week-3-polynomial-regression-assignment.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Regression Week 3: Assessing Fit (polynomial regression)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this notebook you will compare different regression models in order to assess which model fits best. We will be using polynomial regression as a means to examine this topic. In particular you will:\n",
    "* Write a function to take an SArray and a degree and return an SFrame where each column is the SArray to a polynomial value up to the total degree e.g. degree = 3 then column 1 is the SArray column 2 is the SArray squared and column 3 is the SArray cubed\n",
    "* Use matplotlib to visualize polynomial regressions\n",
    "* Use matplotlib to visualize the same polynomial degree on different subsets of the data\n",
    "* Use a validation set to select a polynomial degree\n",
    "* Assess the final fit using test data\n",
    "\n",
    "We will continue to use the House data from previous notebooks."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fire up graphlab create"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#import graphlab\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import sklearn \n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we're going to write a polynomial function that takes an SArray and a maximal degree and returns an SFrame with columns containing the SArray to all the powers up to the maximal degree.\n",
    "\n",
    "The easiest way to apply a power to an SArray is to use the .apply() and lambda x: functions. \n",
    "For example to take the example array and compute the third power we can do as follows: (note running this cell the first time may take longer than expected since it loads graphlab)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.  2.  3.]\n",
      "[1.0, 8.0, 27.0]\n"
     ]
    }
   ],
   "source": [
    "tmp = np.array([1., 2., 3.])\n",
    "tmp_cubed = map(lambda x: x**3, tmp)\n",
    "print tmp\n",
    "print tmp_cubed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can create an empty SFrame using graphlab.SFrame() and then add any columns to it with ex_sframe['column_name'] = value. For example we create an empty SFrame and make the column 'power_1' to be the first power of tmp (i.e. tmp itself)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   power_1\n",
      "0      1.0\n",
      "1      2.0\n",
      "2      3.0\n"
     ]
    }
   ],
   "source": [
    "#ex_sframe = graphlab.SFrame()\n",
    "ex_sframe = pd.DataFrame()\n",
    "ex_sframe['power_1'] = tmp\n",
    "print ex_sframe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Polynomial_sframe function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the hints above complete the following function to create an SFrame consisting of the powers of an SArray up to a specific degree:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def polynomial_sframe(feature, degree):\n",
    "    # assume that degree >= 1\n",
    "    # initialize the SFrame:\n",
    "    poly_sframe = pd.DataFrame()\n",
    "    # and set poly_sframe['power_1'] equal to the passed feature\n",
    "    poly_sframe['power_1'] = feature\n",
    "        \n",
    "    # first check if degree > 1\n",
    "    if degree > 1:\n",
    "        # then loop over the remaining degrees:\n",
    "        # range usually starts at 0 and stops at the endpoint-1. We want it to start at 2 and stop at degree\n",
    "        for power in range(2, degree+1): \n",
    "            # first we'll give the column a name:\n",
    "            name = 'power_' + str(power)\n",
    "            # then assign poly_sframe[name] to the appropriate power of feature\n",
    "            poly_sframe[name] = feature ** power\n",
    "    return poly_sframe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To test your function consider the smaller tmp variable and what you would expect the outcome of the following call:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   power_1  power_2  power_3\n",
      "0      1.0      1.0      1.0\n",
      "1      2.0      4.0      8.0\n",
      "2      3.0      9.0     27.0\n"
     ]
    }
   ],
   "source": [
    "print polynomial_sframe(tmp, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualizing polynomial regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's use matplotlib to visualize what a polynomial regression looks like on some real data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sales = pd.read_csv('kc_house_data.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As in Week 3, we will use the sqft_living variable. For plotting purposes (connecting the dots), you'll need to sort by the values of sqft_living. For houses with identical square footage, we break the tie by their prices."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "sales = sales.sort_values(by= ['sqft_living', 'price'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start with a degree 1 polynomial using 'sqft_living' (i.e. a line) to predict 'price' and plot what it looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "poly1_data = polynomial_sframe(sales['sqft_living'], 1)\n",
    "poly1_data['price'] = sales['price'] # add price to the data since it's the target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>power_1</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>19452</th>\n",
       "      <td>290</td>\n",
       "      <td>142000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15381</th>\n",
       "      <td>370</td>\n",
       "      <td>276000.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       power_1     price\n",
       "19452      290  142000.0\n",
       "15381      370  276000.0"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly1_data.head(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "NOTE: for all the models in this notebook use validation_set = None to ensure that all results are consistent across users."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "#model1 = graphlab.linear_regression.create(poly1_data, target = 'price', features = ['power_1'], validation_set = None)\n",
    "model1 = LinearRegression().fit(X= poly1_data['power_1'].values.reshape(-1,1), y=poly1_data['price'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-43580.743094475125, array([ 280.6235679]))"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#let's take a look at the weights before we plot\n",
    "model1.intercept_, model1.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "pred1 = model1.predict(poly1_data['power_1'].values.reshape(-1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1006764d0>,\n",
       " <matplotlib.lines.Line2D at 0x10ce517d0>]"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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LO59zBv0Wty4VO8nxRDhyrIXy2v1cf/449h9tZsbYoTQ2NUcDYSaGl3muup7z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\nMo6JjWEYhpFx/n80TRQOW8yKMwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cd026d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(poly1_data['power_1'],poly1_data['price'],'.',\n",
    "        poly1_data['power_1'],pred1,'-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's unpack that plt.plot() command. The first pair of SArrays we passed are the 1st power of sqft and the actual price we then ask it to print these as dots '.'. The next pair we pass is the 1st power of sqft and the predicted values from the linear model. We ask these to be plotted as a line '-'. \n",
    "\n",
    "We can see, not surprisingly, that the predicted values all fall on a line, specifically the one with slope 280 and intercept -43579. What if we wanted to plot a second degree polynomial?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>power_1</th>\n",
       "      <th>power_2</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>19452</th>\n",
       "      <td>290</td>\n",
       "      <td>84100</td>\n",
       "      <td>142000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15381</th>\n",
       "      <td>370</td>\n",
       "      <td>136900</td>\n",
       "      <td>276000.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       power_1  power_2     price\n",
       "19452      290    84100  142000.0\n",
       "15381      370   136900  276000.0"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly2_data = polynomial_sframe(sales['sqft_living'], 2)\n",
    "my_features = poly2_data.columns # get the name of the features\n",
    "poly2_data['price'] = sales['price'] # add price to the data since it's the target\n",
    "poly2_data.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "model2 = LinearRegression().fit(X= poly2_data[my_features], y= poly2_data['price'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(199222.27930548205, array([  6.79940947e+01,   3.85812609e-02]))"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model2.intercept_, model2.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pred2 = model2.predict(poly2_data[my_features])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10cf33a50>,\n",
       " <matplotlib.lines.Line2D at 0x10cf33b90>]"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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HXlvPPZeeGDFTQaSHe6yjn1jFq6lpvVhGSA2u8dkeCnbNgUW/gux2cMMUOGVs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\nnbABoE7YAFC3AeP7pH5Xb3+dAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cfe2e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(poly2_data['power_1'],poly2_data['price'],'.',\n",
    "        poly2_data['power_1'], pred2,'-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The resulting model looks like half a parabola. Try on your own to see what the cubic looks like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>power_1</th>\n",
       "      <th>power_2</th>\n",
       "      <th>power_3</th>\n",
       "      <th>price</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>19452</th>\n",
       "      <td>290</td>\n",
       "      <td>84100</td>\n",
       "      <td>24389000</td>\n",
       "      <td>142000.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15381</th>\n",
       "      <td>370</td>\n",
       "      <td>136900</td>\n",
       "      <td>50653000</td>\n",
       "      <td>276000.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       power_1  power_2   power_3     price\n",
       "19452      290    84100  24389000  142000.0\n",
       "15381      370   136900  50653000  276000.0"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly3_data = polynomial_sframe(sales['sqft_living'], 3)\n",
    "my_features = poly3_data.columns # get the name of the features\n",
    "poly3_data['price'] = sales['price'] # add price to the data since it's the target\n",
    "poly3_data.head(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(336819.74822132086,\n",
       " array([ -9.01819864e+01,   8.70465089e-02,  -3.84055260e-06]))"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model3= LinearRegression().fit( X= poly3_data[my_features], y= poly3_data['price'])\n",
    "model3.intercept_, model3.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10e82ef90>,\n",
       " <matplotlib.lines.Line2D at 0x10e700750>]"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Nlk5H8rMdl/L29v2bpf8k3u8w3nQOpmUSkUWqWt7U/dgIAiYrGntKPnwxj57I\nLNVncUJav7+jsQAXT/SdyNjBPWI+aDp2cI8GZWGRGWk7A6G6Mdua1McRrIX5f4a5vwbxwag76fyd\ny3jUFzutO1KmOvWTvXMzJhk2NprJiljPoWTDwFtfTzjGWht/7AytTu2KG6QY3z7mCC4c0rNuegO/\nCBcO6RkzGw0S902l1cexcSk8eAq8fiP0PgF+Oh8Gj4ckA02mnyXKxFhyxtidjUlbok/QYwaWcWfF\nyoyPHhBp684AE55dUnc8aNg3Ei/9ul0b789/6OQ59da/fcwRcYNLtGT6L5Lu49i9E/4xGf59H7Tb\nF875Oxx+ZkrpzJkeqidTY8kZY8HGpCTy2ZnI4frjNRk1R2dyIKhMmlFZd2GMvjhe/dT7Mberqq5h\nwrNL6vqIwq8h+WavZJIakhrlefWb8NLVsPVTGHgRDL8NSjolVYdI1qlv8pUFG5O06OcuorvRIz9B\nhx+MbK70k+qaQF1TUfSdTbyZQIEGyQiBoHLLS5VJB5tEIzgn6uN4ZX4lUnEjp4Xmsk66sW7owxx3\n6plJHTuWpgwQakw2WZ+NSVoyz85UVddwwV/f4dF56xI+oOkXoe/+7TNWv0kzKmP2V6T6oOjWnYGk\n+zii+zVKS4rp1K44cR+HKgtemsKQmSM5NfhP7qsdzak1d3D5P0uaNLxPJp7pMSYbLPXZJK33xFea\nfKcSPVNm9Ot8kc4MntHTV8eb3rni7XfpMPt6jgm9x/uhPkwMjGeF7hlOqampxTbEjMkkS302zS6d\nhy6jRQeWfAw0kHqnenQTY8zpnTXIQasf47hldwFwS+1FTA2OIBTVwNDU/pXoRIlwNpwFHJNLFmxM\nTLE+HQ87tEvak50VoqrqmgaZavEu2Le8VNloE2Of2k845KUb6a+rmBMawK8Cl1JFl5jrNrV/xcY0\nM/nIgo1pINbFasIzS7w2r1ZEoO5OrrEL9vTFVWyNMx10O77h2qJnuNT/GltD+/CzwJXMCB1DvJOZ\nif6V5pip1JhUWbAxDcS6WEVP6VxIwkPIxAsI8TSWbRcp3kObp/oWMql4KmXyFY/VnsIj7S/hPyV7\nQ5xmsrIM9a9Y+rPJRxZsTAMt7aK0MxBiYM9S3o4x2VqqYp2b6LJufMUtxQ8z3L+IFaEenLX7Kj4s\nOow7RnoPiiYzWVpTWPqzCcunZBELNqaBTCQC5JtMBBqIfcEOny8/QS7xV3Bt0TP4UCbXjuWh2lHs\nX7oPd0QGs6sKAAAXm0lEQVT9kyd7AUjnYmFjmhnIv747S302DSQ78VlrFd3cNX1xFY89/wKTZAqH\n+9YyJziAX3MZV511SpP+qWP9HpK9C8qnT7QmNzI1arelPpusCV+U4g3z0pIl89xPvU+Ih+3NmM/u\nYrT/Qb6ilCt2/5wl+5zIhJGHNvni3pSOfhvTzORb350FGxNXvj5wmUnR888MO7QLzy2qSnhXVxOo\nZeHMvzFm9qPw9Sbk6MvZ7+SbuH+vjhmrW75dLExhybe+Ows2JqY7K1a2+EADXvKAItx13oC6O4Hy\nAzs3elfXUzZxS9HDDAssgX2/DWMfh7KjMl63fLtYmMKSb313CcdGE5EeIjJXRJaLSKWI/NyVdxaR\nWSLysfveyZWLiNwrIqtEZKmIDIrY1zi3/sciMi6i/CgRWea2uVfEG1M9nWOYzGhNn56j55wZM7Cs\nbj6bSG3ZzTVFzzKrzXV8x7eSe4suhcvnZiXQgI1zZpom3+YjSpggICLdgG6q+p6I7AMsAsYAlwBb\nVHWyiEwEOqnq9SJyGnAVcBowGLhHVQeLSGdgIVCO1zqzCDhKVbeKyLvAz4D5wEzgXlV9VUR+l8ox\nGvs5LEFgj3idx+GRmlMduDJfdGrnTdSW6vM0YWWlJXXnpNe+JfUy2E72vcekoqn09G3mxeCx/IGL\nuPasEzOaRZbN/RiTrkwlCKScjSYiLwL3ua+TVHWjC0hvqmo/EfmLW37Crb8SOCn8pao/duV/Ad50\nX3NV9VBXPja8XnjbZI+hqhvj1bu1B5t489CA92l5UM+OGUsPzoVO7Yq5+YzDAZjwzJKUH0KNd042\nrF7JTUXTONW/iE+0jJsCl7CuQ3nd3UWsQNCULLLGWOAxuZCTbDQR6QUMxLsD6Rpxcf8c6OqWy4D1\nEZttcGWNlW+IUU4ax4gbbFqzZOahKeRAA97dzDVPvc8FQ3py5w+OZNKMyqRnCI2VCBEMfMOJm15k\nfPvnQfxw4i0cNOQKnihqAzT+DEMmhouJDizRiQvRz0xYIDL5LulgIyJ7A88BV6vqdolo01ZVFZGs\ntr2kcwwRGQ+MB+jZs2eCtVuuZOahaQkUeMwNFNq+bVFSwaZTu+IGzW4n+JZwS9HD9K7dxMzg0fy1\n3eWMaz+UMS7QQOMBpalZZLEC2WPz1sUdPgfIq4f3jIklqcnTRKQYL9A8pqrPu+JNrmkr3K/zhSuv\nAnpEbN7dlTVW3j1GeTrHqEdVp6hquaqWd+kSe4Td1qA1dfaHA06iERD8Itx93gAW/+/wur6eA/iS\n+4vvZlqb3xLCx0W7J3JF4GoWb2vPDc8vqzepWWMBpWNJccz34pVHixXI4n3KCk8hEC/wGZMvkslG\nE+Ah4ENV/WPEWzOAcEbZOODFiPKLXcbYEGCbawqrAIaLSCeXVTYcqHDvbReRIe5YF0ftK5VjmBha\nW6psMre/fbq0q2t+qv1mBz/3P8fstr9gmO99fhc4l1G7J/NW6Nt169cEgkyaUcnQyXPoPfEVfDGy\n1cLHjndHVV0TYOjkOQln4kzlw8EBLqmhqfsxJtuSaUYbClwELBOR8MMHvwQmA0+LyGXAWuBc995M\nvCyxVcBO4FIAVd0iIrcBC9x6t6pquKPgCuBhoAR41X2R6jFMfY0lBbR2H3+xg0NufIVTdR6vFj9O\nd/mSl4ND+E3gh3zGfjG3qa4J1AWSdDP2kmniivd8Tawkhgkj+tX9jmPtx5h8YWOjtVA2vlnjDpO1\n3Fw8jSG+D1keOpBbAhczXw9rtuM3Nj5VvGy2s48qY+6Kzc2W/WYM2NhoJoHWkhSQqk5s53+KnmGs\nfw7baM+NgR/xRPDkBlMzp6IsjVGyG2viip7WubHssvDda00giF+EoGrG5sUxJpMs2LRQ1l5fXxG1\nXOh/g2uKnqU93zAtOJy7as9mO3s3ed+fVdfUXeiTlaiJK5mBNKPvaIKqdU1rFmhMvkn/45zJa9Ze\nv8fxvqXMbHMDk4qnsTTUh1G7J3NL7biMBBrwzvXYwT1ivtfG3zCRIFNDzlgWmikkdmfTgkQ+2Fdk\nHyPoJ+v4ZdHjnOhfytrQ/ozffQ2vh8rxutozp9e+Jdw+xpuFMzzcjwA+n7A7WP9uJzzSQSbuPCwL\nzRQSCzYtRHSTSiCU4wrlUBe2cm3Rs5zrf5P/0I7bAhfySPBUdpPccy6p+vdqL6ny9jFH1AWdeBNX\ntWtTZNM/m1bJgk0BijU0iSUEQAnfMN7/CuOLXqaYWv4eHMn/1Z7Jtgw1l8UTq6smmbuOpg4xk29D\nyBvTGAs2BSbWUCbXPPV+q36GxkeIs/3/5BdFT9NVqnkleDS/rR3LOu2aeOMs6VhSHPPhzvAoApmY\nHz6VrDVjcs2CTYG55aXKpIcyafmUE3xLuaHoCQ7zreO90MH89+6reU8PyXXFiDPAQF15JgbrBJv+\n2RQOCzYF5Kbpy9Keq6WlGSQfcV3xUwzxfci6UBeu2P0zZoYGk+nO/2SUxhjzrDrO7ylcbp37prWx\nYFMgpi+uqhvRuDU7RNYzoehpTvUvYrN25FeBS3gyeDKBHP0pF/uESd8/vEF5os5769w3rY0FmzwW\n2YHsE2nFzWXQQzZxTdFzjPG9zdeU8LvAufw9OJIa9sppvfbeq/6/UOR4dNGKfVLXeW+d+6a1sWCT\np2I9Hd4adaGaK4teYKx/DiF8TAl+jwdqz8h6hlmywpO2LVy7hfIDOzc+Hl1EC5917pvWxgbizFPx\nntNoLfZlG+OLXuYi/xu0IcBTwWHcW3smm+ic66rFJEBpjInYovlF+MO5R1pQMQXDBuJsoaYvrkpp\nSuOWJhxkLvbPog0BZoSO5Z7as1ij3XJdtUYpJJW8EVS1WTRNq2TBJo9MX1zFhGeWEAi1jrvNSPvV\n3cl4QebF0FDuqx3Daj0g11XLuMjxy1IZ2dma20whs2CTR+6sWNnqAk10kJkeGsp9tWfyaZ7fyTRV\n+CHORA91Rn8AqaquYcIzSxqsZ0y+s2CTR1pTH00Zm/mvopmc75/bIoOM4I0WsP2bALE+P/hFknqo\nc9KMygYfQAIhZdKMSgs2pqAkDDYi8jfge8AXqvr/XFln4CmgF7AGOFdVt4qIAPfgTdm8E7hEVd9z\n24wDbnK7vV1Vp7ryo9gzJfRM4Oeqqukco9BENo90jPFgYEt0iKznx0UvMdr3bxThxdBQ/lQ7usUE\nGag/C2e8WTTjZaxFP9QZr++utfbpmcKVzED0DwMjo8omArNVtS8w270GGAX0dV/jgQegLjjdDAwG\njgZuFpFObpsHgMsjthuZzjEKTfgiVFVdg9LyLx6D5CP+Wvx7Xm97PaN8C5gaHMEJu+7mF4GfFHSg\niR6vIPpZmTEDy7jjrCMoKy1B8AJR+HUs9lCnaakS3tmo6j9FpFdU8WjgJLc8FXgTuN6VT1Mvn3qe\niJSKSDe37ixV3QIgIrOAkSLyJtBBVee58mnAGODVVI+hqhtT+9FzZ/riKq55+v2YowW3JEKIYb73\n+XHRywz2rWCr7s1dgbOZGhxONfvkunoJFfuFQDD+L6nYL5z3nR7MXbG50c77eOOXJfNQZ6c46dSd\n2rWOO2HTcqTbZ9M14uL+ORAeXrcMWB+x3gZX1lj5hhjl6Rwj74NNa0lrbsc3nOP/B5f4K+jj+5zP\ntDO3BC7iyeCwnD/xn4pAUGnfxs+O3UGEhgOe7t22iPIDO9fNYZOKZB/qvPmMw5nw7JJ6Qa/YL9x8\nRsMhcozJZ01OEHD9K1n9jJ7uMURkPF5TGz179sx4vZLVWoJMd9nMxf7XOd8/lw6yk/dDB3HV7it5\nNXQ0tQWai7Jjd5C7zxvAmIFlDfpftu4MNOmZmVh3PDHnKjrnSEt9NgUv3SvApnDTlWsm+8KVVwGR\nk7F3d2VV7GkSC5e/6cq7x1g/nWM0oKpTgCngjSCQyg+YKdMXVzX4ZNqyKN+RlVxa9BojfAtQhFdD\nR/O32lEs1r65rlxGhDPEMjUtQDzx5ri546wj6hIOjClU6c5UPwMY55bHAS9GlF8sniHANtcUVgEM\nF5FOLjFgOFDh3tsuIkNcltnFUftK5Rh56ZaXKltkoOnADsb5K6hocz3PtL2VY32V/CV4Bsfvuoer\nAj9rMYEG9mSIZXtagMaCWdj0xVUMnTyH3hNfYejkOUxfHPNzljF5J5nU5yfw7kr2E5ENeFllk4Gn\nReQyYC1wrlt9Jl5K8iq8tORLAVR1i4jcBixw690aThYArmBP6vOr7otUj5GPpi+uamHzzygD5BN+\n6J/NGf53KJHdLAn14brA5bwUPKag+mNS4RNh+uKqrE8LkCiYZWJ2T2NyxQbizJKbpi/j0RYy/0wH\nvub7/ncY65/D4b617NC2vBgcymPBU6jU3rmuXrMoKfZz9lFlPLeoqkEG2R1nHZGRi328wVfDz+0k\net+YbLCBOPNYSwg0RdRygm8pZ/v/yXd979FWalkeOpAbAz/ixeCxfE27XFexWdUEgsxdsZk7zjoi\na531iea4sdk9TSGzYJNh0xdXFXSg6S9rONv/Ft/3v00X2c4W3ZvHg6fwXPB4PtDe5GLa5XSFa5rK\nvbtfJO7cQZ9V18R9ZiYTEqVD2+yeppBZsMmwW16qzHUVUnaQVHG6bz6n++fRz7eB3epnTmgQzwWP\n583QgJxNudxUqTYQNzaMDDTPRb2xYGaze5pCVphXkTzT2FTA+aq3bOR03zxO98/jMN96Qios0H78\nKnAJLwWPKYgn/DNJgLOPKmPuis0xf48COb+o2+yeppBZsGmiWAMt5iMhxJGymlP87/Fd3yIO83mD\nMCwIHcKkwMW8Gjw6b2fBbA4KzF2xOebdgwAXDOmZFxf1bDbjGZNNFmya6PrnlrKrNpTrasTUjm84\n3reMU3zvMcy/mC6ynVr1sUgP4dbARcwMHs3n7Jvrajab0pJidtWG4n4wqHJ9MmB3D8ZkmgWbJrjg\nr+/kVaDxE+RI+YRjfZUM9VUyyPcRbaWW7dqON0NH8kZwEP8IHck29s51VZtdSbGfSd/3xhO7+qn3\nY67jFy+lwO4ejMk8CzZpuGn6Mp6Yvz5u1lJz8RPkUFnH0b4VHOurZLDvQzqI199QGTqQqcERzA0N\nYEGoX8GOTZYJ4f6YcACJF2xy/fs0piVrvVegNOXyGZpS/sNA3yqO8n3EIPmYAb5PaCe7AFgT6spL\nwWN5O3Q474T6s5UOOaljPgr3x4SVxUkhjjfHjDGm6SzYJKl5M86U7vIl/WUN/X1r6S9rOUzW0cPn\nXTBr1cdyPZCngifxXqgvi0KH8Bn7NUO9Clfkg4+WQmxM87Ngk4TsZJwpHdhBT/mCPvI5vWUjvXze\n9z6ysa45LKTCp/ot3teDeDxwCu+F+rJUe7fYccgS8Qn8cHDPBsPGhOebifdQZuQzMpYEYEzzs2CT\nSE01978wm44BaE8Ru/FTSxG1+KnFTzG1FFNLm/B3CbAPNXSUHXRgBx1lBx3ZQWf5D11lK99iC9+S\nLXxLttY1gYEXVD5jXz4NfYvpoeNYoT1ZHjqQldq91QaWaO3b+Pn1md44ZOUHdo4ZLGJ9MIh112JJ\nAMY0Lws2Cbz2yG953Xc/Tb3eB9TPJjrxuXZmufZidmgQn2snNmgXPtVurNWu7KJNZirdwrQt8vHb\ns79dLzjECxZ212JMfrJgk8Bdaw7kDfkxRQTdXUyQorrvQQIUsdt9BdzXf7SE7bRnm7ov2rODvdC0\npw9qefru356du0P1AgJQb0bTTu2KufmMw1MOFHbXYkz+sWDTiOmLq1gZ6sHKehODmnTFukOJZkHC\nmJbJgk0c4bZ/k542fqF92yKqdwasKcsYY8EmnlhT9Jr4wllgZRZYjDExFGywEZGRwD2AH3hQVSdn\ncv82IdUefhHGDu7B7WOOyHVVjDEFqiCDjYj4gT8BpwIbgAUiMkNVl2fqGPEmqmpJ7C7EGNNcCjLY\nAEcDq1R1NYCIPAmMBjIWbGI9ZV6ILKAYY/JBoQabMmB9xOsNwOBMHiD6eQ1fI9MFNzdr1jLGFJpC\nDTZJEZHxwHiAnj17prx95PMa2Z4kzScQUrsTMca0TIUabKqg3sMv3V1ZPao6BZgCUF5e3qTbksg7\nnXT6ctJ9QNEYY1qCQg02C4C+ItIbL8icD/ww2we1J9ONMSY9BRlsVLVWRK4EKvBSn/+mqpU5rpYx\nxpg4CjLYAKjqTGBmruthjDEmMRsZ0hhjTNZZsDHGGJN1FmyMMcZknWiePKiYbSKyGVibYLX9gC+b\noTqZZvVuPoVYZ7B6N7eWVO8DVbVLU3fcaoJNMkRkoaqW57oeqbJ6N59CrDNYvZub1bsha0YzxhiT\ndRZsjDHGZJ0Fm/qm5LoCabJ6N59CrDNYvZub1TuK9dkYY4zJOruzMcYYk3UWbPCmmBaRlSKySkQm\n5kF9eojIXBFZLiKVIvJzV95ZRGaJyMfueydXLiJyr6v/UhEZFLGvcW79j0VkXDPU3S8ii0XkZfe6\nt4jMd3V7SkTauPK27vUq936viH3c4MpXisiIbNfZHbNURJ4VkRUi8qGIHFMg5/sa9zfygYg8ISJ7\n5eM5F5G/icgXIvJBRFnGzq+IHCUiy9w294qIZLHed7q/k6Ui8oKIlEa8F/M8xrvGxPtdZaPeEe/9\nj4ioiOznXjfP+VbVVv2FN5DnJ0AfoA2wBOif4zp1Awa55X2Aj4D+wO+Aia58IvBbt3wa8CogwBBg\nvivvDKx23zu55U5Zrvu1wOPAy+7108D5bvnPwH+75SuAP7vl84Gn3HJ/9ztoC/R2vxt/M5zzqcB/\nueU2QGm+n2+8SQQ/BUoizvUl+XjOgROAQcAHEWUZO7/Au25dcduOymK9hwNFbvm3EfWOeR5p5BoT\n73eVjXq78h54AxivBfZrzvOd1X/gQvgCjgEqIl7fANyQ63pF1fFF4FRgJdDNlXUDVrrlvwBjI9Zf\n6d4fC/wlorzeelmoZ3dgNnAy8LL7Q/wy4h+z7ly7P/hj3HKRW0+iz3/kelmsd0e8i7ZElef7+Q7P\nWNvZncOXgRH5es6BXtS/aGfk/Lr3VkSU11sv0/WOeu9M4DG3HPM8Euca09j/R7bqDTwLHAmsYU+w\naZbzbc1osaeYzptJa1xTx0BgPtBVVTe6tz4HurrleD9Dc/9sdwPXASH3el+gWlVrYxy/rm7u/W1u\n/Vz8PnoDm4G/i9cE+KCItCfPz7eqVgG/B9YBG/HO4SIK45xD5s5vmVuOLm8OP8L7ZA+p17ux/4+M\nE5HRQJWqLol6q1nOtwWbPCYiewPPAVer6vbI99T7SJE3qYQi8j3gC1VdlOu6pKEIr8nhAVUdCOzA\na9apk2/nG8D1cYzGC5YHAO2BkTmtVJry8fwmIiI3ArXAY7muSyIi0g74JfC/uaqDBZskp5hubiJS\njBdoHlPV513xJhHp5t7vBnzhyuP9DM35sw0Fvi8ia4An8ZrS7gFKRSQ8b1Lk8evq5t7vCHzVzHUO\n2wBsUNX57vWzeMEnn883wHeBT1V1s6oGgOfxfg+FcM4hc+e3yi1Hl2eNiFwCfA+4wAVKEtQvVvlX\nxP9dZdpBeB9Klrj/0e7AeyLyrTTqnd75znS7bKF94X2qXe1+EeHOu8NzXCcBpgF3R5XfSf0O1d+5\n5dOp38H3rivvjNcX0cl9fQp0bob6n8SeBIFnqN8BeoVb/in1O6ufdsuHU7+TdTXNkyDwFtDPLU9y\n5zqvzzcwGKgE2rm6TAWuytdzTsM+m4ydXxp2WJ+WxXqPBJYDXaLWi3keaeQaE+93lY16R723hj19\nNs1yvrP6D1woX3jZGB/hZYzcmAf1OQ6vSWEp8L77Og2vjXc28DHwRsQvXoA/ufovA8oj9vUjYJX7\nurSZ6n8Se4JNH/eHucr9Y7V15Xu516vc+30itr/R/SwryVBWURJ1HgAsdOd8uvvnyvvzDdwCrAA+\nAB5xF7q8O+fAE3j9SgG8O8nLMnl+gXJ3Dj4B7iMq2SPD9V6F15cR/t/8c6LzSJxrTLzfVTbqHfX+\nGvYEm2Y53zaCgDHGmKyzPhtjjDFZZ8HGGGNM1lmwMcYYk3UWbIwxxmSdBRtjjDFZZ8HGGGNM1lmw\nMcYYk3UWbIwxxmTd/wdbPBOPr9pzmwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e7883d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pred3= model3.predict(poly3_data[my_features] )\n",
    "\n",
    "plt.plot(  poly3_data['power_1'] , poly3_data['price'] , 'o',\n",
    "           poly3_data['power_1'] , pred3               , '-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now try a 15th degree polynomial:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(279989.61697420682, array([  1.71098448e-05,   4.21658951e-02,   4.60494903e-06,\n",
      "        -4.52668531e-10,  -2.27857379e-14,  -2.34109771e-16,\n",
      "        -5.23220444e-16,   3.52129611e-16,  -2.03911246e-16,\n",
      "        -2.64470147e-16,   1.02317890e-16,   7.18195395e-16,\n",
      "         4.17519616e-16,  -3.94017242e-16,   4.17366833e-17]))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10ec76e50>,\n",
       " <matplotlib.lines.Line2D at 0x10ec76f90>]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cfc2bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "poly15_data = polynomial_sframe(sales['sqft_living'], 15)\n",
    "my_features = poly15_data.columns # get the name of the features\n",
    "poly15_data['price'] = sales['price'] # add price to the data since it's the target\n",
    "#poly15_data.head(2)\n",
    "\n",
    "model15= LinearRegression().fit( X= poly15_data[my_features], y= poly15_data['price'])\n",
    "print(model15.intercept_, model15.coef_)\n",
    "\n",
    "pred15= model15.predict(poly15_data[my_features] )\n",
    "\n",
    "plt.plot(  poly15_data['power_1'] , poly15_data['price'] , 'o',\n",
    "           poly15_data['power_1'] , pred15               , '-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What do you think of the 15th degree polynomial? Do you think this is appropriate? If we were to change the data do you think you'd get pretty much the same curve? Let's take a look."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Changing the data and re-learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We're going to split the sales data into four subsets of roughly equal size. Then you will estimate a 15th degree polynomial model on all four subsets of the data. Print the coefficients (you should use .print_rows(num_rows = 16) to view all of them) and plot the resulting fit (as we did above). The quiz will ask you some questions about these results.\n",
    "\n",
    "To split the sales data into four subsets, we perform the following steps:\n",
    "* First split sales into 2 subsets with `.random_split(0.5, seed=0)`. \n",
    "* Next split the resulting subsets into 2 more subsets each. Use `.random_split(0.5, seed=0)`.\n",
    "\n",
    "We set `seed=0` in these steps so that different users get consistent results.\n",
    "You should end up with 4 subsets (`set_1`, `set_2`, `set_3`, `set_4`) of approximately equal size. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "set_1 = pd.read_csv('wk3_kc_house_set_1_data.csv')\n",
    "set_2 = pd.read_csv('wk3_kc_house_set_2_data.csv')\n",
    "set_3 = pd.read_csv('wk3_kc_house_set_3_data.csv')\n",
    "set_4 = pd.read_csv('wk3_kc_house_set_4_data.csv')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Fit a 15th degree polynomial on set_1, set_2, set_3, and set_4 using sqft_living to predict prices. Print the coefficients and make a plot of the resulting model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "def poly15(sales):\n",
    "    poly15_data = polynomial_sframe(sales['sqft_living'], 15)\n",
    "    my_features = poly15_data.columns # get the name of the features\n",
    "    poly15_data['price'] = sales['price'] # add price to the data since it's the target\n",
    "    #poly15_data.head(2)\n",
    "\n",
    "    model15= LinearRegression().fit( X= poly15_data[my_features], y= poly15_data['price'])\n",
    "    print(model15.intercept_, model15.coef_)\n",
    "\n",
    "    pred15= model15.predict(poly15_data[my_features] )\n",
    "    RSS = np.dot(poly15_data['price']  - pred15  , poly15_data['price']  - pred15  )\n",
    "    print('RSS=', RSS)\n",
    "    \n",
    "    plt.plot(  poly15_data['power_1'] , poly15_data['price'] , 'o',\n",
    "               poly15_data['power_1'] , pred15               , '-')\n",
    "    return (model15.intercept_, model15.coef_)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(274621.56533170014, array([  1.76550428e-05,   4.45509680e-02,   4.13358678e-06,\n",
      "        -4.47829782e-10,  -2.26629101e-14,   8.66459357e-17,\n",
      "        -7.10022593e-16,   2.87387409e-16,  -1.73678869e-16,\n",
      "        -1.27952810e-15,   1.28237831e-16,   5.47423495e-16,\n",
      "         1.94293549e-16,  -3.17429382e-16,  -3.76911003e-16]))\n",
      "('RSS=', 346855028513332.25)\n"
     ]
    },
    {
     "data": {
      "image/png": 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rD6LPzpzQ3hpI+9tgWzBbNsZE5SMpJRPpLAs9RESeEZG1IrJGRH7gyvuLyBIR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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ec2f1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coef1= poly15(sales = set_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(255832.08750764001, array([  3.00702140e-05,   6.13409370e-02,  -2.50249320e-06,\n",
      "         1.11274978e-10,  -1.76127300e-14,   7.95325890e-16,\n",
      "        -3.77211973e-16,  -3.00519069e-16,  -6.03067898e-16,\n",
      "         3.82815008e-16,   7.10119182e-16,   7.56537076e-16,\n",
      "         1.03981187e-15,  -4.62184993e-16,   1.35047128e-15]))\n"
     ]
    },
    {
     "data": {
      "image/png": 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xJ6yMPa9uAklsqSC65DBY3meb2ZePqWZyxcOc6V/KblPJuOZb2FRxSNyu1Yn+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\nYxpMlFJKZez/AyaVNXfSMqkFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1112f15d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coef2= poly15(sales = set_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(251945.72335839365, array([  3.05482239e-05,   6.76830276e-02,  -5.33847268e-06,\n",
      "         4.60969615e-10,  -1.31254010e-14,  -1.48664069e-16,\n",
      "        -3.53096869e-16,   5.66467731e-16,   4.35166869e-16,\n",
      "         5.26252752e-16,  -2.25642047e-16,   1.12771915e-15,\n",
      "         6.15886890e-16,   3.23841045e-16,  -2.48747667e-16]))\n"
     ]
    },
    {
     "data": {
      "image/png": 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wJjDM/ZwA3AOcICJ9gelAJV676nIRWaCq29023wKWAs8C44Hn3DF9nyPVN8P4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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1112dcf90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coef3= poly15(sales = set_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(269734.35257722432, array([  2.92941485e-05,   5.47652842e-02,  -1.43653635e-06,\n",
      "         7.34429521e-11,   3.46617963e-14,  -1.24090168e-15,\n",
      "        -4.00055436e-16,   8.90618730e-16,  -4.98019779e-16,\n",
      "        -5.52234464e-16,   2.73592849e-16,   4.08783287e-16,\n",
      "         2.84653854e-16,  -1.04285631e-15,  -3.20203064e-16]))\n"
     ]
    },
    {
     "data": {
      "image/png": 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BaM9/+F3JFK7y3sjaQH8rkNiSWaMxdfwwa4A/wt7mFt1HpABpMFFZFy1PUvha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\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1113e0fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "coef4 = poly15(sales = set_4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Some questions you will be asked on your quiz:\n",
    "\n",
    "**Quiz Question: Is the sign (positive or negative) for power_15 the same in all four models?**\n",
    "\n",
    "**Quiz Question: (True/False) the plotted fitted lines look the same in all four plots**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Selecting a Polynomial Degree"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Whenever we have a \"magic\" parameter like the degree of the polynomial there is one well-known way to select these parameters: validation set. (We will explore another approach in week 4).\n",
    "\n",
    "We split the sales dataset 3-way into training set, test set, and validation set as follows:\n",
    "\n",
    "* Split our sales data into 2 sets: `training_and_validation` and `testing`. Use `random_split(0.9, seed=1)`.\n",
    "* Further split our training data into two sets: `training` and `validation`. Use `random_split(0.5, seed=1)`.\n",
    "\n",
    "Again, we set `seed=1` to obtain consistent results for different users."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "test_data  = pd.read_csv('wk3_kc_house_test_data.csv')\n",
    "train_data = pd.read_csv('wk3_kc_house_train_data.csv')\n",
    "valid_data = pd.read_csv('wk3_kc_house_valid_data.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next you should write a loop that does the following:\n",
    "* For degree in [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15] (to get this in python type range(1, 15+1))\n",
    "    * Build an SFrame of polynomial data of train_data['sqft_living'] at the current degree\n",
    "    * hint: my_features = poly_data.column_names() gives you a list e.g. ['power_1', 'power_2', 'power_3'] which you might find useful for graphlab.linear_regression.create( features = my_features)\n",
    "    * Add train_data['price'] to the polynomial SFrame\n",
    "    * Learn a polynomial regression model to sqft vs price with that degree on TRAIN data\n",
    "    * Compute the RSS on VALIDATION data (here you will want to use .predict()) for that degree and you will need to make a polynmial SFrame using validation data.\n",
    "* Report which degree had the lowest RSS on validation data (remember python indexes from 0)\n",
    "\n",
    "(Note you can turn off the print out of linear_regression.create() with verbose = False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [],
   "source": [
    "def poly_k(train, valid, k):\n",
    "    \n",
    "    X_train = polynomial_sframe(train['sqft_living'], k)\n",
    "    y_train = train['price']\n",
    "    model= LinearRegression().fit( X_train , y_train)\n",
    "    #print(model.intercept_, model.coef_)\n",
    "    \n",
    "    X_test = polynomial_sframe(valid['sqft_living'], k)\n",
    "    y_test= valid['price']\n",
    "    \n",
    "    pred = model.predict( X_test)\n",
    "    RSS = np.dot(y_test - pred  , y_test  - pred )\n",
    "    #print('RSS=', RSS)\n",
    "    \n",
    "    #plt.plot(  poly_data['power_1'] , sales['price'], 'o',\n",
    "    #           poly_data['power_1'] , pred               , '-')\n",
    "    return RSS\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6\n"
     ]
    }
   ],
   "source": [
    "RSS_list = [ poly_k(train_data, valid_data, k) for k in range(1,16)]\n",
    "print(np.argmin(RSS_list)) # index of min RSS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x10ee49610>"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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6keCYxVUALK4tBbyE4ZxLzhNGHmvr6KGlvpKKkmCEmNKiQhqqSn14EOdcUp4w8lhbe+9k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\nn280oXQHbh8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ee767d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot( range(1,16), RSS_list)\n",
    "plt.title('Validation RSS vs. degree of polynomial')\n",
    "plt.xlabel('Degree of polynomial')\n",
    "plt.ylabel('RSS on validation data')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Quiz Question: Which degree (1, 2, …, 15) had the lowest RSS on Validation data?**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that you have chosen the degree of your polynomial using validation data, compute the RSS of this model on TEST data. Report the RSS on your quiz."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "136767025587282.53"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly_k(train_data, test_data, 6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Quiz Question: what is the RSS on TEST data for the model with the degree selected from Validation data?**"
   ]
  },
  {
   "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": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}