Linear Regression/Linear Regression on Headbrain Dataset.ipynb

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   "source": [
    "#Importing the Modules\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(237, 4)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dataset=pd.read_csv(r'C:\\Users\\My PC\\Desktop\\headbrain.csv')\n",
    "dataset.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Gender</th>\n",
       "      <th>Age Range</th>\n",
       "      <th>Head Size(cm^3)</th>\n",
       "      <th>Brain Weight(grams)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4512</td>\n",
       "      <td>1530</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3738</td>\n",
       "      <td>1297</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4261</td>\n",
       "      <td>1335</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3777</td>\n",
       "      <td>1282</td>\n",
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       "      <th>4</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>4177</td>\n",
       "      <td>1590</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "   Gender  Age Range  Head Size(cm^3)  Brain Weight(grams)\n",
       "0       1          1             4512                 1530\n",
       "1       1          1             3738                 1297\n",
       "2       1          1             4261                 1335\n",
       "3       1          1             3777                 1282\n",
       "4       1          1             4177                 1590"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Analyzing the Dataset\n",
    "dataset.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>Gender</th>\n",
       "      <th>Age Range</th>\n",
       "      <th>Head Size(cm^3)</th>\n",
       "      <th>Brain Weight(grams)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>232</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3214</td>\n",
       "      <td>1110</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>233</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3394</td>\n",
       "      <td>1215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>234</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3233</td>\n",
       "      <td>1104</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>235</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3352</td>\n",
       "      <td>1170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>236</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3391</td>\n",
       "      <td>1120</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "     Gender  Age Range  Head Size(cm^3)  Brain Weight(grams)\n",
       "232       2          2             3214                 1110\n",
       "233       2          2             3394                 1215\n",
       "234       2          2             3233                 1104\n",
       "235       2          2             3352                 1170\n",
       "236       2          2             3391                 1120"
      ]
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     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "dataset.tail(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Gender</th>\n",
       "      <th>Age Range</th>\n",
       "      <th>Head Size(cm^3)</th>\n",
       "      <th>Brain Weight(grams)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>237.000000</td>\n",
       "      <td>237.000000</td>\n",
       "      <td>237.000000</td>\n",
       "      <td>237.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>1.434599</td>\n",
       "      <td>1.535865</td>\n",
       "      <td>3633.991561</td>\n",
       "      <td>1282.873418</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.496753</td>\n",
       "      <td>0.499768</td>\n",
       "      <td>365.261422</td>\n",
       "      <td>120.340446</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2720.000000</td>\n",
       "      <td>955.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>3389.000000</td>\n",
       "      <td>1207.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>3614.000000</td>\n",
       "      <td>1280.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>2.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>3876.000000</td>\n",
       "      <td>1350.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>2.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>4747.000000</td>\n",
       "      <td>1635.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "           Gender   Age Range  Head Size(cm^3)  Brain Weight(grams)\n",
       "count  237.000000  237.000000       237.000000           237.000000\n",
       "mean     1.434599    1.535865      3633.991561          1282.873418\n",
       "std      0.496753    0.499768       365.261422           120.340446\n",
       "min      1.000000    1.000000      2720.000000           955.000000\n",
       "25%      1.000000    1.000000      3389.000000          1207.000000\n",
       "50%      1.000000    2.000000      3614.000000          1280.000000\n",
       "75%      2.000000    2.000000      3876.000000          1350.000000\n",
       "max      2.000000    2.000000      4747.000000          1635.000000"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "dataset.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "X=dataset[\"Head Size(cm^3)\"].values\n",
    "Y=dataset[\"Brain Weight(grams)\"].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The mean of the Head Size Values is 3633.9915611814345\n",
      "The mean of the Brain Weight Values is 1282.873417721519\n",
      "The total number of values available are 237\n"
     ]
    }
   ],
   "source": [
    "print(\"The mean of the Head Size Values is %r\" %(np.mean(X)))\n",
    "print(\"The mean of the Brain Weight Values is %r\" %(np.mean(Y)))\n",
    "print(\"The total number of values available are %r\" %(len(X)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using Traditional Mathematics to derive a Model "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The two coefficients are 0.26342933948939945 and 325.57342104944223\n"
     ]
    }
   ],
   "source": [
    "mean_X=np.mean(X)\n",
    "mean_Y=np.mean(Y)\n",
    "length=len(X)\n",
    "numerator=0\n",
    "denominator=0\n",
    "for i in range(length):\n",
    "    numerator+=(X[i]-mean_X)*(Y[i]-mean_Y)\n",
    "    denominator+=(X[i]-mean_X)**2\n",
    "b1=numerator/denominator\n",
    "b0=mean_Y-(b1*mean_X)\n",
    "print(\"The two coefficients are %r and %r\" %(b1,b0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That means Brain Weight=0.26342933948939945 + 325.57342104944223 * HeadSize which is our Linear Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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": [
    "max_x = np.max(X) + 100\n",
    "min_x = np.min(X) - 100\n",
    "\n",
    "# Calculating line values x and y\n",
    "x = np.linspace(min_x, max_x, 1000)\n",
    "y = b0 + b1 * x\n",
    "\n",
    "# Ploting Line\n",
    "plt.plot(x, y, color='#58b970', label='Regression Line')\n",
    "# Ploting Scatter Points\n",
    "plt.scatter(X, Y, c='#ef5423', label='Scatter Plot')\n",
    "\n",
    "plt.xlabel('Head Size in cm3')\n",
    "plt.ylabel('Brain Weight in grams')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "72.1206213783709\n"
     ]
    }
   ],
   "source": [
    "# Calculating Root Mean Squared Error\n",
    "\n",
    "rmse = 0\n",
    "for i in range(length):\n",
    "    y_pred = b0 + b1 * X[i]\n",
    "    rmse += (Y[i] - y_pred) ** 2\n",
    "rmse = np.sqrt(rmse/length)\n",
    "print(rmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using Scikit-Learn Machine Learning Library Approach"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.metrics import mean_squared_error\n",
    "linear=LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "X=X.reshape(length,1)\n",
    "linear=linear.fit(X,Y)\n",
    "Y_pred=linear.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "72.1206213783709\n"
     ]
    }
   ],
   "source": [
    "# Calculating the Root-Mean Squared Error\n",
    "mse=mean_squared_error(Y,Y_pred)\n",
    "rmse=np.sqrt(mse)\n",
    "print(rmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# END of the CODE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}