Regression Analysis in python and R

Basic_regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "mtcars=pd.read_csv('/home/anshul/data-sets/mtcars.csv')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<ol class=list-inline>\n",
       "\t<li>'mpg'</li>\n",
       "\t<li>'cyl'</li>\n",
       "\t<li>'disp'</li>\n",
       "\t<li>'hp'</li>\n",
       "\t<li>'drat'</li>\n",
       "\t<li>'wt'</li>\n",
       "\t<li>'qsec'</li>\n",
       "\t<li>'vs'</li>\n",
       "\t<li>'am'</li>\n",
       "\t<li>'gear'</li>\n",
       "\t<li>'carb'</li>\n",
       "</ol>\n"
      ],
      "text/latex": [
       "\\begin{enumerate*}\n",
       "\\item 'mpg'\n",
       "\\item 'cyl'\n",
       "\\item 'disp'\n",
       "\\item 'hp'\n",
       "\\item 'drat'\n",
       "\\item 'wt'\n",
       "\\item 'qsec'\n",
       "\\item 'vs'\n",
       "\\item 'am'\n",
       "\\item 'gear'\n",
       "\\item 'carb'\n",
       "\\end{enumerate*}\n"
      ],
      "text/markdown": [
       "1. 'mpg'\n",
       "2. 'cyl'\n",
       "3. 'disp'\n",
       "4. 'hp'\n",
       "5. 'drat'\n",
       "6. 'wt'\n",
       "7. 'qsec'\n",
       "8. 'vs'\n",
       "9. 'am'\n",
       "10. 'gear'\n",
       "11. 'carb'\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       " [1] \"mpg\"  \"cyl\"  \"disp\" \"hp\"   \"drat\" \"wt\"   \"qsec\" \"vs\"   \"am\"   \"gear\"\n",
       "[11] \"carb\""
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "names(mtcars)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Unnamed: 0',\n",
       " 'mpg',\n",
       " 'cyl',\n",
       " 'disp',\n",
       " 'hp',\n",
       " 'drat',\n",
       " 'wt',\n",
       " 'qsec',\n",
       " 'vs',\n",
       " 'am',\n",
       " 'gear',\n",
       " 'carb']"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "map(lambda x: x.encode(\"utf-8\"),mtcars.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Coefficients: \\n', array([-5.34447157]))\n"
     ]
    }
   ],
   "source": [
    "from sklearn import linear_model\n",
    "import numpy as np\n",
    "X = [[x] for x in mtcars[\"wt\"].values]\n",
    "y=mtcars[\"mpg\"]\n",
    "\n",
    "lm=linear_model.LinearRegression()\n",
    "lm.fit(X,y)\n",
    "\n",
    "# The coefficients\n",
    "print('Coefficients: \\n', lm.coef_)\n",
    "# The mean square error\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = mpg ~ wt)\n",
       "\n",
       "Coefficients:\n",
       "(Intercept)           wt  \n",
       "     37.285       -5.344  \n"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "attach(mtcars)\n",
    "bmodel=lm(mpg~wt)\n",
    "bmodel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Residual sum of squares: 8.70\n",
      "Variance score: 0.75\n"
     ]
    }
   ],
   "source": [
    "print(\"Residual sum of squares: %.2f\"\n",
    "      % np.mean((lm.predict(X) - y) ** 2))\n",
    "# Explained variance score: 1 is perfect prediction\n",
    "print('Variance score: %.2f' % lm.score(X, y))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = mpg ~ wt)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-4.5432 -2.3647 -0.1252  1.4096  6.8727 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept)  37.2851     1.8776  19.858  < 2e-16 ***\n",
       "wt           -5.3445     0.5591  -9.559 1.29e-10 ***\n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 3.046 on 30 degrees of freedom\n",
       "Multiple R-squared:  0.7528,\tAdjusted R-squared:  0.7446 \n",
       "F-statistic: 91.38 on 1 and 30 DF,  p-value: 1.294e-10\n"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(bmodel)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "</svg>\n"
      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mtcars$new=predict(bmodel,mtcars)\n",
    "d=mtcars[,c(\"mpg\",\"new\")]\n",
    "plot(d)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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ss1m6dGkuuOCClMvlnHHGGfniF7+Yl19+ech+N954Y+rq6ob9OO+882o0OQAAjB9uwRqh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\nAABAYf4/S6MOpj/8Ve4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.scatter(y,lm.predict(X),  color='black')\n",
    "\n",
    "plt.show()\n",
    "from IPython.display import Image\n",
    "Image(filename='/home/anshul/lr.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = mpg ~ wt + cyl + gear + wt + hp)\n",
       "\n",
       "Coefficients:\n",
       "(Intercept)           wt          cyl         gear           hp  \n",
       "    36.6895      -3.0226      -0.8126       0.3626      -0.0217  \n"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bmodel=lm(mpg~wt+cyl+gear+wt+hp)\n",
    "bmodel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Coefficients: \\n', array([-1.51131728, -0.81259895,  0.36259005, -1.51131728, -0.02170211]))\n"
     ]
    }
   ],
   "source": [
    "X = [x for x in mtcars.loc[:,[\"wt\",\"cyl\",\"gear\",\"wt\",\"hp\"]].values]\n",
    "y=mtcars[\"mpg\"]\n",
    "\n",
    "lm.fit(X,y)\n",
    "# The coefficients\n",
    "print('Coefficients: \\n', lm.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = mpg ~ wt + cyl + gear + wt + hp)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-3.4710 -1.7876 -0.6517  1.2362  5.9677 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)    \n",
       "(Intercept) 36.68953    5.97025   6.145 1.44e-06 ***\n",
       "wt          -3.02263    0.85116  -3.551  0.00143 ** \n",
       "cyl         -0.81260    0.66320  -1.225  0.23106    \n",
       "gear         0.36259    1.00000   0.363  0.71974    \n",
       "hp          -0.02170    0.01574  -1.379  0.17922    \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 2.551 on 27 degrees of freedom\n",
       "Multiple R-squared:  0.8439,\tAdjusted R-squared:  0.8208 \n",
       "F-statistic: 36.49 on 4 and 27 DF,  p-value: 1.599e-10\n"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(bmodel)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Residual sum of squares: 5.49\n",
      "Variance score: 0.84\n"
     ]
    }
   ],
   "source": [
    "print(\"Residual sum of squares: %.2f\"\n",
    "      % np.mean((lm.predict(X) - y) ** 2))\n",
    "# Explained variance score: 1 is perfect prediction\n",
    "print('Variance score: %.2f' % lm.score(X, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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       "</g>\n",
       "</svg>\n"
      ],
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/svg+xml": {
       "isolated": true
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mtcars$new=predict(bmodel,mtcars)\n",
    "d=mtcars[,c(\"mpg\",\"new\")]\n",
    "plot(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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fU/jQQw95BgQAYBby/drUeQYEAAAojAABAAAKI0AAAIDCCBAAAKAwAgQAACiMAAEAAAoj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\nAQIAABTm/wP2y+B88wmGAAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.scatter(y,lm.predict(X),  color='black')\n",
    "\n",
    "plt.show()\n",
    "Image(filename='/home/anshul/lr2.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = mpg ~ wt + cyl + gear + wt + hp + carb + disp + \n",
       "    drat + vs + qsec)\n",
       "\n",
       "Coefficients:\n",
       "(Intercept)           wt          cyl         gear           hp         carb  \n",
       "   17.59704     -3.93430     -0.44543      1.22953     -0.02022     -0.26242  \n",
       "       disp         drat           vs         qsec  \n",
       "    0.01275      1.10054     -0.22311      0.57571  \n"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bmodel=lm(mpg~wt+cyl+gear+wt+hp+carb+disp+drat+vs+qsec)\n",
    "bmodel"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('Coefficients: \\n', array([-1.96715177, -0.4454288 ,  1.22952745, -1.96715177, -0.0202156 ,\n",
      "       -0.26242241,  0.01274525,  1.10054141, -0.22310953,  0.57571041]))\n"
     ]
    }
   ],
   "source": [
    "X = [x for x in mtcars.loc[:,[\"wt\",\"cyl\",\"gear\",\"wt\",\"hp\",\"carb\",\"disp\",\"drat\",\"vs\",\"qsec\"]].values]\n",
    "y=mtcars[\"mpg\"]\n",
    "lm.fit(X,y)\n",
    "# The coefficients\n",
    "print('Coefficients: \\n', lm.coef_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "\n",
       "Call:\n",
       "lm(formula = mpg ~ wt + cyl + gear + wt + hp + carb + disp + \n",
       "    drat + vs + qsec)\n",
       "\n",
       "Residuals:\n",
       "    Min      1Q  Median      3Q     Max \n",
       "-2.9886 -1.6738 -0.3834  0.9796  5.4395 \n",
       "\n",
       "Coefficients:\n",
       "            Estimate Std. Error t value Pr(>|t|)  \n",
       "(Intercept) 17.59704   18.41902   0.955   0.3498  \n",
       "wt          -3.93430    1.90734  -2.063   0.0511 .\n",
       "cyl         -0.44543    1.02029  -0.437   0.6667  \n",
       "gear         1.22953    1.43393   0.857   0.4004  \n",
       "hp          -0.02022    0.02199  -0.919   0.3679  \n",
       "carb        -0.26242    0.83653  -0.314   0.7567  \n",
       "disp         0.01275    0.01805   0.706   0.4876  \n",
       "drat         1.10054    1.63356   0.674   0.5075  \n",
       "vs          -0.22311    2.08103  -0.107   0.9156  \n",
       "qsec         0.57571    0.71086   0.810   0.4267  \n",
       "---\n",
       "Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1\n",
       "\n",
       "Residual standard error: 2.68 on 22 degrees of freedom\n",
       "Multiple R-squared:  0.8596,\tAdjusted R-squared:  0.8022 \n",
       "F-statistic: 14.97 on 9 and 22 DF,  p-value: 1.855e-07\n"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(bmodel)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Residual sum of squares: 4.94\n",
      "Variance score: 0.86\n"
     ]
    }
   ],
   "source": [
    "print(\"Residual sum of squares: %.2f\"\n",
    "      % np.mean((lm.predict(X) - y) ** 2))\n",
    "# Explained variance score: 1 is perfect prediction\n",
    "print('Variance score: %.2f' % lm.score(X, y))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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jgAAAAIURQAAAgMIIIAAAQGEEEAAAoDACCAAAUBgBBAAAKIwAAgAAFEYAAQAACiOAAAAA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\nAGwEBAAA2AgIAACwERAAAGAjIAAAwCa0EfnwqPrbfAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.scatter(y,lm.predict(X),  color='black')\n",
    "\n",
    "plt.show()\n",
    "Image(filename='/home/anshul/lr3.png')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      ],
      "text/plain": [
       "plot without title"
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     },
     "metadata": {
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    }
   ],
   "source": [
    "mtcars$new=predict(bmodel,mtcars)\n",
    "d=mtcars[,c(\"mpg\",\"new\")]\n",
    "plot(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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