degree of the polynomial (p) :-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Predicted vs Real')\n",
    "plt.xlabel('Actual Rings')\n",
    "plt.ylabel(\"Predicted Rings\")\n",
    "plt.scatter(X_test['Rings'],poly_pred(X_test)[1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multivariate Nonlinear Regression Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Multivariate nonlinear regression model using polynomial regression to predict Rings :-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def multi_poly_pred(data):#Function for prediction of data\n",
    "    l = []\n",
    "    for i in [2,3,4,5]:\n",
    "        polynomial_features = PolynomialFeatures(degree = i)\n",
    "        input_var = np.array(data.iloc[:,:-1])\n",
    "        x_poly = polynomial_features.fit_transform(input_var)\n",
    "        Rings = np.array(data['Rings'])\n",
    "        regressor = LinearRegression()\n",
    "        regressor.fit(x_poly, Rings)\n",
    "        y_pred = regressor.predict(x_poly)\n",
    "        error = sqrt(mean_squared_error(data['Rings'], y_pred))\n",
    "        l.append(error)\n",
    "    ls = [round(x,3) for x in l]\n",
    "    return [ls,y_pred]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The prediction accuracy on the training and test data for the different values of degree of \n",
    "the polynomial (p = 2, 3, 4, 5) using root mean squared error (RMSE) :-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "RMSE for Training data :-\n",
      "RMSE Error for p = 2 is 2.08\n",
      "RMSE Error for p = 3 is 1.99\n",
      "RMSE Error for p = 4 is 1.84\n",
      "RMSE Error for p = 5 is 1.64\n",
      "\n",
      "RMSE for Test data :-\n",
      "RMSE Error for p = 2 is 2.05\n",
      "RMSE Error for p = 3 is 1.93\n",
      "RMSE Error for p = 4 is 3.29\n",
      "RMSE Error for p = 5 is 2.02\n"
     ]
    }
   ],
   "source": [
    "p = [2,3,4,5]\n",
    "print(\"\\nRMSE for Training data :-\")\n",
    "for i in range(len(p)):\n",
    "    print(\"RMSE Error for p = %d is %.2f\"%(p[i],multi_poly_pred(X_train)[0][i]))\n",
    "print(\"\\nRMSE for Test data :-\")\n",
    "for i in range(len(p)):\n",
    "    print(\"RMSE Error for p = %d is %.2f\"%(p[i],multi_poly_pred(X_test)[0][i]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the RMSE vs degree of polynomial graph :-\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot2('Traning Data',[2,3,4,5],multi_poly_pred(X_train)[0])\n",
    "plot2('Test Data',[2,3,4,5],multi_poly_pred(X_test)[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the best fit curve using the best fit model on the training data :-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Best Fit Polynomial') #plotting scatter plot for best fit polynomial\n",
    "plt.xlabel('Shell weight')\n",
    "plt.ylabel(\"Predicted Rings\")\n",
    "plt.scatter(X_train['Shell weight'],multi_poly_pred(X_train)[1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the scatter plot of the actual number of Rings (x-axis) vs the predicted number of Rings (y-axis) on the test data for the best degree of the polynomial (p) :-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Predicted vs Real')\n",
    "plt.xlabel('Actual Rings')\n",
    "plt.ylabel(\"Predicted Rings\")\n",
    "plt.scatter(X_test['Rings'],multi_poly_pred(X_test)[1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After applying Four different regression model, we found Multivariate Nonlinear Regression Model for p = 5 to be better than others as it has the least RMSE values than the other models for both training as well test data in predicting no. of rings in Abalone."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Deployment of the model :-"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = X_train.iloc[:, :-1]\n",
    "y = X_train.iloc[:, -1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[7.25213991]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "regressor = LinearRegression()\n",
    "\n",
    "#Fitting model with trainig data\n",
    "regressor.fit(X, y)\n",
    "\n",
    "# Saving model to disk\n",
    "pickle.dump(regressor, open('model.pkl','wb'))\n",
    "\n",
    "# Loading model to compare the results\n",
    "model = pickle.load(open('model.pkl','rb'))\n",
    "print(model.predict([[0.350, 0.265, 0.090, 0.2255, 0.0995,0.0485, 0.070]]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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