3.0 week-3-polynomial-regression-assignment-blank.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"
   ]
  },
  {
   "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": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "This non-commercial license of GraphLab Create for academic use is assigned to msn4eg@gmail.com and will expire on April 03, 2018.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "[INFO] graphlab.cython.cy_server: GraphLab Create v2.1 started. Logging: /tmp/graphlab_server_1493201355.log\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1.0, 2.0, 3.0]\n",
      "[1.0, 8.0, 27.0]\n"
     ]
    }
   ],
   "source": [
    "tmp = graphlab.SArray([1., 2., 3.])\n",
    "tmp_cubed = tmp.apply(lambda x: x**3)\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": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---------+\n",
      "| power_1 |\n",
      "+---------+\n",
      "|   1.0   |\n",
      "|   2.0   |\n",
      "|   3.0   |\n",
      "+---------+\n",
      "[3 rows x 1 columns]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "ex_sframe = graphlab.SFrame()\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": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def polynomial_sframe(feature, degree):\n",
    "    # assume that degree >= 1\n",
    "    # initialize the SFrame:\n",
    "    poly_sframe = graphlab.SFrame()\n",
    "    # and set poly_sframe['power_1'] equal to the passed feature\n",
    "    poly_sframe['power_1'] = feature\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",
    "            powered = feature.apply(lambda x:x**power)\n",
    "            poly_sframe[name] = powered\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": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+---------+---------+---------+\n",
      "| power_1 | power_2 | power_3 |\n",
      "+---------+---------+---------+\n",
      "|   1.0   |   1.0   |   1.0   |\n",
      "|   2.0   |   4.0   |   8.0   |\n",
      "|   3.0   |   9.0   |   27.0  |\n",
      "+---------+---------+---------+\n",
      "[3 rows x 3 columns]\n",
      "\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": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sales = graphlab.SFrame('kc_house_data.gl/')"
   ]
  },
  {
   "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": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "sales = sales.sort(['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": 10,
   "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": "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": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Linear regression:\n",
      "--------------------------------------------------------\n",
      "Number of examples          : 21613\n",
      "Number of features          : 1\n",
      "Number of unpacked features : 1\n",
      "Number of coefficients    : 2\n",
      "Starting Newton Method\n",
      "--------------------------------------------------------\n",
      "+-----------+----------+--------------+--------------------+---------------+\n",
      "| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |\n",
      "+-----------+----------+--------------+--------------------+---------------+\n",
      "| 1         | 2        | 1.030843     | 4362074.696077     | 261440.790724 |\n",
      "+-----------+----------+--------------+--------------------+---------------+\n",
      "SUCCESS: Optimal solution found.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "model1 = graphlab.linear_regression.create(poly1_data, target = 'price', features = ['power_1'], validation_set = None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">index</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">value</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">stderr</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">(intercept)</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-43579.0852515</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4402.68969743</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">280.622770886</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.93639855513</td>\n",
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       "[2 rows x 4 columns]<br/>\n",
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      "text/plain": [
       "Columns:\n",
       "\tname\tstr\n",
       "\tindex\tstr\n",
       "\tvalue\tfloat\n",
       "\tstderr\tfloat\n",
       "\n",
       "Rows: 2\n",
       "\n",
       "Data:\n",
       "+-------------+-------+----------------+---------------+\n",
       "|     name    | index |     value      |     stderr    |\n",
       "+-------------+-------+----------------+---------------+\n",
       "| (intercept) |  None | -43579.0852515 | 4402.68969743 |\n",
       "|   power_1   |  None | 280.622770886  | 1.93639855513 |\n",
       "+-------------+-------+----------------+---------------+\n",
       "[2 rows x 4 columns]"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#let's take a look at the weights before we plot\n",
    "model1.get(\"coefficients\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fbfc603e150>,\n",
       " <matplotlib.lines.Line2D at 0x7fbf47429690>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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r3HRTbDkvKhp1NiikXfzJsOPjHfrX5X/Vr8z9ina/prtO/vNkvfOVO3Xrrq25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\nzmLKylykg2HDnKh89astozC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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbf47500790>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(poly1_data['power_1'],poly1_data['price'],'.',\n",
    "        poly1_data['power_1'], model1.predict(poly1_data),'-')"
   ]
  },
  {
   "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": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Linear regression:\n",
      "--------------------------------------------------------\n",
      "Number of examples          : 21613\n",
      "Number of features          : 2\n",
      "Number of unpacked features : 2\n",
      "Number of coefficients    : 3\n",
      "Starting Newton Method\n",
      "--------------------------------------------------------\n",
      "+-----------+----------+--------------+--------------------+---------------+\n",
      "| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |\n",
      "+-----------+----------+--------------+--------------------+---------------+\n",
      "| 1         | 2        | 0.028780     | 5913020.984255     | 250948.368758 |\n",
      "+-----------+----------+--------------+--------------------+---------------+\n",
      "SUCCESS: Optimal solution found.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "poly2_data = polynomial_sframe(sales['sqft_living'], 2)\n",
    "my_features = poly2_data.column_names() # get the name of the features\n",
    "poly2_data['price'] = sales['price'] # add price to the data since it's the target\n",
    "model2 = graphlab.linear_regression.create(poly2_data, target = 'price', features = my_features, validation_set = None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">index</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">value</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">stderr</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">(intercept)</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">199222.496445</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7058.00483552</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">67.9940640677</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">5.28787201316</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_2</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0385812312789</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.000898246547032</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[3 rows x 4 columns]<br/>\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tname\tstr\n",
       "\tindex\tstr\n",
       "\tvalue\tfloat\n",
       "\tstderr\tfloat\n",
       "\n",
       "Rows: 3\n",
       "\n",
       "Data:\n",
       "+-------------+-------+-----------------+-------------------+\n",
       "|     name    | index |      value      |       stderr      |\n",
       "+-------------+-------+-----------------+-------------------+\n",
       "| (intercept) |  None |  199222.496445  |   7058.00483552   |\n",
       "|   power_1   |  None |  67.9940640677  |   5.28787201316   |\n",
       "|   power_2   |  None | 0.0385812312789 | 0.000898246547032 |\n",
       "+-------------+-------+-----------------+-------------------+\n",
       "[3 rows x 4 columns]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model2.get(\"coefficients\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fbf45b2d890>,\n",
       " <matplotlib.lines.Line2D at 0x7fbf45b2d950>]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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+/hpOOcWFUYvA2LFw/vm1d6clIu9ZIseSarInePzgI9bT9LILKGjchMVXLqbN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\nfO/c5YHyH+vF20YUWxP8M2Q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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbf45b940d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(poly2_data['power_1'],poly2_data['price'],'.',\n",
    "        poly2_data['power_1'], model2.predict(poly2_data),'-')"
   ]
  },
  {
   "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": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Linear regression:\n",
      "--------------------------------------------------------\n",
      "Number of examples          : 21613\n",
      "Number of features          : 3\n",
      "Number of unpacked features : 3\n",
      "Number of coefficients    : 4\n",
      "Starting Newton Method\n",
      "--------------------------------------------------------\n",
      "+-----------+----------+--------------+--------------------+---------------+\n",
      "| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |\n",
      "+-----------+----------+--------------+--------------------+---------------+\n",
      "| 1         | 2        | 0.047023     | 3261066.736007     | 249261.286346 |\n",
      "+-----------+----------+--------------+--------------------+---------------+\n",
      "SUCCESS: Optimal solution found.\n",
      "\n"
     ]
    }
   ],
   "source": [
    "poly3_data = polynomial_sframe(sales['sqft_living'],3)\n",
    "features_3 = poly3_data.column_names()\n",
    "poly3_data['price'] = sales['price']\n",
    "model3 =  graphlab.linear_regression.create(poly3_data ,target = 'price' ,features = features_3 ,validation_set = None )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">index</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">value</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">stderr</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">(intercept)</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">336788.117952</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">10661.0153713</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-90.1476236119</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">10.6222891844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_2</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.087036715081</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.00296630623148</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_3</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-3.8398521196e-06</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.2417490959e-07</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[4 rows x 4 columns]<br/>\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tname\tstr\n",
       "\tindex\tstr\n",
       "\tvalue\tfloat\n",
       "\tstderr\tfloat\n",
       "\n",
       "Rows: 4\n",
       "\n",
       "Data:\n",
       "+-------------+-------+-------------------+------------------+\n",
       "|     name    | index |       value       |      stderr      |\n",
       "+-------------+-------+-------------------+------------------+\n",
       "| (intercept) |  None |   336788.117952   |  10661.0153713   |\n",
       "|   power_1   |  None |   -90.1476236119  |  10.6222891844   |\n",
       "|   power_2   |  None |   0.087036715081  | 0.00296630623148 |\n",
       "|   power_3   |  None | -3.8398521196e-06 | 2.2417490959e-07 |\n",
       "+-------------+-------+-------------------+------------------+\n",
       "[4 rows x 4 columns]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model3.get(\"coefficients\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fbf459d41d0>,\n",
       " <matplotlib.lines.Line2D at 0x7fbf459d4290>]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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2NWvqDrWF2bLFLUP9zW82vDhbIiLmW3V+ZF0ywQC1csNteZ8znvwBkUO+oOyy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\nsA5YRsC3AnwPF8q8ltph0cf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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbf45a8b710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(poly3_data['power_1'],poly3_data['price'],'.',\n",
    "         poly3_data['power_1'],model3.predict(poly3_data),'-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now try a 15th degree polynomial:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Linear regression:\n",
      "--------------------------------------------------------\n",
      "Number of examples          : 21613\n",
      "Number of features          : 15\n",
      "Number of unpacked features : 15\n",
      "Number of coefficients    : 16\n",
      "Starting Newton Method\n",
      "--------------------------------------------------------\n",
      "+-----------+----------+--------------+--------------------+---------------+\n",
      "| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |\n",
      "+-----------+----------+--------------+--------------------+---------------+\n",
      "| 1         | 2        | 0.045779     | 2662308.584337     | 245690.511190 |\n",
      "+-----------+----------+--------------+--------------------+---------------+\n",
      "SUCCESS: Optimal solution found.\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\"><table frame=\"box\" rules=\"cols\">\n",
       "    <tr>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">name</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">index</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">value</th>\n",
       "        <th style=\"padding-left: 1em; padding-right: 1em; text-align: center\">stderr</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">(intercept)</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">73619.7521128</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">932386.423529</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_1</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">410.287462535</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">4736.29685183</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_2</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-0.230450714428</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9.86053264076</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_3</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7.58840542453e-05</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">0.0111697433406</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_4</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-5.65701802662e-09</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">7.69719606122e-06</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_5</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-4.57028130577e-13</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.404224608e-09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_6</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.6636020643e-17</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">9.86624558935e-13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_7</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">3.3858476929e-21</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.85621322144e-16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_8</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.14723104085e-25</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">2.13709634069e-20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">power_9</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">None</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">-4.65293586092e-30</td>\n",
       "        <td style=\"padding-left: 1em; padding-right: 1em; text-align: center; vertical-align: top\">1.22655026064e-24</td>\n",
       "    </tr>\n",
       "</table>\n",
       "[16 rows x 4 columns]<br/>Note: Only the head of the SFrame is printed.<br/>You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns.\n",
       "</div>"
      ],
      "text/plain": [
       "Columns:\n",
       "\tname\tstr\n",
       "\tindex\tstr\n",
       "\tvalue\tfloat\n",
       "\tstderr\tfloat\n",
       "\n",
       "Rows: 16\n",
       "\n",
       "Data:\n",
       "+-------------+-------+--------------------+-------------------+\n",
       "|     name    | index |       value        |       stderr      |\n",
       "+-------------+-------+--------------------+-------------------+\n",
       "| (intercept) |  None |   73619.7521128    |   932386.423529   |\n",
       "|   power_1   |  None |   410.287462535    |   4736.29685183   |\n",
       "|   power_2   |  None |  -0.230450714428   |   9.86053264076   |\n",
       "|   power_3   |  None | 7.58840542453e-05  |  0.0111697433406  |\n",
       "|   power_4   |  None | -5.65701802662e-09 | 7.69719606122e-06 |\n",
       "|   power_5   |  None | -4.57028130577e-13 |  3.404224608e-09  |\n",
       "|   power_6   |  None |  2.6636020643e-17  | 9.86624558935e-13 |\n",
       "|   power_7   |  None |  3.3858476929e-21  | 1.85621322144e-16 |\n",
       "|   power_8   |  None | 1.14723104085e-25  | 2.13709634069e-20 |\n",
       "|   power_9   |  None | -4.65293586092e-30 | 1.22655026064e-24 |\n",
       "+-------------+-------+--------------------+-------------------+\n",
       "[16 rows x 4 columns]\n",
       "Note: Only the head of the SFrame is printed.\n",
       "You can use print_rows(num_rows=m, num_columns=n) to print more rows and columns."
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "poly15_data = polynomial_sframe(sales['sqft_living'],15)\n",
    "features_15 = poly15_data.column_names()\n",
    "poly15_data['price'] = sales['price']\n",
    "model15 = graphlab.linear_regression.create(poly15_data ,target='price',features=features_15,validation_set=None)\n",
    "model15.get('coefficients')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fbf45895d90>,\n",
       " <matplotlib.lines.Line2D at 0x7fbf45895e50>]"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Ov/JK8szm9xtjDNe8dw3XnHgNJ3Y80W9zlAYmVRZkU8FREkYs6VxiTf3irb9y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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbf459183d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(poly15_data['power_1'],poly15_data['price'],'.',\n",
    "         poly15_data['power_1'],model15.predict(poly15_data),'-')"
   ]
  },
  {
   "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": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "s1 ,s2=sales.random_split(.5,seed=0)\n",
    "set_1,set_2=s1.random_split(.5,seed=0)\n",
    "set_3,set_4=s2.random_split(.5,seed=0)"
   ]
  },
  {
   "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": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_gen(data,degree):\n",
    "    polyz_data = polynomial_sframe(data['sqft_living'],degree)\n",
    "    features_z = polyz_data.column_names()\n",
    "    polyz_data['price'] = data['price']\n",
    "    model = graphlab.linear_regression.create(polyz_data ,target='price',features=features_z,validation_set=None,verbose = False)\n",
    "    model.get('coefficients').print_rows(num_rows = 16)\n",
    "    plt.plot(polyz_data['power_1'],polyz_data['price'],'.',\n",
    "         polyz_data['power_1'],model.predict(polyz_data),'-')\n",
    "    return model\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------------+-------+--------------------+-------------------+\n",
      "|     name    | index |       value        |       stderr      |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "| (intercept) |  None |   223312.750249    |   1256782.60077   |\n",
      "|   power_1   |  None |   118.086127587    |   6007.14384425   |\n",
      "|   power_2   |  None |  -0.0473482011344  |    11.969007003   |\n",
      "|   power_3   |  None | 3.25310342469e-05  |  0.0131429551736  |\n",
      "|   power_4   |  None | -3.32372152561e-09 | 8.85414511316e-06 |\n",
      "|   power_5   |  None | -9.75830457761e-14 | 3.83982596813e-09 |\n",
      "|   power_6   |  None | 1.15440303426e-17  |  1.0847728091e-12 |\n",
      "|   power_7   |  None | 1.05145869404e-21  | 1.93625236102e-16 |\n",
      "|   power_8   |  None | 3.46049616546e-26  |  1.8950619488e-20 |\n",
      "|   power_9   |  None | -1.09654454168e-30 |        nan        |\n",
      "|   power_10  |  None | -2.42031812009e-34 |  3.4981969864e-29 |\n",
      "|   power_11  |  None | -1.99601206824e-38 | 2.50800893225e-33 |\n",
      "|   power_12  |  None | -1.07709903827e-42 | 1.15429777633e-36 |\n",
      "|   power_13  |  None | -2.72862818141e-47 | 1.56910289863e-40 |\n",
      "|   power_14  |  None | 2.44782693088e-51  | 7.93831963225e-45 |\n",
      "|   power_15  |  None | 5.01975232933e-55  | 1.49249715723e-49 |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "[16 rows x 4 columns]\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Class                          : LinearRegression\n",
       "\n",
       "Schema\n",
       "------\n",
       "Number of coefficients         : 16\n",
       "Number of examples             : 5404\n",
       "Number of feature columns      : 15\n",
       "Number of unpacked features    : 15\n",
       "\n",
       "Hyperparameters\n",
       "---------------\n",
       "L1 penalty                     : 0.0\n",
       "L2 penalty                     : 0.01\n",
       "\n",
       "Training Summary\n",
       "----------------\n",
       "Solver                         : newton\n",
       "Solver iterations              : 1\n",
       "Solver status                  : SUCCESS: Optimal solution found.\n",
       "Training time (sec)            : 0.0516\n",
       "\n",
       "Settings\n",
       "--------\n",
       "Residual sum of squares        : 3.34673575141e+14\n",
       "Training RMSE                  : 248858.8222\n",
       "\n",
       "Highest Positive Coefficients\n",
       "-----------------------------\n",
       "(intercept)                    : 223312.7502\n",
       "power_1                        : 118.0861\n",
       "power_3                        : 0.0\n",
       "power_6                        : 0.0\n",
       "power_7                        : 0.0\n",
       "\n",
       "Lowest Negative Coefficients\n",
       "----------------------------\n",
       "power_2                        : -0.0473\n",
       "power_4                        : -0.0\n",
       "power_5                        : -0.0\n",
       "power_9                        : -0.0\n",
       "power_10                       : -0.0"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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CYxhGWlG0uohnvniGMWeOSfpS0fFkcIfBGR/IM3O+LcMwMp7N321m5BsjGfOrMbQ6KLOi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\nYxiGYdQK/w9tqtWhYlt5+wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbf453a3190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_gen(set_1,15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "+-------------+-------+--------------------+-------------------+\n",
      "|     name    | index |       value        |       stderr      |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "| (intercept) |  None |   89836.5077327    |   1575072.52605   |\n",
      "|   power_1   |  None |   319.806946764    |   9306.12882948   |\n",
      "|   power_2   |  None |  -0.103315397042   |   23.4277359048   |\n",
      "|   power_3   |  None | 1.06682476069e-05  |  0.0331642866136  |\n",
      "|   power_4   |  None | 5.75577097718e-09  |  2.9410878859e-05 |\n",
      "|   power_5   |  None | -2.5466346476e-13  | 1.72262411743e-08 |\n",
      "|   power_6   |  None | -1.09641345061e-16 |  6.8337583788e-12 |\n",
      "|   power_7   |  None | -6.36458441713e-21 | 1.84750094523e-15 |\n",
      "|   power_8   |  None | 5.52560416991e-25  | 3.35734055021e-19 |\n",
      "|   power_9   |  None | 1.35082038963e-28  | 3.79203635463e-23 |\n",
      "|   power_10  |  None |  1.1840818825e-32  |        nan        |\n",
      "|   power_11  |  None | 1.98348000558e-37  |        nan        |\n",
      "|   power_12  |  None | -9.9253359041e-41  |        nan        |\n",
      "|   power_13  |  None | -1.60834847047e-44 |        nan        |\n",
      "|   power_14  |  None | -9.12006024287e-49 | 2.33825680386e-43 |\n",
      "|   power_15  |  None | 1.68636658328e-52  |  6.7296077272e-48 |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "[16 rows x 4 columns]\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Class                          : LinearRegression\n",
       "\n",
       "Schema\n",
       "------\n",
       "Number of coefficients         : 16\n",
       "Number of examples             : 5398\n",
       "Number of feature columns      : 15\n",
       "Number of unpacked features    : 15\n",
       "\n",
       "Hyperparameters\n",
       "---------------\n",
       "L1 penalty                     : 0.0\n",
       "L2 penalty                     : 0.01\n",
       "\n",
       "Training Summary\n",
       "----------------\n",
       "Solver                         : newton\n",
       "Solver iterations              : 1\n",
       "Solver status                  : SUCCESS: Optimal solution found.\n",
       "Training time (sec)            : 0.0549\n",
       "\n",
       "Settings\n",
       "--------\n",
       "Residual sum of squares        : 2.97698928927e+14\n",
       "Training RMSE                  : 234840.0672\n",
       "\n",
       "Highest Positive Coefficients\n",
       "-----------------------------\n",
       "(intercept)                    : 89836.5077\n",
       "power_1                        : 319.8069\n",
       "power_3                        : 0.0\n",
       "power_4                        : 0.0\n",
       "power_8                        : 0.0\n",
       "\n",
       "Lowest Negative Coefficients\n",
       "----------------------------\n",
       "power_2                        : -0.1033\n",
       "power_5                        : -0.0\n",
       "power_6                        : -0.0\n",
       "power_7                        : -0.0\n",
       "power_12                       : -0.0"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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NPU172NCwgS2fbWklIJGisnX3Vnbt2cVhBxxGn4P6RH2N6z+OsX3HEioIZfuy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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbf4547bfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_gen(set_2,15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Linear regression:\n",
      "--------------------------------------------------------\n",
      "Number of examples          : 5409\n",
      "Number of features          : 15\n",
      "Number of unpacked features : 15\n",
      "Number of coefficients    : 16\n",
      "Starting Newton Method\n",
      "--------------------------------------------------------\n",
      "+-----------+----------+--------------+--------------------+---------------+\n",
      "| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |\n",
      "+-----------+----------+--------------+--------------------+---------------+\n",
      "| 1         | 2        | 0.029321     | 2269769.506521     | 251460.072754 |\n",
      "+-----------+----------+--------------+--------------------+---------------+\n",
      "SUCCESS: Optimal solution found.\n",
      "\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "|     name    | index |       value        |       stderr      |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "| (intercept) |  None |   87317.9795547    |        nan        |\n",
      "|   power_1   |  None |   356.304911045    |        nan        |\n",
      "|   power_2   |  None |  -0.164817442809   |        nan        |\n",
      "|   power_3   |  None | 4.40424992697e-05  |        nan        |\n",
      "|   power_4   |  None | 6.48234876179e-10  |        nan        |\n",
      "|   power_5   |  None | -6.75253226587e-13 |        nan        |\n",
      "|   power_6   |  None | -3.36842592661e-17 |        nan        |\n",
      "|   power_7   |  None | 3.60999704242e-21  |        nan        |\n",
      "|   power_8   |  None | 6.46999725625e-25  |        nan        |\n",
      "|   power_9   |  None | 4.23639388865e-29  |        nan        |\n",
      "|   power_10  |  None | -3.62149427043e-34 |        nan        |\n",
      "|   power_11  |  None | -4.27119527274e-37 |        nan        |\n",
      "|   power_12  |  None | -5.61445971705e-41 | 3.22504679661e-36 |\n",
      "|   power_13  |  None | -3.87452772861e-45 | 3.81940189807e-40 |\n",
      "|   power_14  |  None | 4.69430359483e-50  | 1.00042633659e-44 |\n",
      "|   power_15  |  None | 6.39045885992e-53  |        nan        |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "[16 rows x 4 columns]\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Class                          : LinearRegression\n",
       "\n",
       "Schema\n",
       "------\n",
       "Number of coefficients         : 16\n",
       "Number of examples             : 5409\n",
       "Number of feature columns      : 15\n",
       "Number of unpacked features    : 15\n",
       "\n",
       "Hyperparameters\n",
       "---------------\n",
       "L1 penalty                     : 0.0\n",
       "L2 penalty                     : 0.01\n",
       "\n",
       "Training Summary\n",
       "----------------\n",
       "Solver                         : newton\n",
       "Solver iterations              : 1\n",
       "Solver status                  : SUCCESS: Optimal solution found.\n",
       "Training time (sec)            : 0.0465\n",
       "\n",
       "Settings\n",
       "--------\n",
       "Residual sum of squares        : 3.42022797736e+14\n",
       "Training RMSE                  : 251460.0728\n",
       "\n",
       "Highest Positive Coefficients\n",
       "-----------------------------\n",
       "(intercept)                    : 87317.9796\n",
       "power_1                        : 356.3049\n",
       "power_3                        : 0.0\n",
       "power_4                        : 0.0\n",
       "power_7                        : 0.0\n",
       "\n",
       "Lowest Negative Coefficients\n",
       "----------------------------\n",
       "power_2                        : -0.1648\n",
       "power_5                        : -0.0\n",
       "power_6                        : -0.0\n",
       "power_10                       : -0.0\n",
       "power_11                       : -0.0"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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c6KQydxNvonzDhpqr8JcsqT3PkUxIcabnX9JFuC3b92/nv177L/rf25/9B/bz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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbf455b50d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_gen(set_3,15)"
   ]
  },
  {
   "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": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Linear regression:\n",
      "--------------------------------------------------------\n",
      "Number of examples          : 5402\n",
      "Number of features          : 15\n",
      "Number of unpacked features : 15\n",
      "Number of coefficients    : 16\n",
      "Starting Newton Method\n",
      "--------------------------------------------------------\n",
      "+-----------+----------+--------------+--------------------+---------------+\n",
      "| Iteration | Passes   | Elapsed Time | Training-max_error | Training-rmse |\n",
      "+-----------+----------+--------------+--------------------+---------------+\n",
      "| 1         | 2        | 0.035244     | 2314893.173827     | 244563.136754 |\n",
      "+-----------+----------+--------------+--------------------+---------------+\n",
      "SUCCESS: Optimal solution found.\n",
      "\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "|     name    | index |       value        |       stderr      |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "| (intercept) |  None |   259020.879454    |   1545198.28029   |\n",
      "|   power_1   |  None |   -31.7277162076   |    9987.4875763   |\n",
      "|   power_2   |  None |   0.109702769619   |    26.738101963   |\n",
      "|   power_3   |  None | -1.58383847337e-05 |  0.0392428614089  |\n",
      "|   power_4   |  None | -4.47660623786e-09 |  3.515833293e-05  |\n",
      "|   power_5   |  None | 1.13976573482e-12  | 2.00754862175e-08 |\n",
      "|   power_6   |  None | 1.97669120547e-16  | 7.24105980967e-12 |\n",
      "|   power_7   |  None | -6.15783678661e-21 | 1.43187601549e-15 |\n",
      "|   power_8   |  None | -4.88012304074e-24 |        nan        |\n",
      "|   power_9   |  None | -6.62186781351e-28 |        nan        |\n",
      "|   power_10  |  None | -2.70631583161e-32 | 5.65043690743e-27 |\n",
      "|   power_11  |  None | 6.72370411466e-36  | 9.67662635909e-31 |\n",
      "|   power_12  |  None | 1.74115646268e-39  |        nan        |\n",
      "|   power_13  |  None | 2.09188375728e-43  |        nan        |\n",
      "|   power_14  |  None | 4.78015566061e-48  | 2.37859778541e-43 |\n",
      "|   power_15  |  None | -4.74535333101e-51 | 1.16454261473e-47 |\n",
      "+-------------+-------+--------------------+-------------------+\n",
      "[16 rows x 4 columns]\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Class                          : LinearRegression\n",
       "\n",
       "Schema\n",
       "------\n",
       "Number of coefficients         : 16\n",
       "Number of examples             : 5402\n",
       "Number of feature columns      : 15\n",
       "Number of unpacked features    : 15\n",
       "\n",
       "Hyperparameters\n",
       "---------------\n",
       "L1 penalty                     : 0.0\n",
       "L2 penalty                     : 0.01\n",
       "\n",
       "Training Summary\n",
       "----------------\n",
       "Solver                         : newton\n",
       "Solver iterations              : 1\n",
       "Solver status                  : SUCCESS: Optimal solution found.\n",
       "Training time (sec)            : 0.0535\n",
       "\n",
       "Settings\n",
       "--------\n",
       "Residual sum of squares        : 3.23099712695e+14\n",
       "Training RMSE                  : 244563.1368\n",
       "\n",
       "Highest Positive Coefficients\n",
       "-----------------------------\n",
       "(intercept)                    : 259020.8795\n",
       "power_2                        : 0.1097\n",
       "power_5                        : 0.0\n",
       "power_6                        : 0.0\n",
       "power_11                       : 0.0\n",
       "\n",
       "Lowest Negative Coefficients\n",
       "----------------------------\n",
       "power_1                        : -31.7277\n",
       "power_3                        : -0.0\n",
       "power_4                        : -0.0\n",
       "power_7                        : -0.0\n",
       "power_8                        : -0.0"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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XV+cy1to6NpPss9VvrdZLH75UD77uYD3zd2dqzZoa3du0t93ri0su3tdjFDYm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\nyIWdtGmkiDwmIqtE5GUR+Wa+7RKRXiK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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fbf455d44d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_gen(set_4,15)"
   ]
  },
  {
   "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": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "training_and_validation , testing = sales.random_split(.9,seed=1)\n",
    "training , validation = training_and_validation.random_split(0.5, seed=1)"
   ]
  },
  {
   "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": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Degree: 1, RSS: $676709775198048.250000\n",
      "Degree: 2, RSS: $607090530698013.500000\n",
      "Degree: 3, RSS: $616714574532759.375000\n",
      "Degree: 4, RSS: $609129230654382.625000\n",
      "Degree: 5, RSS: $599177138583682.000000\n",
      "Degree: 6, RSS: $589182477809203.625000\n",
      "Degree: 7, RSS: $591717038417878.250000\n",
      "Degree: 8, RSS: $601558237776796.125000\n",
      "Degree: 9, RSS: $612563853988437.000000\n",
      "Degree: 10, RSS: $621744288936065.000000\n",
      "Degree: 11, RSS: $627012012703947.625000\n",
      "Degree: 12, RSS: $627757914772014.250000\n",
      "Degree: 13, RSS: $624738503262080.375000\n",
      "Degree: 14, RSS: $619369705904740.500000\n",
      "Degree: 15, RSS: $613089202413658.875000\n"
     ]
    }
   ],
   "source": [
    "def model_gen2(data,degree):\n",
    "    polyz_data = polynomial_sframe(data['sqft_living'],degree)\n",
    "    features_z = polyz_data.column_names()\n",
    "    polyz_data['price'] = data['price']\n",
    "    model = graphlab.linear_regression.create(polyz_data ,target='price',features=features_z,validation_set=None,verbose = False)\n",
    "    #model.get('coefficients').print_rows(num_rows = 16)\n",
    "    return model\n",
    "\n",
    "for power in range(1, 15+1):\n",
    "    modeln = model_gen2(training,power)\n",
    "    validation_data = polynomial_sframe(validation['sqft_living'], power)\n",
    "    validation_data['price'] = validation['price'] # add price to the data since it's the target\n",
    "    \n",
    "    predict = modeln.predict(validation_data)\n",
    "    residual = validation_data['price'] - predict\n",
    "    residual_squared = residual * residual\n",
    "    RSS = residual_squared.sum()\n",
    "    print (\"Degree: %s, RSS: $%.6f\" % (power, RSS))\n",
    "    modeln=None\n",
    "    "
   ]
  },
  {
   "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": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Degree: 6, RSS: $125529337847968.750000\n"
     ]
    }
   ],
   "source": [
    "power =6\n",
    "modeln = model_gen2(training,power)\n",
    "validation_data = polynomial_sframe(testing['sqft_living'], power)\n",
    "validation_data['price'] = testing['price'] # add price to the data since it's the target\n",
    "    \n",
    "predict = modeln.predict(validation_data)\n",
    "residual = validation_data['price'] - predict\n",
    "residual_squared = residual * residual\n",
    "RSS = residual_squared.sum()\n",
    "print (\"Degree: %s, RSS: $%f\" % (power, RSS))\n",
    " "
   ]
  },
  {
   "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": 82,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Degree: 1, RSS: $129030470094700.109375\n",
      "Degree: 2, RSS: $125190117212860.078125\n",
      "Degree: 3, RSS: $125939457007405.750000\n",
      "Degree: 4, RSS: $127147719016435.250000\n",
      "Degree: 5, RSS: $127037730210195.656250\n",
      "Degree: 6, RSS: $125529337847968.750000\n",
      "Degree: 7, RSS: $124608773610140.296875\n",
      "Degree: 8, RSS: $124458964534447.843750\n",
      "Degree: 9, RSS: $124525299776491.187500\n",
      "Degree: 10, RSS: $124602928485211.281250\n",
      "Degree: 11, RSS: $124641733743965.093750\n",
      "Degree: 12, RSS: $124646108317087.546875\n",
      "Degree: 13, RSS: $124632209805092.000000\n",
      "Degree: 14, RSS: $124612578389305.671875\n",
      "Degree: 15, RSS: $124593903712855.171875\n"
     ]
    }
   ],
   "source": [
    "for power in range(1, 15+1):\n",
    "    modeln = model_gen2(training,power)\n",
    "    validation_data = polynomial_sframe(testing['sqft_living'], power)\n",
    "    validation_data['price'] = testing['price'] # add price to the data since it's the target\n",
    "    \n",
    "    predict = modeln.predict(validation_data)\n",
    "    residual = validation_data['price'] - predict\n",
    "    residual_squared = residual * residual\n",
    "    RSS = residual_squared.sum()\n",
    "    print (\"Degree: %s, RSS: $%.6f\" % (power, RSS))\n",
    "    modeln=None\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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