CaaL-data-OLS.ipynb

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   "source": [
    "# Large Data Analytics \n",
    "## Part 1: Ordinary Least Squares\n",
    "\n",
    "This is part 1 of ipython notebook that illustrates 'Large Data Analytics' talk given by *Todd Munson* and *Stefan Wild* using energy data from University of Chicago buildings."
   ]
  },
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   "source": [
    "## Sections\n",
    "- [Introduction](#intro)\n",
    "- [What is ordinary least square (OLS)](#ols-intro)\n",
    "- [Dataset](#dataset)\n",
    "- [Import data into ipython notebook](#import-data)\n",
    "- [Pick building and term to work on](#building)\n",
    "- [Calculating OLS using IPython](#ols)\n",
    "    - [Example 1: Effect of Temperature on Energy Use](#ols)\n",
    "        - [Basic Algorithm](#basic)\n",
    "        - [First Algorithm for small variables](#first)\n",
    "        - [Second Algorithm for small variables](#second)\n",
    "        - [Comparison with inbuilt methods](#section)\n",
    "    \n",
    "    \n",
    "-----------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "<a id='intro'></a>"
   ]
  },
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   "cell_type": "markdown",
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   "source": [
    "## Introduction\n",
    "\n",
    "<span style=\"color:red\"> @Todd: Could you expand on some of this text? </span>\n",
    "\n",
    "#### Where does big data come from?\n",
    "- Companies like Google and Netflix\n",
    "- Large data sets associated with network traffic\n",
    "- Scientific applications like fluid flow simulations\n",
    "- Measured data from sensors and experiments \n",
    "\n",
    "**In this illustration: we will use electricity meter data from University of Chicago buildings**\n",
    "\n",
    "#### What do analysts do with big data?\n",
    "- Marketing, making recommendations\n",
    "- Estimating human behavior and finding anomalies\n",
    "- System state estimation\n",
    "- Inverse problems\n",
    "\n",
    "#### How do we do it?\n",
    "- Feature extraction and machine learning\n",
    "- Regression models and classification\n",
    "- Data assimilation\n",
    "\n",
    "#### Why is big data hard?\n",
    "- Real data is messy\n",
    "- Online updates to the data\n",
    "- Tradeoff complexity and data access\n",
    "- Few complete passes through the data\n",
    "- Sometimes access each piece of data only once\n",
    "- May not look at some data at all\n",
    "\n",
    "\n",
    "------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id = \"ols-intro\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## What is ordinary least square (OLS)?\n",
    "\n",
    "<span style=\"color:red\"> @Todd: could you expand here. </span>\n",
    "- What is in layman (non mathematical :-) ) terms?\n",
    "- What is its general purpose? \n",
    "- Where is it used?\n",
    "- What are its limitations?\n",
    "\n",
    "\n",
    "-----------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "<a id=\"dataset\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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   "source": [
    "## Dataset\n",
    "\n",
    "In 2015, the 160 campus buildings and grounds used $40 million worth of energy. Analyzing the data trends will help improve our understanding of campus energy usage and increase energy efficiency!\n",
    "\n",
    "Dataset consists of the following:\n",
    "\n",
    "- Campus electricity data for ## buildings (## meters) from 2014 to 2016, at 15 minute intervals.\n",
    "\n",
    "- Weather station data for the same time interval\n",
    "\n",
    "\n",
    "The files can be downloaded here:\n",
    "\n",
    "<span style=\"color:red\"> !! Radha will make shorter versions of the csv files and upload to this girhub repo !! </span> \n",
    "\n",
    "https://rdcep.squarespace.com/caal-activities/fall-hackathon-2016\n",
    "\n",
    "Click on ***comed data*** for energy usage data and ***weather*** for temperature data.\n",
    "\n",
    "\n",
    "--------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id=\"import-data\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Import data into ipython notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### Import python libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "from numpy import linalg as la\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### Read Files"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python2.7/site-packages/IPython/core/interactiveshell.py:2717: DtypeWarning: Columns (10,11) have mixed types. Specify dtype option on import or set low_memory=False.\n",
      "  interactivity=interactivity, compiler=compiler, result=result)\n"
     ]
    }
   ],
   "source": [
    "df = pd.read_csv('uc_comed_two_years_final.csv', header = 'infer')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "df_temp = pd.read_csv('weather_prepared_final.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### Keeping useful columns and converting date-time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "df_new = df.filter(['DATETIME', 'TERM', 'BD_ID', 'DISCRIPT1', 'USAGE'])\n",
    "df_new['DATETIME'] = pd.to_datetime(df_new['DATETIME'])\n",
    "df_temp_new = df_temp.filter(['DATE', 'STATION', 'TEMPERATURE', 'HUMIDITY'])\n",
    "df_temp_new['DATE'] = pd.to_datetime(df_temp_new['DATE'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id='building'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Pick building and term to work on"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### Function to choose data based on term, building_name, and weather_station"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true,
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    "editable": true
   },
   "outputs": [],
   "source": [
    "def get_data(term, building_name, weather_station = 'Regenstein Library Weather Station'):\n",
    "    ## PICK USAGE DATA BASED ON TERM AND BUILDING_NAME\n",
    "    usage = df_new[(df_new['TERM'] == term) & (df_new['DISCRIPT1'] == building_name)]\n",
    "    \n",
    "    ## GET START AND END DATE OF THE TERM\n",
    "    start_date = usage.iloc[0]['DATETIME']\n",
    "    end_date = usage.iloc[-1]['DATETIME']\n",
    "    \n",
    "    ## PICK WEATHER STATION FOR TEMP\n",
    "    df_T = df_temp_new[(df_temp_new['STATION'] == weather_station)]\n",
    "    \n",
    "    df_bool1 = (df_temp_new['DATE'] == start_date)\n",
    "    index1 = df_bool1[df_bool1 == True].index.tolist()[0]\n",
    "    \n",
    "    df_bool2 = (df_temp_new['DATE'] == end_date)\n",
    "    index2 = df_bool2[df_bool2 == True].index.tolist()[0]\n",
    "    \n",
    "    try: \n",
    "        temp = df_T.loc[index1:index2+1] \n",
    "    except:\n",
    "        temp = df_T.loc[index1:end]\n",
    "    \n",
    "    usage_temp = pd.merge(left = usage, right = temp, left_on='DATETIME', right_on = 'DATE', how='left')\n",
    "    return(usage_temp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "##### values for term, building_name, weather_station below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "terms = df_new.TERM.unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "building_names = df_new.DISCRIPT1.unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "weather_stations = df_temp_new.STATION.unique()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "#### Select TERM, BUILDING_NAME & Get Dataframe"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "usage_temp = get_data('Summer 2015', 'Regenstein Library', 'Regenstein Library Weather Station')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "##### plot of Energy use vs time, Temperature vs time & Humidity vs time"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x10fb62e50>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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2SFWRVIwYx4atyQetqeb+W7Z+u+90JpXlDKCKJCluR3gQBt09sdaKeus9x9td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\nD096wA5vakFmAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f46dd50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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c7+1zIYD7KjkZSXzlI6nupdWbCnygEXZCf+qmVwaoJUrNrwc9BzdbECp1glKe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\nDn3fl59+oP6NBjV/X/uUYH/NRAgSvo3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+CGkBNIT+6WkoAHDtuUcAUIKLTz+1mrZo/HDt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\njuM4Tln8L8q9IyoN4GxRAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10f8a4e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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d6oJH4W/Lt+D3i9ZH/i4lsI+p/wKPrBvbaxQf/ktz7VZt1tRkXRHVF1OVzSzQ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\njuM4OeGGxHEcx8kJNySO4zhOTvwvDaSWf/cppLUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fb25590>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "usage_temp.plot(x = 'DATETIME', y = 'USAGE')\n",
    "usage_temp.plot(x = 'DATETIME', y = 'TEMPERATURE')\n",
    "usage_temp.plot(x = 'DATETIME', y = 'HUMIDITY')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "----------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id='ols'></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "# Calculating Ordinary Least Square using IPython:\n",
    "## Example 1: Effect of weather on energy use"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "Using university electricity data, we would like to find how temperature and humidity affects energy use. \n",
    "\n",
    "### Terminology \n",
    "\n",
    "<span style=\"color:red\"> @Todd: does this section make sense? </span>\n",
    "\n",
    "In this example, temperature and humidity are **properties** that affects our **observation**, energy use. A **model** is a relationship that describes how a property might affect the observation. Model consists of **coefficients**, which are multiplicative factors for properties. \n",
    "\n",
    "***Model: coefficient x property = model_observation*** \n",
    "\n",
    "We would like to get the **model_observation** to be as close to the real observation as possible. This is achieved by appropriately varying the coefficient values. The best possible set of coefficient values will have the least amount of difference between the model_observation and real observation. \n",
    "\n",
    "### Data Representation\n",
    "\n",
    "<span style=\"color:red\"> @Todd: does this section make sense? </span>\n",
    "\n",
    "- **A is matrix with first column temperature and second column humidity.** \n",
    "    - Number of columns = 2 (temperature and humidity)\n",
    "    - Each row of temperature and humidity corresponds to a particular time.\n",
    "    - There are as many entries as the number of time steps. \n",
    "    - Number of rows = number of time steps\n",
    "    \n",
    "    \n",
    "- **b is a column of energy use**\n",
    "    - Number of columns = 1 (energy use)\n",
    "    - Each row corresponds to a particular time, that matches with the times in A matrix\n",
    "        - Eg., If the first row in A matrix corresponds to 00:30 AM on 2016-1-1, the first row in b also corresponds to the same time\n",
    "    - Number of rows = number of time steps\n",
    "    \n",
    "    \n",
    "- **x is matrix of coefficients, and Model is Ax **\n",
    "    - [recap matrix multiplication](https://en.wikipedia.org/wiki/Matrix_multiplication)\n",
    "    - x has 2 rows corresponding to the two columns in A\n",
    "    - x has only 1 column\n",
    "    \n",
    "    \n",
    "- **y is the residual**\n",
    "    - this is the difference between the observation predicted by the model (Ax) and the actual value of observation (b)\n",
    "    - Hence, \\\\(y = Ax - b\\\\)\n",
    "    - y has 1 column and as many rows as the number of time steps\n",
    "    \n",
    "\n",
    "Mathematically, Ordinary Least Square (OLS) amounts to minimizing the following\n",
    "\n",
    "<span style=\"color:red\"> @Todd: need your help explaining this.. </span>\n",
    "Minimizing two norm: \n",
    "\n",
    "\\\\(\\parallel y \\parallel_2^2  =  \\sum_i y_i^2 \\\\)\n",
    "\n",
    "\\\\(\\underset{x}{\\min} \\parallel Ax − b \\parallel^2 \\\\)\n",
    "\n",
    "\n",
    "\n",
    "  Data representation: A ∈ Rm×n\n",
    "  Vector of observations: b ∈ Rn\n",
    "  m is the number of measurements\n",
    "  n is the number of variables\n",
    "  Both can be very large"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Step 1: Cleaning the data\n",
    "\n",
    "As mentioned earlier, real data can be messy. In our example, if we look at the plots of temperature vs time and humdity vs time, we see that for some chunk of dates, we have no observations. We will start by dropping those dates from our calculations. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "usage_temp = usage_temp.dropna(subset = ['TEMPERATURE', 'HUMIDITY'])\n",
    "## droppin NaN values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Step 2: Creating column A (column of property: temperature)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 76.8,  72.5],\n",
       "       [ 76.1,  68.6],\n",
       "       [ 75.7,  73.3],\n",
       "       ..., \n",
       "       [ 65.5,  95.1],\n",
       "       [ 66.4,  94. ],\n",
       "       [ 66.6,  96.3]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A1 = np.array(usage_temp['TEMPERATURE'])\n",
    "## first column: temperature\n",
    "A2 = np.array(usage_temp['HUMIDITY'])\n",
    "## second column: humidity\n",
    "A = np.column_stack((A1,A2))\n",
    "## combine two columns to get A matrix\n",
    "\n",
    "A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Step 3: Creating column b (column of observation: energy use)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 284.04,  282.24,  280.8 , ...,  541.39,  536.75,  539.25])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = np.array(usage_temp['USAGE'])\n",
    "b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id = \"basic\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## The basic algorithm\n",
    "\n",
    "To calculate x, here is the basic algorithm\n",
    "\n",
    "<span style=\"color:red\"> @Todd: need your help explaining this.. </span>\n",
    "\n",
    "\\\\(x = (A^T A)^{-1} A^T b\\\\)\n",
    "\n",
    "- Standard errors use \\\\(diag((A^T A)^{−1})\\\\)   \n",
    "- Two cases\n",
    "  - Number of variables is small\n",
    "  - Number of variables is large -- we will ignore large\n",
    "  \n",
    "### Step 4: Calculating x and standard errors using basic algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 6.99019751, -0.30183171]),\n",
       " array([], dtype=float64),\n",
       " 2,\n",
       " array([ 58798879.11304498,   1118438.76695503]))"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Aprime = A.conj().T\n",
    "## Calculating A'\n",
    "## Converting the equation to numpy formula..\n",
    "x = la.lstsq(Aprime.dot(A), Aprime.dot(b))\n",
    "## \n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  4.48884136e-07,   4.62226476e-07])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = Aprime.dot(A)\n",
    "stderrs = np.diag(la.inv(B))\n",
    "stderrs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id = \"first\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Algorithm for small number of variables\n",
    "\n",
    "<span style=\"color:red\"> @Todd: need your help explaining this.. </span>\n",
    "<span style=\"color:red\"> Why is this preferred for small variables? </span>\n",
    "\n",
    "  - Form the matrix \\\\(B = A^T A\\\\)\n",
    "  - Requires O(mn2) operations\n",
    "  - Control roundoff errors for large m\n",
    "  - Dense linear algebra\n",
    "  - Form the inverse of B\n",
    "    - Requires O(n3) operations\n",
    "  - Control roundoff errors for large m\n",
    "  - Dense linear algebra\n",
    "  - Solve\n",
    "  - \\\\(x=B^{-1} A^T b\\\\)\n",
    "    - Requires O(n3 + mn) operations\n",
    "  - Dense linear algebra\n",
    "  - Compute standard errors using \\\\(diag(B^{−1} )\\\\)\n",
    "  \n",
    "### Step 5: Calculating x and standard errors using algorithm for small number of variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6.99019751, -0.30183171])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Aprime = A.conj().T\n",
    "x = la.lstsq(Aprime.dot(A), Aprime.dot(b))\n",
    "x[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  4.48884136e-07,   4.62226476e-07])"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = Aprime.dot(A)\n",
    "stderrs = np.diag(la.inv(B))\n",
    "stderrs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id = \"second\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Second Algorithm for small number of variables\n",
    "\n",
    "<span style=\"color:red\"> @Todd: need your help explaining this.. </span>\n",
    "<span style=\"color:red\"> What is the difference between these two algorithms? </span>\n",
    "\n",
    "   - Form the matrix \\\\(B = A^T A\\\\)\n",
    "\n",
    "     - Requires O(mn2) operations\n",
    "  - Control roundoff errors for large m\n",
    "  - Compute Cholesky factorization \\\\(B = L^T L\\\\) for lower triangular L\n",
    "  - Solve \\\\(x = L^{−1} L^{−T} A^T b\\\\)\n",
    "  - Compute standard errors (how?)\n",
    "  \n",
    "### Step 6: Calculating x and standard errors using second algorithm for small number of variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5513.38142522,     0.        ],\n",
       "       [ 5230.34430161,  1470.86424481]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "L = la.cholesky(B).T\n",
    "## cholesky factorization of a matrix (chol(a) in matlab \n",
    "## returns an upper triangular matrix, \n",
    "## but linalg.cholesky(a) returns a lower triangular matrix)\n",
    "Lprime = L.conj().T\n",
    "Lprime"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 6.99019751, -0.30183171])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = la.lstsq(L, la.lstsq(Lprime, Aprime.dot(b))[0])\n",
    "x[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### To do.. \n",
    "\n",
    "<span style=\"color:red\"> Radha will plot the fit vs data here </span>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "<a id= \"compare\"></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Comparison with inbuilt methods\n",
    "\n",
    "Python programming language also has inbuilt functions to calculate ordinary least squares. Here is how we can use those\n",
    "\n",
    "<span style=\"color:red\"> @Todd: When can we use this? Pitfall? </span>\n",
    "\n",
    "<span style=\"color:red\"> @Todd: I am not sure how to compare the two results.. </span>\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>          <td>USAGE</td>      <th>  R-squared:         </th> <td>   0.288</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.288</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   1183.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 12 Jun 2017</td> <th>  Prob (F-statistic):</th>  <td>  0.00</td>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>11:07:07</td>     <th>  Log-Likelihood:    </th> <td> -35717.</td> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>  5842</td>      <th>  AIC:               </th> <td>7.144e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>  5839</td>      <th>  BIC:               </th> <td>7.146e+04</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     2</td>      <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>    \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "       <td></td>          <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th>   <td> -368.2643</td> <td>   22.232</td> <td>  -16.565</td> <td> 0.000</td> <td> -411.847</td> <td> -324.682</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>TEMPERATURE</th> <td>   10.6719</td> <td>    0.234</td> <td>   45.599</td> <td> 0.000</td> <td>   10.213</td> <td>   11.131</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>HUMIDITY</th>    <td>    1.1716</td> <td>    0.116</td> <td>   10.104</td> <td> 0.000</td> <td>    0.944</td> <td>    1.399</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>28.361</td> <th>  Durbin-Watson:     </th> <td>   0.074</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.000</td> <th>  Jarque-Bera (JB):  </th> <td>  39.536</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.012</td> <th>  Prob(JB):          </th> <td>2.60e-09</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.402</td> <th>  Cond. No.          </th> <td>1.56e+03</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                  USAGE   R-squared:                       0.288\n",
       "Model:                            OLS   Adj. R-squared:                  0.288\n",
       "Method:                 Least Squares   F-statistic:                     1183.\n",
       "Date:                Mon, 12 Jun 2017   Prob (F-statistic):               0.00\n",
       "Time:                        11:07:07   Log-Likelihood:                -35717.\n",
       "No. Observations:                5842   AIC:                         7.144e+04\n",
       "Df Residuals:                    5839   BIC:                         7.146e+04\n",
       "Df Model:                           2                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "===============================================================================\n",
       "                  coef    std err          t      P>|t|      [0.025      0.975]\n",
       "-------------------------------------------------------------------------------\n",
       "Intercept    -368.2643     22.232    -16.565      0.000    -411.847    -324.682\n",
       "TEMPERATURE    10.6719      0.234     45.599      0.000      10.213      11.131\n",
       "HUMIDITY        1.1716      0.116     10.104      0.000       0.944       1.399\n",
       "==============================================================================\n",
       "Omnibus:                       28.361   Durbin-Watson:                   0.074\n",
       "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               39.536\n",
       "Skew:                          -0.012   Prob(JB):                     2.60e-09\n",
       "Kurtosis:                       3.402   Cond. No.                     1.56e+03\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "[2] The condition number is large, 1.56e+03. This might indicate that there are\n",
       "strong multicollinearity or other numerical problems.\n",
       "\"\"\""
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.formula.api as sm\n",
    "model = sm.ols(formula='USAGE ~ TEMPERATURE + HUMIDITY', data=usage_temp)\n",
    "result = model.fit()\n",
    "result.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "------------------------\n",
    "\n",
    "------------------------"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "## Work in progress...."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Todd's notes\n",
    "Basic Algorithm\n",
    "\n",
    "- Assuming A has full column rank\n",
    "\n",
    "\\\\(x = (A^T A)^{-1} A^T b\\\\)\n",
    "\n",
    "where \\\\(A^T A \\in R^{n×n}\\\\) is symmetric\n",
    "\n",
    "- Standard errors use \\\\(diag((A^T A)^{−1})\\\\)   \n",
    "- Two cases\n",
    "  - Number of variables is small\n",
    "  - Number of variables is large -- we will ignore large\n",
    "  \n",
    "##### Matlab\n",
    "\n",
    "x = (A' \\* A) \\\\(A’ \\* b);\n",
    "\n",
    "stderrs = diag(inv(A’ \\* A));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "deletable": true,
    "editable": true
   },
   "source": [
    "### Todd's notes\n",
    "Generalized Least Squares\n",
    "\n",
    "##### Matlab code\n",
    "\n",
    "Give the previosly defined A and b,\n",
    "\n",
    "B = A’ \\* (Sigma \\\\A);\n",
    "\n",
    "L = chol(B);\n",
    "\n",
    "x = L \\\\(L’ \\\\(A’ * (Sigma \\\\b)));\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.        , -0.53512818],\n",
       "       [-0.53512818,  1.        ]])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Sigma = np.corrcoef(A1, A2)\n",
    "Sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "ename": "LinAlgError",
     "evalue": "Incompatible dimensions",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mLinAlgError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-22-5f9d2d2749f5>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mB\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mAprime\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mla\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlstsq\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mSigma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mA\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m/usr/local/lib/python2.7/site-packages/numpy/linalg/linalg.pyc\u001b[0m in \u001b[0;36mlstsq\u001b[0;34m(a, b, rcond)\u001b[0m\n\u001b[1;32m   1924\u001b[0m     \u001b[0mldb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1925\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mm\u001b[0m \u001b[0;34m!=\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1926\u001b[0;31m         \u001b[0;32mraise\u001b[0m \u001b[0mLinAlgError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Incompatible dimensions'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1927\u001b[0m     \u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mresult_t\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_commonType\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1928\u001b[0m     \u001b[0mresult_real_t\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_realType\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresult_t\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mLinAlgError\u001b[0m: Incompatible dimensions"
     ]
    }
   ],
   "source": [
    "B = Aprime.dot(la.lstsq(Sigma, A))"
   ]
  }
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