10a. Linear Regression.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Simple Linear Regression\n",
    "* y = ax + b\n",
    "* LinearRegression finds the best line using training dataset that could predict house price (dependent variable) based on square footage ( independent variable/ features )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x72ba3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(1)\n",
    "x = 10 * rng.rand(50)\n",
    "y = 2 * x - 5 + rng.randn(50)\n",
    "plt.scatter(x, y);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "# Model Selection\n",
    "model = LinearRegression(fit_intercept=True)\n",
    "s = x.shape\n",
    "data_in = x.reshape(s[0],1)\n",
    "s = y.shape\n",
    "data_out = y.reshape(s[0],1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Training the model\n",
    "model.fit(data_in,data_out)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Creating test case\n",
    "x_new = [[12]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 19.32792864]])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Predicting the moddel\n",
    "model.predict(x_new)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "x_test = np.linspace(10,12,1000)\n",
    "y_predict = model.predict(x_test.reshape(1000,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x72d2e80>]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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zaRULmVlH4D537w/sBow1M4/e5w+ZioBINXj11RAD/du/hctDdOsWd4tEspNVj6AU1COQ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\nrkkiIlJKWV191Mw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      "text/plain": [
       "<matplotlib.figure.Figure at 0x90c7400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plt.scatter(x, y);\n",
    "plt.plot(x_test,y_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-4.99857709])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.intercept_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Linear regression algo predicted slope = 2.02, & intercept = -4.9"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* LinearRegression estimator is much more capable than this. y = ax1 + bx2 + cx3. Here x1,x2 & x3\n",
    "are different features \n",
    "* Polynomial regression - degree of more than one"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = np.arange(10)\n",
    "y = x*x*x - x*x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0,   0,   4,  18,  48, 100, 180, 294, 448, 648])"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x967d978>]"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SS+Dmm+H++2GnnfKOpr74ClUz63QRqRRz++2pHOPEXj73ljGzqhQBF18MU6ZAsQj9++cd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\nKKRNo/FZ724AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x95be630>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  2.,   4.,   8.],\n",
       "       [  3.,   9.,  27.],\n",
       "       [  4.,  16.,  64.]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "\n",
    "x = np.array([2, 3, 4])\n",
    "\n",
    "poly = PolynomialFeatures(3, include_bias=False)\n",
    "\n",
    "poly.fit_transform(x[:, None])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x9aeba90>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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OkqQeY/hLUgkZ/uo6LpIntZ/hr67izEypM+zwVdco48xMqRXs8FVP88T3UucY/uoaLpKn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\nhr8kldD/B+hNJQ3w4DX7AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x989fd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(1)\n",
    "x = 10 * rng.rand(50)\n",
    "y = np.sin(x) + 0.1 * rng.randn(50)\n",
    "\n",
    "plt.scatter(x.reshape(50,1),y.reshape(50,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Evaluating the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Pizza data creation\n",
    "import pandas as pd\n",
    "pizza = pd.DataFrame(data={ 'size':[6,8,10,14,18], 'price':[7,9,13,17.5,18]})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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l9O9fNz4kMzPrBjNdz2Bt+vc7U93aN0QD10OrORaZY5E5Fs3x3ERmZua5iczMek3LprBO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\nnAzMzAz4/zy1r4fd8Dm1AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa90add8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.title('Pizza vs Price')\n",
    "plt.xlabel('Diameter in inches')\n",
    "plt.ylabel('Price in dollars')\n",
    "\n",
    "plt.plot(pizza['size'], pizza['price'], 'm.')\n",
    "plt.axis([0,25,0,25])\n",
    "plt.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pizza_price_model = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "pizza_price_model.fit(pizza[['size']], pizza[['price']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "test_pizza = pd.DataFrame(data={ 'size':[7,12,15,24,28], 'price':[11,19,23,27,28]})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.59083669065206779"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Evaluating the model\n",
    "pizza_price_model.score(test_pizza[['size']],test_pizza[['price']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Improve model by addding poynomial feature\n",
    "# Quadtratic Feature\n",
    "quadratic_featureizer = PolynomialFeatures(degree=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[   1.,    6.,   36.],\n",
       "       [   1.,    8.,   64.],\n",
       "       [   1.,   10.,  100.],\n",
       "       [   1.,   14.,  196.],\n",
       "       [   1.,   18.,  324.]])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quadratic_featureizer.fit_transform(pizza[['size']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "quad_model = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "float() argument must be a string or a number",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-69-4755c542b4d3>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mquad_model\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mquadratic_featureizer\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mpizza\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'price'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;32mC:\\Users\\ZekeLabs\\Anaconda2\\envs\\gl-env\\lib\\site-packages\\sklearn\\linear_model\\base.pyc\u001b[0m in \u001b[0;36mfit\u001b[1;34m(self, X, y, sample_weight)\u001b[0m\n\u001b[0;32m    425\u001b[0m         \u001b[0mn_jobs_\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mn_jobs\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    426\u001b[0m         X, y = check_X_y(X, y, accept_sparse=['csr', 'csc', 'coo'],\n\u001b[1;32m--> 427\u001b[1;33m                          y_numeric=True, multi_output=True)\n\u001b[0m\u001b[0;32m    428\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    429\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msample_weight\u001b[0m \u001b[1;32mis\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mNone\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;32mand\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0matleast_1d\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0msample_weight\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[1;33m>\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mC:\\Users\\ZekeLabs\\Anaconda2\\envs\\gl-env\\lib\\site-packages\\sklearn\\utils\\validation.pyc\u001b[0m in \u001b[0;36mcheck_X_y\u001b[1;34m(X, y, accept_sparse, dtype, order, copy, force_all_finite, ensure_2d, allow_nd, multi_output, ensure_min_samples, ensure_min_features, y_numeric, warn_on_dtype, estimator)\u001b[0m\n\u001b[0;32m    508\u001b[0m     X = check_array(X, accept_sparse, dtype, order, copy, force_all_finite,\n\u001b[0;32m    509\u001b[0m                     \u001b[0mensure_2d\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mallow_nd\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mensure_min_samples\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 510\u001b[1;33m                     ensure_min_features, warn_on_dtype, estimator)\n\u001b[0m\u001b[0;32m    511\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[0mmulti_output\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    512\u001b[0m         y = check_array(y, 'csr', force_all_finite=True, ensure_2d=False,\n",
      "\u001b[1;32mC:\\Users\\ZekeLabs\\Anaconda2\\envs\\gl-env\\lib\\site-packages\\sklearn\\utils\\validation.pyc\u001b[0m in \u001b[0;36mcheck_array\u001b[1;34m(array, accept_sparse, dtype, order, copy, force_all_finite, ensure_2d, allow_nd, ensure_min_samples, ensure_min_features, warn_on_dtype, estimator)\u001b[0m\n\u001b[0;32m    391\u001b[0m         \u001b[1;31m# make sure we acually converted to numeric:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    392\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[0mdtype_numeric\u001b[0m \u001b[1;32mand\u001b[0m \u001b[0marray\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mdtype\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mkind\u001b[0m \u001b[1;33m==\u001b[0m \u001b[1;34m\"O\"\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 393\u001b[1;33m             \u001b[0marray\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0marray\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfloat64\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    394\u001b[0m         \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mallow_nd\u001b[0m \u001b[1;32mand\u001b[0m \u001b[0marray\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[1;33m>=\u001b[0m \u001b[1;36m3\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    395\u001b[0m             raise ValueError(\"Found array with dim %d. %s expected <= 2.\"\n",
      "\u001b[1;31mTypeError\u001b[0m: float() argument must be a string or a number"
     ]
    }
   ],
   "source": [
    "quad_model.fit(quadratic_featureizer, pizza[['price']])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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