{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression 101"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is our first basic regression example.\n",
    "\n",
    "In this example, we won't be doing anything complicated or using complex databases yet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn import linear_model\n",
    "lr = linear_model.LinearRegression() #In sklearn we define an object as our ML operator\n",
    "import pylab as plt\n",
    "%matplotlib inline \n",
    "#again, this is only in jupyter notebooks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0  1  4  9 16 25 36 49 64 81]\n"
     ]
    }
   ],
   "source": [
    "#Let's create some data\n",
    "x = np.arange(0,10,1) #Data from 0 to 10 in steps of 1\n",
    "y = np.power(x,2)\n",
    "print y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x10e19fbd0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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9AJn588z8Sc1lDcpPgBXgxRGxD3gR8P16S9q5zPw34McXLL4BONl/fRK4caP91NFDfzfw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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e0cd910>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#lr.fit(x,y)#<-- This doesn't work!!\n",
    "#We need to reshape from 1D to 2D vectors\n",
    "\n",
    "x = x[:,None]\n",
    "y = y[:,None]\n",
    "lr.fit(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 9.]]\n",
      "[-12.]\n"
     ]
    }
   ],
   "source": [
    "print lr.coef_\n",
    "print lr.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The resulting weight is:\n",
    "\n",
    "$y = 9x - 12$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "predict_y = lr.predict(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x10e1d5610>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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krWIPnRuSSMPMDF/DoY+Tp47dkKTVw3dDEo0Ce/gabLOz8Hu/11r75sor+7L2jRuSaFSZ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\neQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e1d5a50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, predict_y, c ='red')\n",
    "plt.scatter(x, y, c ='blue')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "lr.fit_intercept = False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 7.10526316]]\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "lr.fit(x,y)\n",
    "print lr.coef_\n",
    "print lr.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x11396e990>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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duCjdLDV+XtedpQJK37S3t5NI1LF793PABKCF6upptLZu1Ey/jETZeCUi+erSLPUynPU4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\niMSEAr6ISEz8f9dc/JtkeFa9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e297490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "predict_y_2 = lr.predict(x)\n",
    "plt.plot(x, predict_y, c ='red')\n",
    "plt.scatter(x, y, c ='blue')\n",
    "plt.plot(x, predict_y_2, c ='orange')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  0.   0.]\n",
      " [  1.   1.]\n",
      " [  2.   4.]\n",
      " [  3.   9.]\n",
      " [  4.  16.]\n",
      " [  5.  25.]\n",
      " [  6.  36.]\n",
      " [  7.  49.]\n",
      " [  8.  64.]\n",
      " [  9.  81.]]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "poly = PolynomialFeatures(2, include_bias = False)\n",
    "x_2 = poly.fit_transform(x)\n",
    "print x_2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  1.06625262e-15   1.00000000e+00]]\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "lr.intercept_ = True\n",
    "lr.fit(x_2,y)\n",
    "print lr.coef_\n",
    "print lr.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x113b51650>]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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hPvzYGS5fBN3TKn1qaWkpI0eOZNmyZSxdupQOHTrU71ilVhT4IuKzcwN8+v/h61fg8xYw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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e21bf50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "predict_y_3 = lr.predict(x_2)\n",
    "plt.plot(x, predict_y, c ='red',label = 'First Attempt')\n",
    "plt.scatter(x, y, c ='blue')\n",
    "plt.plot(x, predict_y_2, c ='orange', label = 'Second Attempt (no intercept)')\n",
    "plt.plot(x, predict_y_3, c ='black', label = 'Different features')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x113ca2d90>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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E5KgxJv81YJVSqhQKDfYHDsCoUbBrF8yYUXT6JvMs/DETfn8d6rSDa+dAvZI3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\n5SY04CullJvQgK+UUm7i/wGvK53p9B5LywAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113ac7250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "predict_y_3 = lr.predict(x_2)\n",
    "plt.plot(x, predict_y, c ='red',label = 'First Attempt')\n",
    "plt.scatter(x, y, c ='blue')\n",
    "plt.plot(x, predict_y_2, c ='orange', label = 'Second Attempt (no intercept)')\n",
    "plt.plot(x, predict_y_3, c ='black', label = 'Different features')\n",
    "\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[   0.    0.    0.]\n",
      " [   1.    1.    1.]\n",
      " [   2.    4.    8.]\n",
      " [   3.    9.   27.]\n",
      " [   4.   16.   64.]\n",
      " [   5.   25.  125.]\n",
      " [   6.   36.  216.]\n",
      " [   7.   49.  343.]\n",
      " [   8.   64.  512.]\n",
      " [   9.   81.  729.]]\n",
      "[[  1.10220646e-14   1.00000000e+00  -8.18288691e-17]]\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "poly = PolynomialFeatures(3, include_bias = False)\n",
    "x_3 = poly.fit_transform(x)\n",
    "print x_3\n",
    "lr.intercept_ = True\n",
    "lr.fit(x_3,y)\n",
    "print lr.coef_\n",
    "print lr.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x113e1ab90>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LSE5OjsBgpToU+CJS0aFd8NYk+P5N2N8Zkt+HnkmVP/XQIX70ox+Rl5fHJ598Qt++fet2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\nLsYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113c59090>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "predict_y_4 = lr.predict(x_3)\n",
    "plt.plot(x, predict_y, c ='red',label = 'First Attempt')\n",
    "plt.scatter(x, y, c ='blue')\n",
    "plt.plot(x, predict_y_2, c ='orange', label = 'Second Attempt (no intercept)')\n",
    "plt.plot(x, predict_y_3, c ='black', label = 'Different features')\n",
    "plt.plot(x, predict_y_4, c ='black', label = '3rd Degree')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  2.24780234e+01  -9.92113537e-01  -1.35619565e-02]]\n",
      "0.0\n"
     ]
    }
   ],
   "source": [
    "y_noise = np.random.rand(10,1)\n",
    "y_n = y + 100*y_noise\n",
    "lr.fit(x_3,y_n)\n",
    "print lr.coef_\n",
    "print lr.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10e1e9a10>]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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k5OQEXU5S0lIHUhsEPktHqtfSpUvp3LkzY8aMUdhXIy11IMlKgV9LLFiwgBtu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\nRFKEAl9EJEX8f4DRxHyHem67AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113d1c4d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "predict_y_n = lr.predict(x_3)\n",
    "plt.scatter(x, y, c ='blue')\n",
    "plt.scatter(x, y_n, c ='red')\n",
    "plt.plot(x, predict_y_n, c ='black', label = '3rd Degree')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10e146450>]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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1eqUkRSIuYt4V6OrufzGzQ4E3gYuAsdRf03aKrml7YNydk046iUmTJnH++ecH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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x113dcf390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "poly = PolynomialFeatures(5, include_bias = False)\n",
    "x_5 = poly.fit_transform(x)\n",
    "lr.fit(x_5,y_n)\n",
    "predict_y_n = lr.predict(x_5)\n",
    "plt.scatter(x, y, c ='blue')\n",
    "plt.scatter(x, y_n, c ='red')\n",
    "plt.plot(x, predict_y_n, c ='black', label = '3rd Degree')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  8.81265360e+01,  -4.95593700e+01,   1.15051496e+01,\n",
       "         -1.07447535e+00,   3.35709123e-02]])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}