pydata_atx_eda.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Table of Contents\n",
    "* [1. Introduction to Exploratory Data Analysis with Python](#1.-Introduction-to-Exploratory-Data-Analysis-with-Python)\n",
    "\t* [1.1 Speaker, Present](#1.1-Speaker,-Present)\n",
    "\t* [1.2 Speaker, Past](#1.2-Speaker,-Past)\n",
    "\t* [1.3 Audience (You)](#1.3-Audience-%28You%29)\n",
    "* [2. Topics of the Talk](#2.-Topics-of-the-Talk)\n",
    "\t* [2.1 Python Tools for Data](#2.1-Python-Tools-for-Data)\n",
    "\t* [2.2 Exploring Data](#2.2-Exploring-Data)\n",
    "\t* [2.3 Modeling Data](#2.3-Modeling-Data)\n",
    "\t* [2.4 Recommended Reading/Viewing](#2.4-Recommended-Reading/Viewing)\n",
    "* [3. Organizing Code](#3.-Organizing-Code)\n",
    "\t* [3.1 Reusable Code, Reproducible Results](#3.1-Reusable-Code,-Reproducible-Results)\n",
    "\t* [3.2 Imports: Standard Library](#3.2-Imports:-Standard-Library)\n",
    "\t* [3.3 Imports: PyData Ecosystem](#3.3-Imports:-PyData-Ecosystem)\n",
    "\t* [3.4 Migrating from Python2 to Python3](#3.4-Migrating-from-Python2-to-Python3)\n",
    "\t* [3.5 Example: Using Functions to Simulate Data](#3.5-Example:-Using-Functions-to-Simulate-Data)\n",
    "\t* [3.6 Writing Functions, No More Giant Scripts](#3.6-Writing-Functions,-No-More-Giant-Scripts)\n",
    "\t* [3.7 Writing Functions, Simplify Interfaces](#3.7-Writing-Functions,-Simplify-Interfaces)\n",
    "\t* [3.8 Writing Functions, Better Docstrings](#3.8-Writing-Functions,-Better-Docstrings)\n",
    "\t* [3.9 Using Your Functions](#3.9-Using-Your-Functions)\n",
    "* [4. Organizing Data:](#4.-Organizing-Data:)\n",
    "\t* [4.1 Lists](#4.1-Lists)\n",
    "\t* [4.2 Numpy Arrays](#4.2-Numpy-Arrays)\n",
    "\t* [4.3 Dictionaries as \"Records\"](#4.3-Dictionaries-as-\"Records\")\n",
    "\t* [4.4 \"Records and Tables\"](#4.4-\"Records-and-Tables\")\n",
    "\t* [4.5 DataFrames as \"Tables\"](#4.5-DataFrames-as-\"Tables\")\n",
    "\t* [4.6 Classes as Data Containers](#4.6-Classes-as-Data-Containers)\n",
    "* [5. Data Visualization](#5.-Data-Visualization)\n",
    "\t* [5.1 Line and Scatter Plots](#5.1-Line-and-Scatter-Plots)\n",
    "\t* [5.2 Figures with Multiple Axes](#5.2-Figures-with-Multiple-Axes)\n",
    "\t* [5.3 Publication Figures](#5.3-Publication-Figures)\n",
    "* [6. The Shape of The Data](#6.-The-Shape-of-The-Data)\n",
    "\t* [6.1 Histograms](#6.1-Histograms)\n",
    "\t* [6.2 CDFs](#6.2-CDFs)\n",
    "\t* [6.3 Center of the Distribution](#6.3-Center-of-the-Distribution)\n",
    "\t* [6.4 Spread of the Distribution](#6.4-Spread-of-the-Distribution)\n",
    "\t* [6.5 Spread, Inter-Quartile Range (IQR)](#6.5-Spread,-Inter-Quartile-Range-%28IQR%29)\n",
    "\t* [6.6 Spread, Standard Devaition](#6.6-Spread,-Standard-Devaition)\n",
    "* [7. Summarizing the Distribution](#7.-Summarizing-the-Distribution)\n",
    "\t* [7.1 Box-and-Whisker Plots](#7.1-Box-and-Whisker-Plots)\n",
    "\t* [7.2 Kernel Density Estimation](#7.2-Kernel-Density-Estimation)\n",
    "\t* [7.3 Violin Plots (combined: boxplot + kde)](#7.3-Violin-Plots-%28combined:-boxplot-+-kde%29)\n",
    "* [8. Modeling Data](#8.-Modeling-Data)\n",
    "\t* [8.1 Transition from Descriptive to Inferential](#8.1-Transition-from-Descriptive-to-Inferential)\n",
    "\t* [8.2 Modeling the Distribution (single variable)](#8.2-Modeling-the-Distribution-%28single-variable%29)\n",
    "\t* [8.3 Example: Find the best parameters (mu, sigma) to use in a parametric model](#8.3-Example:-Find-the-best-parameters-%28mu,-sigma%29-to-use-in-a-parametric-model)\n",
    "* [9. Models and Parameter Estimation](#9.-Models-and-Parameter-Estimation)\n",
    "\t* [9.1 Method of Moments](#9.1-Method-of-Moments)\n",
    "\t* [9.2 Method of Maximum Likelihood](#9.2-Method-of-Maximum-Likelihood)\n",
    "* [10. Parameter Variation and \"Uncertainty of the Estimate\"](#10.-Parameter-Variation-and-\"Uncertainty-of-the-Estimate\")\n",
    "\t* [10.1 Sampling](#10.1-Sampling)\n",
    "\t* [10.2 Resampling](#10.2-Resampling)\n",
    "\t* [10.3 Sample Distribution](#10.3-Sample-Distribution)\n",
    "\t* [10.4 Sampling Variance](#10.4-Sampling-Variance)\n",
    "\t* [10.5 Resampling from the Population](#10.5-Resampling-from-the-Population)\n",
    "\t* [10.6 Spread of the Estimate](#10.6-Spread-of-the-Estimate)\n",
    "* [11. Modeling 2-variable Data](#11.-Modeling-2-variable-Data)\n",
    "\t* [11.1 Tune the parameter values to make the model fit the data...](#11.1-Tune-the-parameter-values-to-make-the-model-fit-the-data...)\n",
    "\t* [11.2 Linear Regression as Optimization](#11.2-Linear-Regression-as-Optimization)\n",
    "\t* [11.3 Linear Regression, Analytic Solution](#11.3-Linear-Regression,-Analytic-Solution)\n",
    "\t* [11.4 Resampling to Visualize Uncertainty in Parameter Estimates](#11.4-Resampling-to-Visualize-Uncertainty-in-Parameter-Estimates)\n",
    "* [12. Linear  Regression in Practice](#12.-Linear--Regression-in-Practice)\n",
    "\t* [12.1 Linear Regression with scipy.optimize](#12.1-Linear-Regression-with-scipy.optimize)\n",
    "\t* [12.2 Linear Regression with statsmodels](#12.2-Linear-Regression-with-statsmodels)\n",
    "\t* [12.3 Linear Regression with statsmodels and pandas](#12.3-Linear-Regression-with-statsmodels-and-pandas)\n",
    "\t* [12.4 Linear Regression with scikit-learn](#12.4-Linear-Regression-with-scikit-learn)\n",
    "* [13. The End](#13.-The-End)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 1. Introduction to Exploratory Data Analysis with Python"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Time: 2018-March-27, 7-8pm (ish)\n",
    "* Space: HomeAway\n",
    "* City: Austin TX\n",
    "* Speaker: Jason Vestuto"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.1 Speaker, Present"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Space and Geophysics Lab, University of Texas at Austin.\n",
    "    * data: RINEX, HFD5, legacy binary, legacy ASCII, time series, raw rx outputs\n",
    "    * times: atomic clocks, RF signals/hardware/dsp, ionospheric/troposhperic delays\n",
    "    * positions: orbits, tectonic plate motion, survey positions, WGS84 reference frame\n",
    "    * informal: lead dev for analysis group, git help desk, configuration management guy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Community\n",
    "    * not as much as I'd lile, but trying (let me know how the talk goes)\n",
    "    * have dabbled with open-source projects (matplotlib, numpy, conda)\n",
    "    * attend SciPy Conference (2014, 2015, 2017, 2018)\n",
    "    * [reusable-python](https://github.com/vestuto/reusable-python): some notes I wrote on organizing python code into packages, using conda\n",
    "    * [GPSTk](https://github.com/SGL-UT/GPSTk): Python SWIG wrapped C++ library of GPS/GNSS data tools. Not my project, but part of the job."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.2 Speaker, Past"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plan? What plan...\n",
    "* coding & stats: no formal education, learned at work, from others open projects\n",
    "* edu: Public schools/libraries, BS Phsyics, MS Physics, MEd Science Edu\n",
    "* jobs: ARLUT, Anaconda/Continuum, community college teacher, high school teacher, math editor, guitar tech."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tools, sorted autobiographically...\n",
    "* Apple IIE, Basic, FORTRAN77, Excel, Mathematica\n",
    "* Bash/GNU, Perl, C, Emacs, IDL, SuperMongo, gnu-plot, CVS\n",
    "* MATLAB, Octave, SVN, FORTRAN98, C++, Perforce\n",
    "* python, git, GitLab, conda, jupyter, PyCharm\n",
    "* O'Reilly Books, Stack-Overflow\n",
    "* GitHub, Slack, Mattermost"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1.3 Audience (You)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Assumptions\n",
    "* already installed \"pydata stack\" (e.g. [Anaconda Distribution](https://docs.anaconda.com/anaconda/install/))\n",
    "* some experience with coding\n",
    "* some experience with descriptive statistics\n",
    "* ideally some exposure to `python`, `jupyter notebook`, `numpy`\n",
    "\n",
    "Reality?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 2. Topics of the Talk"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is EDA? Ask Wikipedia...\n",
    "\n",
    "> \"In statistics, exploratory data analysis (EDA) is an approach to analyzing data sets to summarize their main characteristics, often with visual methods. A statistical model can be used or not, but primarily EDA is for seeing what the data can tell us beyond the formal modeling or hypothesis testing task. Exploratory data analysis was promoted by John Tukey to encourage statisticians to explore the data, and possibly formulate hypotheses that could lead to new data collection and experiments. \" - [EDA entry in Wikipedia](https://en.wikipedia.org/wiki/Exploratory_data_analysis) \n",
    "\n",
    "\n",
    "Better still, ask John Tukey...\n",
    "\n",
    "\n",
    "> \" [P]rocedures for analyzing data, techniques for interpreting the results of such procedures, ways of planning the gathering of data to make its analysis easier, more precise or more accurate, and all the machinery and results of (mathematical) statistics which apply to analyzing data.\" - John Tukey \n",
    "\n",
    "Who the heck is John Tukey?\n",
    "* Bell Labs\n",
    "* Cooley–Tukey FFT algorithm\n",
    "* worked a bit with John von Neumann\n",
    "* coined the word \"bit\"\n",
    "* boxplots\n",
    "\n",
    "So we should look at at least the following stuff:\n",
    "* data gathering, storing, organizing\n",
    "* data visualization\n",
    "* descriptive statistics\n",
    "* inferential statistics\n",
    "* statistical modeling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.1 Python Tools for Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* [Python](https://www.python.org/psf/) - the language\n",
    "* [conda](https://conda.io/docs/user-guide/install/download.html) - configuration management\n",
    "* [Jupyter](http://jupyter.org) - interactive shell, notebooks, IDE\n",
    "* [Numpy](http://www.numpy.org) - arrays, fast array computing, fast math\n",
    "* [Pandas](http://pandas.pydata.org) - DataFrames, data analysis, database-liek operations\n",
    "* [Scipy](https://www.scipy.org/getting-started.html) - scientific computing\n",
    "* [Matplotlib](https://matplotlib.org) - data visualization, general purpose\n",
    "* [Seaborn](https://seaborn.pydata.org) - data visualization for statistics\n",
    "* [Statsmodels](http://www.statsmodels.org/stable/index.html) - statistics\n",
    "* [Scikit-Learn](http://scikit-learn.org/stable/) - machine learning, modeling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.2 Exploring Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Data Visualization\n",
    "* Descriptive statistics\n",
    "* Characterizing the Data Distribution\n",
    "* Parametric Modeling of Data, single variable"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.3 Modeling Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Inferential statistics\n",
    "* A little computational stats\n",
    "* Parameter Estimation\n",
    "* Sampling, Bootstrap Resampling\n",
    "* Estimation Uncertainty\n",
    "* Modeling Data, two variables\n",
    "* Linear regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2.4 Recommended Reading/Viewing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Books/Notebooks:\n",
    "    * [Vanderplas, Whirlwind Tour of Python](https://jakevdp.github.io/WhirlwindTourOfPython/)\n",
    "    * [Vanderplas, Python Datascience Handbook](https://jakevdp.github.io/PythonDataScienceHandbook/)\n",
    "    * [Scipy Lecture Notes](https://www.scipy-lectures.org)\n",
    "    * [Downey, Think Python](http://greenteapress.com/wp/think-python-2e/)\n",
    "    * [Downey, Think Stats](http://greenteapress.com/wp/think-stats-2e/)\n",
    "    * [Boslaugh, Statistics in a Nutshell](http://shop.oreilly.com/product/0636920023074.do)\n",
    "    * [Fonnesbeck, Statistical Analysis](https://github.com/fonnesbeck/statistical-analysis-python-tutorial)\n",
    "\n",
    "\n",
    "* Talks/Tutorials:\n",
    "    * [JupyterCon2017, Granger, Jupyter Lab](https://www.youtube.com/watch?v=w7jq4XgwLJQ)\n",
    "    * [SciPy2017, Niederhut, Numpy](https://www.youtube.com/watch?v=lKcwuPnSHIQ)\n",
    "    * [SciPy2017, Root, Matplotlib](https://www.youtube.com/watch?v=rARMKS8jE9g)\n",
    "    * [PyCon2016, Vanderplas, Statistics for Hackers](https://www.youtube.com/watch?v=Iq9DzN6mvYA)\n",
    "    * [SciPy2017, Fonnesbeck, Statistical Thinking](https://www.youtube.com/watch?v=TGGGDpb04Yc)\n",
    "    * [SciPy2015, Downey, Computational Stats](https://www.youtube.com/watch?v=fMycLa1bsno)\n",
    "    * [SciPy2013, Fonnesbeck, Statistical Data Analysis](https://www.youtube.com/watch?v=5_rcdhBXD-0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 3. Organizing Code"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.1 Reusable Code, Reproducible Results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[The Six Stages of Computational Science](https://opendatascience.com/blog/the-six-stages-of-computational-science/) - Please read this!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.2 Imports: Standard Library"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Importing ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['pydata_atx_eda_vestuto_20180327.ipynb',\n",
       " '.DS_Store',\n",
       " '.ipynb_checkpoints',\n",
       " 'pydata.png']"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import os\n",
    "os.listdir()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "datetime.datetime(2018, 3, 27, 18, 21, 13, 818684)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import datetime as dt\n",
    "dt.datetime.now()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.141592653589793"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import math\n",
    "math.pi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.3 Imports: PyData Ecosystem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Extending the python standard library..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3.141592653589793"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "np.pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy\n",
    "import pandas\n",
    "import matplotlib\n",
    "import seaborn\n",
    "import scipy\n",
    "import statsmodels\n",
    "import sklearn"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Most common aliases used by others ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import datetime as dt\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "from matplotlib import ticker\n",
    "from scipy import optimize\n",
    "import pandas as pd\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.4 Migrating from Python2 to Python3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make your code work in both py2 and py3..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import division, print_function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.5 Example: Using Functions to Simulate Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* there are other tutorials on data loading, data cleaning\n",
    "* simulating data gives you some useful examples of `numpy.random` and `numpy.ndarray`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "np.random.seed(seed=42)\n",
    "\n",
    "center = 0\n",
    "spread = 1\n",
    "npts   = 20\n",
    "\n",
    "data   = np.random.normal(center, spread, npts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.49671415, -0.1382643 ,  0.64768854,  1.52302986, -0.23415337,\n",
       "       -0.23413696,  1.57921282,  0.76743473, -0.46947439,  0.54256004])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[0:10]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.6 Writing Functions, No More Giant Scripts"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* if all your code is nothing but giant scripts, all your coworkers hate you\n",
    "* if they don't say it, they think it while drinking at night\n",
    "* step 1: admit you ahve a problem\n",
    "* step 2: define a function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def load_data_norm(npts=100, mu=0, sigma=1):\n",
    "    z = np.random.normal(mu, sigma, npts)\n",
    "    return z"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.46564877, -0.2257763 ,  0.0675282 , -1.42474819, -0.54438272,\n",
       "        0.11092259, -1.15099358,  0.37569802, -0.60063869, -0.29169375])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "z = load_data_norm(10)\n",
    "z"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.7 Writing Functions, Simplify Interfaces"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* seriously, use functions\n",
    "* customized interfaces are awesome"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def load_data_line(npts=101):\n",
    "    x = np.linspace(0, 10, npts)\n",
    "    noise = np.random.normal(0, 1, npts)\n",
    "    y = x + 0.5*noise\n",
    "    return x, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  0.    2.5   5.    7.5  10. ]\n",
      "[ -0.30085331   3.42613909   4.99325139   6.97114454  10.41127246]\n"
     ]
    }
   ],
   "source": [
    "x, y = load_data_line(5)\n",
    "print(x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.8 Writing Functions, Better Docstrings"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* good: Don't ignore the linter in your IDE\n",
    "* better: consciously pick a style guide, document it\n",
    "* great: use pylint tests, hook them into your CI, auto-run every time you `git push`\n",
    "* awesome: have an opinion about PEP8, custom edit your .pylintrc\n",
    "* loved by all: write good docstrings FFS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def load_data_line(npts=101, a0=0, a1=1, ae=0.5):\n",
    "    \"\"\"\n",
    "    Purpose: Generates (x,y) data with some random noise\n",
    "        x is np.linspace(0, 10, npts)\n",
    "        y is a1*x + a0 + ae*noise\n",
    "        noise is np.random.normal(mu, sigma,npts)\n",
    "    Usage:\n",
    "        x, y = load_data_line()\n",
    "        lines = plt.plot(x, y)\n",
    "    Args:\n",
    "        npts (int): Number of points in the data set returned\n",
    "        a0 (float): y-intercept\n",
    "        a1 (float): slope dy/dx \n",
    "    Returns:\n",
    "        x (np.ndarray): an array of npts evenly spaced from 0 to 10\n",
    "        y (np.ndarray): computed as a0 + (a1*x) + noise\n",
    "    \"\"\"\n",
    "    xmin  = 0\n",
    "    xmax  = 10\n",
    "    mu    = 0\n",
    "    sigma = 1\n",
    "    x = np.linspace(xmin, xmax, npts)\n",
    "    e = np.random.normal(mu, sigma, npts)\n",
    "    y = a0 + (a1*x) + ae*e\n",
    "    return x, y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.9 Using Your Functions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[  0.    2.5   5.    7.5  10. ]\n",
      "[ -0.61042182   2.6044318    4.02016494   6.83590698  10.09843062]\n"
     ]
    }
   ],
   "source": [
    "x, y = load_data_line(npts=5)\n",
    "\n",
    "print(x)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# load_data_line?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WH8Xa3CTcHu1vUzueMw3dZCVGk+19IDpSlDmCr79vLfvKM9iQP/FDTiFCmQR0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\nZZTdAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114daf978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y = load_data_line()\n",
    "lines = plt.plot(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 4. Organizing Data:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need some structures ot hold and organize our data in memory\n",
    "\n",
    "Commonly used...\n",
    "* collections: python lists\n",
    "* key-values, records: python dictionaries\n",
    "* arrays of floats: numpy array\n",
    "* tabular data: pandas DataFrames"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.1 Lists"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Store some data ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['hello', 42, 3.14159]"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_list = ['hello', 42, 3.14159]\n",
    "data_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_list = list( range(10) )\n",
    "data_list"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_list = [1*n for n in range(10)]\n",
    "data_list"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Retrieve some data ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_list[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 3]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_list[2:4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_list*2  # concatenation? WTH?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# data_list + 10  # Cannot do it!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.2 Numpy Arrays"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Store some data in a more powerful container ..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_array = np.array(data_list)\n",
    "data_array"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# data_array?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(data_array) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.int64"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(data_array[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  2,  4,  6,  8, 10, 12, 14, 16, 18])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# (broadcasting) + (vector math)\n",
    "\n",
    "data_array * 2 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([10, 11, 12, 13, 14, 15, 16, 17, 18, 19])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_array + 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "45"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_array.sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.5"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data_array.mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0.  ,   0.01,   0.02, ...,   9.98,   9.99,  10.  ])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "array = np.linspace(0, 10, 1001)\n",
    "array"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.3 Dictionaries as \"Records\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'year': 2018, 'doy': 82, 'type': 'temperature', 'value': 73, 'units': 'degF'}\n"
     ]
    }
   ],
   "source": [
    "record = dict( year=2018, doy=82, type='temperature', value=73, units='degF')\n",
    "\n",
    "print(record)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.4 \"Records and Tables\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* python: lists of dictionaries\n",
    "* pandas: DataFrames"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'year': 2018, 'doy': 82, 'type': 'temperature', 'value': 73, 'units': 'degF'}\n",
      "{'year': 2018, 'doy': 83, 'type': 'temperature', 'value': 75, 'units': 'degF'}\n",
      "{'year': 2018, 'doy': 84, 'type': 'temperature', 'value': 77, 'units': 'degF'}\n",
      "{'year': 2018, 'doy': 85, 'type': 'temperature', 'value': 79, 'units': 'degF'}\n",
      "{'year': 2018, 'doy': 86, 'type': 'temperature', 'value': 81, 'units': 'degF'}\n"
     ]
    }
   ],
   "source": [
    "table = []\n",
    "\n",
    "for n in [0,1,2,3,4]:\n",
    "    new_record = record.copy()\n",
    "    new_record['doy'] += n\n",
    "    new_record['value'] += 2*n\n",
    "    table.append(new_record)\n",
    "\n",
    "for record in table:\n",
    "    print(record)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.5 DataFrames as \"Tables\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* \"pandas\" ~ \"panel data\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>doy</th>\n",
       "      <th>type</th>\n",
       "      <th>units</th>\n",
       "      <th>value</th>\n",
       "      <th>year</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>82</td>\n",
       "      <td>temperature</td>\n",
       "      <td>degF</td>\n",
       "      <td>73</td>\n",
       "      <td>2018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>83</td>\n",
       "      <td>temperature</td>\n",
       "      <td>degF</td>\n",
       "      <td>75</td>\n",
       "      <td>2018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>84</td>\n",
       "      <td>temperature</td>\n",
       "      <td>degF</td>\n",
       "      <td>77</td>\n",
       "      <td>2018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>85</td>\n",
       "      <td>temperature</td>\n",
       "      <td>degF</td>\n",
       "      <td>79</td>\n",
       "      <td>2018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>86</td>\n",
       "      <td>temperature</td>\n",
       "      <td>degF</td>\n",
       "      <td>81</td>\n",
       "      <td>2018</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   doy         type units  value  year\n",
       "0   82  temperature  degF     73  2018\n",
       "1   83  temperature  degF     75  2018\n",
       "2   84  temperature  degF     77  2018\n",
       "3   85  temperature  degF     79  2018\n",
       "4   86  temperature  degF     81  2018"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.DataFrame(table)\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.6 Classes as Data Containers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "class DataBucket():\n",
    "    def __init__(self, name='unknown', speed=2.5):\n",
    "        self.name      = name\n",
    "        self.speed     = speed\n",
    "        self.creation  = dt.datetime.now()\n",
    "        self.times     = np.linspace(0, 10, 11)\n",
    "        self.distances = self.speed*self.times"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "db = DataBucket('parrot')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.5"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "db.speed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "datetime.datetime(2018, 3, 27, 18, 21, 17, 322768)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "db.creation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  0. ,   2.5,   5. ,   7.5,  10. ,  12.5,  15. ,  17.5,  20. ,\n",
       "        22.5,  25. ])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "db.distances"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 5. Data Visualization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.1 Line and Scatter Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = load_data_norm(100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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yGzst5/Dmm/f6risRUXF+vbuB/fnFLA7tTEFVGHZOxOyUx81Cxe6xQXcdaznz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x114dafeb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# simplest\n",
    "\n",
    "line = plt.plot(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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n1QubQjF0jHNpZRovJvMSkwn8t3f+NwDAz//g51U3jdXnt5hdRK6Uw6beTdj/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\nIpF0GVLYJRKJpMv4f4g4/hJ8VytbAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11726fdd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# a little customization\n",
    "\n",
    "line = plt.plot(data, color='green', marker='o')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EzjQeqGbms7Oz0Z6y7qbolmXZLVcCtXlKCXZJvyNpRdK2pMWsryPY66kufaVFBWTRQVj2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\nSAzBDgCJIdgBIDH/D591We8afFDdAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117381048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# more general\n",
    "\n",
    "fig, ax = plt.subplots()\n",
    "\n",
    "options = dict(linestyle=\" \", marker=\"o\", markersize=4, color=\"black\")\n",
    "\n",
    "lines   = ax.plot(data, **options)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.2 Figures with Multiple Axes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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H3sI8Pi7/mCH/M4TnNj6X6NBExIcidfzLznZNjVNS3LawMJ5RiUcJliQ/L8Ha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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1173813c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y = load_data_line()\n",
    "\n",
    "fig_options = dict(nrows=1, ncols=3, figsize=(12,4))\n",
    "fig, axes = plt.subplots(**fig_options)\n",
    "\n",
    "# pre-define line options, e.g. color, line style, marker symbol, etc\n",
    "line_options = ['slot0', 'slot1', 'slot2']\n",
    "line_options[0] = dict(linestyle=\"-\",  marker=\" \", color=\"red\")\n",
    "line_options[1] = dict(linestyle=\"--\", marker=\"s\", color=\"green\")\n",
    "line_options[2] = dict(linestyle=\" \",  marker=\"o\", color=\"blue\")\n",
    "\n",
    "# plot lines on 3 separate axes\n",
    "line0 = axes[0].plot(x,   y, **line_options[0])\n",
    "line1 = axes[1].plot(x, 2*y, **line_options[1])\n",
    "line5 = axes[2].plot(x, 4*y, **line_options[2])\n",
    "\n",
    "# apply the same change to all axes\n",
    "for axis in fig.axes:\n",
    "    axis.grid(True, which='major')\n",
    "\n",
    "# so that tick labels don't overlap\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.3 Publication Figures"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_data_fancy(x, y):\n",
    "    \"\"\"\n",
    "    Purpose: Make a pretty plot of some line data (x, y)\n",
    "    Args:\n",
    "        x (np.ndarray): array of distance values, units=meters\n",
    "        y (np.ndarray): array of time values, units=seconds\n",
    "    Returns:\n",
    "        fig (plt.figure): matplotlib figure object\n",
    "    Raise:\n",
    "        None\n",
    "    \"\"\"\n",
    "    fig, axis = plt.subplots()\n",
    "    data_opts     = dict(linestyle=\" \", marker=\"o\", label=\"My Data\")\n",
    "    model_opts    = dict(linestyle=\"-\", linewidth=8, alpha=0.5, label=\"My Model\")\n",
    "    threhold_opts = dict(linestyle=\"-\", linewidth=10, alpha=0.3, label=\"Threshold\")\n",
    "    axis.plot(x, y, color=\"black\", **data_opts)\n",
    "    axis.plot(x, x, color=\"red\",   **model_opts)\n",
    "    axis.axvline(5, color=\"green\", **threhold_opts)\n",
    "    axis.axvline(0, color=\"black\")\n",
    "    axis.axhline(0, color=\"black\")\n",
    "    axis.grid(True, which=\"both\")\n",
    "    axis.set_ylim([-2.5, 12.5])\n",
    "    axis.set_xlim([-2.5, 12.5])\n",
    "    axis.xaxis.set_major_locator(ticker.MultipleLocator(2.5))\n",
    "    axis.xaxis.set_minor_locator(ticker.MultipleLocator(0.5))\n",
    "    axis.yaxis.set_major_locator(ticker.MultipleLocator(5.0))\n",
    "    axis.yaxis.set_minor_locator(ticker.MultipleLocator(1.0))\n",
    "    axis.set_ylabel('Distance (meters)')\n",
    "    axis.set_xlabel('Time (seconds)')\n",
    "    axis.set_title('Fig. 1.2: Tweek All The Things')\n",
    "    axis.legend()\n",
    "    return fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "plot_data_fancy?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XApXc8MnPP/P+n/7E2T/95PW0Q+nVkWVdUlrKlwOhwUB51y6cds01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\nlI8AiayilG9BxZ0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11738d6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y  = load_data_line(npts=101)\n",
    "\n",
    "fig = plot_data_fancy(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 6. The Shape of The Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.1 Histograms"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* feel intuitive\n",
    "* human has to manually chose bins (width and location)\n",
    "* \"The Binning Problem\" is unavoidable"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SjTAOnsnMCCmLHqhKQ2PP4Gu0Xo29GGIhYa8YFndyuaUtrzVSIMRXNwlq7KaG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\nWKoMK9gtFoulyvh/JwyNRiaxxSUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11738d7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = load_data_norm(1000)\n",
    "line = plt.plot(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lVTXRzyCSvA5YrKqTSX5r3O+36Qq9ql692vYkvwa8GHg4CSxPHzyU5BVVdXFSuVZxD8vH\n5m9IoffLleRNwOuA3bWBx6gO8f2atIEuYaGfSHIly2V+T1V9dNJ5LldV30pyP8ufQUz6Q+WbgNuS\n/A7wHODnk3ygqt4wjjfbMlMuVfXlqnphVc1U1QzLvxq/fCPKvJ8kO1es7gUen1SWlZLsYflXvduq\n6vuTzrNJeQmLIWR5NPVe4HRVvWvSeZ6WZOrpo7iSPJfl+zRM/Oewqu6qqmu7zroD+My4yhy2UKFv\ncoeSPJLkSyxPCW2KQ7mAvwOeDxzvDqn8x0kHAkjyu0nOA68CPpbkk5PK0n1o/PQlLE4DRzbDJSyS\nfBD4PHB9kvNJ9k86U+cm4I3Azd2/qVPd6HPStgP3dz+DD7I8hz7WQwQ3I88UlaRGOEKXpEZY6JLU\nCAtdkhphoUtSIyx0SWqEhS5JjbDQJakRFrokNeJ/ASIBHH5bF5zyAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1172119e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.linspace(-4, +4, 51)\n",
    "count, bins, patches = plt.hist(x, bins, cumulative=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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RH1+SpEWlz9vPrgM+C5yT5L4kVwKbgAuT3Av8dLcuSZLmqLfnkVfVFdNsWtvXMSVJWmqc\n2U2SpIYZ5JIkNcwglySpYQa5JEkN6+1iN2k2O3funHbbmjVrZt0uLSXT/X049Hdhtu1avOyRS5LU\nMINckqSGObQuSfKrrIbZI5ckqWEGuSRJDXNoXb3xKlpp4XDofPGyRy5JUsMMckmSGubQuqbl0Lik\nQxyaX7jskUuS1DCDXJKkhjm0vkQ5TCZJi4M9ckmSGmaQS5LUMINckqSGGeSSJDVsLEGe5KIkX07y\nlSQbx1GDJEmLwcivWk9yDPAHwIXAfcAXk2yrqrtGXUvLZrvqfBRXpTthjKSjyd8pczOOHvkLga9U\n1Ver6ofAnwHrxlCHJEnNG0eQPwP45qT1+7o2SZJ0hBbshDBJNgAbutWHk3z5KH306cC3jtJnjZvn\nsjB5LguT57IweS5Te+awO44jyO8Hzpy0fkbX9gRVtRnYfLQPnmRXVU0c7c8dB89lYfJcFibPZWHy\nXOZvHEPrXwTOTnJWkqcAlwPbxlCHJEnNG3mPvKoeSfLLwMeBY4APVNWdo65DkqTFYCzfkVfVXwF/\nNY5j08Nw/Rh5LguT57IweS4Lk+cyT6mqcRxXkiQdBU7RKklSw5Z0kCd5Y5JKcvq4a5mrJL+Z5EtJ\nbk3yiSQ/Nu6a5irJu5Lc053P9UlOGXdNc5Xk3yW5M8ljSZq8InexTKWc5ANJDiS5Y9y1zFeSM5Pc\nlOSu7v+vq8Zd01wkOS7JF5Lc1p3H28dd03wlOSbJLUluHPWxl2yQJzkTeDnwjXHXMk/vqqrnVtVq\n4EbgbeMuaB62A8+uqucCfwu8ecz1zMcdwKXAp8ddyFxMmkr5FcC5wBVJzh1vVXP2QeCicRdxlDwC\nvLGqzgXOB36p0T+XHwAvq6rzgNXARUnOH3NN83UVcPc4Drxkgxx4D/BrQNMXCVTVg5NWT6Dh86mq\nT1TVI93q5xjMMdCkqrq7qo7WJEbjsGimUq6qTwMPjLuOo6Gq9lbVzd3yQwyCo7mZMWvg4W712O6n\n2d9dSc4AXgW8bxzHX5JBnmQdcH9V3TbuWo6GJO9I8k3gZ2m7Rz7ZLwIfHXcRS5hTKS9wSVYBzwM+\nP95K5qYbir4VOABsr6omz6Pzuww6ho+N4+ALdorW+UrySeBfTLHprcBbGAyrN2Gmc6mqG6rqrcBb\nk7wZ+GXgv420wCMw27l0+7yVwRDitaOs7UgNcy5SH5I8DfgwcPVho3LNqKpHgdXdtTDXJ3l2VTV3\nHUOSVwMHqmp3kjXjqGHRBnlV/fRU7UmeA5wF3JYEBsO3Nyd5YVXtG2GJQ5vuXKZwLYP78xdskM92\nLkleB7waWFsL/N7II/hzadFQUylr9JIcyyDEr62qj4y7nvmqqu8kuYnBdQzNBTlwAXBxklcCxwEn\nJfmTqvq5URWw5IbWq+r2qnp6Va2qqlUMhgyfv1BDfDZJzp60ug64Z1y1zFeSixgMT11cVd8bdz1L\nnFMpL0AZ9D7eD9xdVe8edz1zlWTZobtSkhwPXEijv7uq6s1VdUaXJ5cDnxpliMMSDPJFaFOSO5J8\nicHXBU3ejtJ5L3AisL27ne4Px13QXCV5TZL7gBcBf5nk4+Ou6Uh0Fx0emkr5bmBrq1MpJ7kO+Cxw\nTpL7klw57prm4QLg54GXdX9Hbu16gq1ZAdzU/d76IoPvyEd+29Zi4cxukiQ1zB65JEkNM8glSWqY\nQS5JUsMMckmSGmaQS5LUMINcWuC6J159Lclp3fqp3fqqw/a7KcnPHNZ2dZJrZvn8h2fafgR1/vck\n93e3RN2T5JokT+q2/UaSxTyBjjQ2Brm0wFXVN4FrgE1d0yZgc1V9/bBdr2MwIcVkl3fto/Ke7kl8\n5wLPAV4CUFVvq6pPjrAOackwyKU2vAc4P8nVwE8B/3OKfT4EvKqbie3QQzV+DPg/SZ6WZEeSm5Pc\n3j046AmSrJn8LOUk7+2mzCXJC5L8dZLdST6eZMUs9T6FwXSVf9+9/4NJXtstfz3J2yfV8qyu/SWT\nJjm5JcmJR/DfR1qyDHKpAVX1I+BXGQT61d364fs8AHyBwTPEYdAb39rNWf+PwGuq6vnAS4Hf6ab7\nnFU3t/fvA6+tqhcAHwDeMc3u/7V7otVe4G+r6tZp9vtWV8s1wK90bb8C/FLXo/83wPeHqU9a6gxy\nqR2vYBCQz55hn8nD65OH1QP8Vjcl5icZPJJ0+ZDHPac75vYupH+d6Z8Vf2ho/enACUkOH+o/5NDD\nPnYDq7rlvwHeneQNwCmTnk0vaQYGudSAJKsZPFjifAa93umGtm8A1iZ5PvDPqmp31/6zwDLgBV3Q\n7mcw9D3ZIzzxd8Kh7QHurKrV3c9zqmrGxwB3IwYfA148zS4/6F4fpXsKY1VtAv4jcDzwN4eG3CXN\nzCCXFrhuCPwaBkPq3wDexdTfkVNVDwM3MRj+nnyR28kMnpn8oyQvBZ45xdv3AOcmeWr3ZKq1XfuX\ngWVJXtTVc2ySfzlEzRcAfzfkaZLkx7unE76TwYM0DHJpCAa5tPD9J+AbVbW9W/9fwE8meck0+18H\nnMcTg/xaYCLJ7cAvMMUjI7ur47cyeCb0VuCWrv2HwGuBdya5DbgV+NfTHPvQd+R3AMd0tQ7r6klP\n8vsR8NEjeK+0ZPn0M0mSGmaPXJKkhhnkkiQ1zCCXJKlhBrkkSQ0zyCVJaphBLklSwwxySZIaZpBL\nktSw/wfoAyBZHdD5KwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117b3b470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.linspace(-4, +4, 51)\n",
    "plot_opts = dict(rwidth=0.8, color='black', alpha=0.25)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8,4))\n",
    "count, bins, patches = ax.hist(x, bins, cumulative=False, **plot_opts)\n",
    "yl = ax.set_ylabel('Bin Counts')\n",
    "xl = ax.set_xlabel('X Value Bins')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1000.0"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sum(count)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GZRHqVfXbUx1PcjRwOHBTEhgM8X4jyQlV9f0Rljhr013LFK5ksEbAkg31ma4lyeuAlwEv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\nAwBb0wXN12VBAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117cd6c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.linspace(-4, +4, 51)\n",
    "plot_opts = dict(rwidth=0.8, color='black', alpha=0.25)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8,4))\n",
    "pdf, bins, patches = ax.hist(x, bins, normed=True, cumulative=False, **plot_opts)\n",
    "yl = ax.set_ylabel('PDF')\n",
    "xl = ax.set_xlabel('X Value Bins')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0000000000000009"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta_x = np.abs(bins[1] - bins[0])\n",
    "np.sum( pdf*delta_x )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hqv0+m8mEUEZV/aWqTno39zP9XEVIUNUTqnqph/ac8O5UJao6Dlyc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\nxkQZK/zGGBNl/j9wyJmvraQ3IgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117171828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = load_data_norm(1000)\n",
    "axis = sns.distplot(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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VTKulSZlQ0pbSyedpuXyZuvl5FvbtI9vWFndEIvcukWBh3z4sm6Xp2rX1y4ts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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117b62390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = load_data_norm(1000)\n",
    "fig, axis = plt.subplots(figsize=(8,4))\n",
    "hist_opts = dict(rwidth=0.8, alpha=0.25, color='black')\n",
    "kde_opts  = dict(alpha=0.25, color='red')\n",
    "axis = sns.distplot(x, kde=True, ax=axis, hist_kws=hist_opts, kde_kws=kde_opts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.2 CDFs"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Less intuitive than histograms (at first)\n",
    "* Bin definition is **optional**\n",
    "* Much more useful for data that is **NOT** gaussian (non-normal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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4wfXHl3qgiVw2YraS/BPwM+c4dCvwDgangubdU9VVVXdV1a3ArUm2AW8CbpuEuro+tzKY\nxt85HzVdbF1auJI8B/gY8NazZsJjU1VngJd0174+keS6qhrrNZUkrwFOVtW9SV5xqce7LEKgql51\nrvYkPw+sBL6WBAanNu5LsqaqToyrrnO4k8GzE/MSAheqK8kbgdcAa2se7yGexb+vcbuo5U/0hCRP\nYxAAd1bVx8ddz9mq6j+SfIHBNZVxX1i/AXhtklcDzwCem+TDVfX6SzHYZX06qKq+UVU/XVUrqmoF\ng2n7y+YjAC4kyaqh3fXAN8dVy7Ak6xhMQ19bVf897nomlMufzEIGP4G9HzhUVe8adz2PSzL1+N1v\nSZ4J/AoT8PewqrZV1bLuO2sD8PlLFQBwmYfAhLs9yYNJvs7gdNVE3DYH/DXwk8De7vbVvx13QQBJ\nfj3JUeDlwKeSfHZctXQXzh9f/uQQsHsSlj9J8hHgy8ALkxxNsmncNXVuAN4AvLL7f+qB7qfccVsC\nfKH7O/hVBtcELuntmJPIJ4YlqWHOBCSpYYaAJDXMEJCkhhkCktQwQ0CSGmYISFLDDAFJapghIEkN\n+18e9R6RKvEuhwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1181bbd30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.linspace(-4, +4, 51)\n",
    "fig, axis = plt.subplots()\n",
    "count, bins, patches = axis.hist(x, bins, cumulative=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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grj1xgNeRRI6Iyl3iXmWtn6ueWEJeYSl3TB/OJcf18TqSyBHTnLvEvXm5hXy8YTc3Thms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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117fcdfd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = load_data_norm(npts=1000)\n",
    "xs = np.sort(x)\n",
    "percentiles = np.linspace(0, 1, len(xs))\n",
    "line = plt.plot(xs, percentiles)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Make it pretty..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MyUtzuiwRRynIRSTsdfj8fHXpZl7ZWoHXbzn/tEx+8dkpZKfoSWUiCnIRCVsdPj/PrzvA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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118008e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = load_data_norm(npts=1000)\n",
    "xs = np.sort(x)\n",
    "percentiles = np.linspace(0, 1, len(xs))\n",
    "\n",
    "fig, axis = plt.subplots(figsize=(8,4))\n",
    "axis.plot(xs, percentiles)\n",
    "\n",
    "axis.set_xlim([-2,2])\n",
    "axis.yaxis.set_major_locator(ticker.MultipleLocator(0.25))\n",
    "axis.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Ur13XgN+n+/1kYdE3VuQcmk4NcLRzmM9eUUlVSa7X5YjMmsJd5Cz9YyF2HOzk0vJ8rl9e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\nQQp3EZHyYOrHAAAACElEQVQU9P8BPSPlN/zShIMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117c72400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = load_data_norm(1000)\n",
    "axis = sns.distplot(x, kde=True, \n",
    "                    hist_kws=dict(cumulative=True), \n",
    "                    kde_kws=dict(cumulative=True))\n",
    "axis.set_xlim(x.min(), x.max());"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.3 Center of the Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.029090626844311743"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.044742172917806647"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.median(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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JrUmeSfKFqnqgu78yr+LYXv7PGQB88zmarfQMvzXJ73X3V7v7j5P8apID8ykLAAAWbyth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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117864dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.linspace(-4, +4, 51)\n",
    "plot_opts = dict(rwidth=0.8, color='black', alpha=0.25)\n",
    "\n",
    "fig, axis = plt.subplots(figsize=(12,4))\n",
    "count, bins, patches = axis.hist(x, bins, cumulative=False, **plot_opts)\n",
    "\n",
    "v5o = axis.axvline(np.median(x), color='red')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PLuaKiQVMLc73OKWISHxSacv7cs5xuLGNV7YfYtXuI/zlrQqa2oIAnDuiD9eU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\nZ9xMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117167438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xs = np.sort(x)\n",
    "percentiles = np.linspace(0, 1, len(xs))\n",
    "\n",
    "fig, axis = plt.subplots(figsize=(8,4))\n",
    "line = axis.plot(xs, percentiles)\n",
    "\n",
    "axis.yaxis.set_major_locator(ticker.MultipleLocator(0.25))\n",
    "\n",
    "hl = axis.axhline(.50, color='red')\n",
    "vl = axis.axvline(np.median(x), color='red')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.4 Spread of the Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Range\n",
    "* IQR\n",
    "* Standard deviation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "min = -2.900, max = 3.098, range = 5.998\n"
     ]
    }
   ],
   "source": [
    "xmin = x.min()\n",
    "xmax = x.max()\n",
    "xrng = xmax - xmin\n",
    "summary = 'min = {:0.3f}, max = {:0.3f}, range = {:0.3f}'.format(xmin, xmax, xrng)\n",
    "print(summary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5th = -1.671, 95th = 1.654, confidence = 3.325\n"
     ]
    }
   ],
   "source": [
    "q05 = np.percentile(x, 5)\n",
    "q95 = np.percentile(x, 95)\n",
    "confidence = q95 - q05\n",
    "summary = '5th = {:0.3f}, 95th = {:0.3f}, confidence = {:0.3f}'.format(q05, q95, confidence)\n",
    "print(summary)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.5 Spread, Inter-Quartile Range (IQR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "25th = -0.681, 85th = 0.672, IQR = 1.354\n"
     ]
    }
   ],
   "source": [
    "q25 = np.percentile(x, 25)\n",
    "q75 = np.percentile(x, 75)\n",
    "IQR = q75 - q25\n",
    "summary = '25th = {:0.3f}, 85th = {:0.3f}, IQR = {:0.3f}'.format(q25, q75, IQR)\n",
    "print(summary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gtEyTAADmZj3TKqwcxDQZGQYAYLSMDLNua/2/eQ9VADAPfv/wcowMAwAwWsIwAACjdUHT\nJKrq5iS/nuSSJHd1951TqYq58DUSAJgGODbrHhmuqkuS/LskP53kuiTvq6rrplUYAADM2oVMk3hb\nkj/t7q9393NJfjvJnumUBQAAs3ch0yRen+Rb51w/meTvnN+oqvYl2TdcPltVj1/AZ67HjyT5sw3+\nzK1On62N/lqb2ffX5XnNh37oQ5fM9DM20l/mNbks3553GVPxYl54x/ffMev/Fv8m106frY3+Wpt5\n9dffnqTRzJdW6+4DSQ7M+nNWUlVHu3txXp+/FemztdFfa6O/1q6qjvZz+mxS/o6tnT5bG/21Npu9\nvy5kmsRTSd5wzvXVwz0AANgSLiQMfzHJjqp6Y1W9Isl7k9w3nbIAAGD21j1Norufr6pfTPIHWVpa\n7RPd/djUKpueuU3R2ML02dror7XRX2unz9ZGf62dPlsb/bU2m7q/qrvnXQMAAMyFHegAABgtYRgA\ngNEaVRiuqg9XVVfVj8y7ls2sqv5VVX2lqo5V1eeq6m/Nu6bNrqo+VlVfG/rt3qp67bxr2syq6h9X\n1WNV9WJVbdrlduatqm6uqser6k+rav+869nsquoTVXWmqh6ddy1bQVW9oarur6qvDv8ePzjvmjaz\nqrq8qv6oqr489NevzLumraKqLqmqL1XVZ+Zdy3JGE4ar6g1JfirJN+ddyxbwse7+8e7emeQzSf7l\nvAvaAg4nub67fzzJnyS5Y871bHaPJvlHST4/70I2K1ver8snk9w87yK2kOeTfLi7r0tyQ5IP+Dv2\nsn6Q5J3d/ZYkO5PcXFU3zLmmreKDSY7Pu4iVjCYMJ/m3SX4piScGV9Hd5+4OdUX02aq6+3Pd/fxw\n+WCW1t1mBd19vLs3ejfKrcaW92vU3Z9P8ufzrmOr6O6T3f3IcP6dLIWV18+3qs2rlzw7XF42/PH7\ncRVVdXWSdyW5a961rGQUYbiq9iR5qru/PO9atoqq+tdV9a0kPxsjw2v1C0n+27yLYMtbbst7QYWZ\nqKprk7w1yUPzrWRzG77uP5bkTJLD3a2/VvdrWRqMfHHehaxk5tsxb5Sq+sMkr1vmpY8k+eUsTZFg\n8HL91d2HuvsjST5SVXck+cUkH93QAjeh1fpsaPORLH31ePdG1rYZTdJfwPxV1auS/H6S28/7ZpDz\ndPcLSXYOz4XcW1XXd7c56iuoqncnOdPdD1fVrnnXs5KLJgx3943L3a+qH0vyxiRfrqpk6evrR6rq\nbd19agNL3FRW6q9l3J3kv0YYXrXPquqfJHl3kt1tAe+1/B1jeba8Z+aq6rIsBeG7u/vT865nq+ju\nZ6rq/izNUReGV/b2JO+pqp9JcnmS11TVb3X3++dc119z0U+T6O4/7u4f7e5ru/vaLH3V+BNjDsKr\nqaod51zuSfK1edWyVVTVzVn6Gug93f29edfDRcGW98xULY0QfTzJ8e7+1XnXs9lV1cJLKwVV1SuT\n3BS/H19Wd9/R3VcP+eu9Sf77ZgvCyQjCMOtyZ1U9WlVfydL0EsvtrO43krw6yeFhSbr/MO+CNrOq\n+odV9WSSv5vkv1TVH8y7ps1meCDzpS3vjye5Z5Nueb9pVNWnknwhyZuq6smqum3eNW1yb0/yc0ne\nOfzcOjaM4LG87UnuH343fjFLc4Y35VJhrI3tmAEAGC0jwwAAjJYwDADAaAnDAACMljAMAMBoCcMA\nAIyWMAwAwGgJwwAAjNb/BZKou7MQvuIgAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117ba3cc0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.linspace(-4, +4, 51)\n",
    "plot_opts = dict(rwidth=0.8, color='black', alpha=0.25)\n",
    "\n",
    "fig, axis = plt.subplots(figsize=(12,4))\n",
    "count, bins, patches = axis.hist(x, bins, cumulative=False, **plot_opts)\n",
    "\n",
    "v25 = axis.axvline(q25, color='green')\n",
    "v75 = axis.axvline(q75, color='green')\n",
    "ylim = [0, 80]\n",
    "axis.set_ylim(ylim)\n",
    "fill = axis.fill_betweenx(ylim, q25, q75, alpha=0.25, color='green')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vR04tnDs8h9Ue26Q2DZd26XdPcgihCbgT+FyM8achhAnAdiACfw9MijG+58WO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\nH6vaarXI4rEiAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117814eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "q25 = np.percentile(x, 25)\n",
    "q50 = np.percentile(x, 50)\n",
    "q75 = np.percentile(x, 75)\n",
    "\n",
    "xs = np.sort(x)\n",
    "percentiles = np.linspace(0, 100, len(xs))\n",
    "\n",
    "fig, axis = plt.subplots(figsize=(12,4))\n",
    "axis.plot(xs, percentiles)\n",
    "\n",
    "axis.yaxis.set_major_locator(ticker.MultipleLocator(25))\n",
    "axis.yaxis.set_minor_locator(ticker.MultipleLocator(5))\n",
    "\n",
    "h25 = axis.axhline(25, color='green')\n",
    "h75 = axis.axhline(75, color='green')\n",
    "v25 = axis.axvline(q25, color='green')\n",
    "v75 = axis.axvline(q75, color='green')\n",
    "axis.fill_betweenx([25,75], q25, q75, alpha=0.25, color='green')\n",
    "axis.set_ylim([0,100])\n",
    "axis.grid(True, which='major')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6.6 Spread, Standard Devaition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* this assumes a model for the data\n",
    "* if the data is not guassian, this won't always \"line up\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean = -0.029, std = 1.018\n"
     ]
    }
   ],
   "source": [
    "x_mean = np.mean(x) \n",
    "x_std = np.std(x)\n",
    "\n",
    "summary = 'mean = {:0.3f}, std = {:0.3f}'.format(x_mean, x_std)\n",
    "print(summary)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0, 100)"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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d7GqPzJqQ4OwZKc48PkVdlRfkSZIGJ0OypF677Y8FdrVHPnhJljlT/ViRJA1+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\n6SD/H60PcrRF39fVAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117ca31d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "left   = x_mean - x_std\n",
    "center = x_mean\n",
    "right  = x_mean + x_std\n",
    "\n",
    "xs = np.sort(x)\n",
    "percentiles = np.linspace(0, 100, len(xs))\n",
    "\n",
    "fig, axis = plt.subplots(figsize=(12,4))\n",
    "axis.plot(xs, percentiles)\n",
    "\n",
    "pl = 50-34.1\n",
    "pc = 50\n",
    "pr = 50+34.1\n",
    "\n",
    "\n",
    "axis.yaxis.set_major_locator(ticker.MultipleLocator(25))\n",
    "axis.yaxis.set_minor_locator(ticker.MultipleLocator(5))\n",
    "\n",
    "hl = axis.axhline(pl, color='green')\n",
    "hc = axis.axhline(pc, color='red')\n",
    "hr = axis.axhline(pr, color='green')\n",
    "\n",
    "vl = axis.axvline(left, color='green')\n",
    "vc = axis.axvline(center, color='red')\n",
    "vr = axis.axvline(right, color='green')\n",
    "axis.fill_betweenx([pl, pr], left, right, alpha=0.25, color='green')\n",
    "axis.set_ylim([0,100])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 7. Summarizing the Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.1 Box-and-Whisker Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAD8CAYAAABjAo9vAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nHQCSIewAkAxhB4BkCDsAJEPYASCZ/wcqmVEl7LWbFgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117d18dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = load_data_norm(1000)\n",
    "\n",
    "box_dict = plt.boxplot(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'boxes': [<matplotlib.lines.Line2D at 0x117fc7cf8>],\n",
       " 'caps': [<matplotlib.lines.Line2D at 0x117f25898>,\n",
       "  <matplotlib.lines.Line2D at 0x1181a51d0>],\n",
       " 'fliers': [<matplotlib.lines.Line2D at 0x117b58dd8>],\n",
       " 'means': [],\n",
       " 'medians': [<matplotlib.lines.Line2D at 0x1181a55f8>],\n",
       " 'whiskers': [<matplotlib.lines.Line2D at 0x117fc7a20>,\n",
       "  <matplotlib.lines.Line2D at 0x117f25908>]}"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "box_dict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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oIYiICKCEICIikSDzEMqVmcW67wIrdoiIlJwSwhXQB7gkWaFfWArdr5r/36v1y58SggRT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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117c60438>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "data_list = []\n",
    "for n in range(4):\n",
    "    x = load_data_norm(1000)\n",
    "    data_list.append( x )\n",
    "\n",
    "fig, ax  = plt.subplots()\n",
    "box_dict = ax.boxplot(data_list)\n",
    "xlabels  = ax.set_xticklabels(['Sample1', 'Sample2', 'Sample3', 'Sample4'])\n",
    "ylabel   = ax.set_ylabel('X Values')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.2 Kernel Density Estimation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* If you do NOT want a parametric model of a distribution of data...\n",
    "* The shape of the distribution can be estimated without assumptions about a general form"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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F05wlKzmWWy/L4ddvN9hJ3jDh13r8Jvz9/LU6clJiWb/CpnCGiyfeCtwRek5K\nHKdOD/NcZZMt0R0G7IjfsL2unTfr2vnCdYV2T10zruKsJHJSYnn8jaN2W8YwYL/lEU5V+cmLh8hO\njuXjq2wKpxmfiHBdcRY1J3v446FWp8sxU2TBH+G21rax41gH968tJi7a7XQ5JogtK0glNyWOX7xe\n53QpZor8Cn4RuU1EakSkVkQeGGe/iMg/ePfvFZErfPYdE5F9IrJHRCoCWbyZGlXlRy8eIi8tnruu\nsnFbc3FRLhefWT2fbUfa2d/Y5XQ5ZgomDH4RcQOPAOuAMuAeESk7p9k6oMT7sQH453P236SqK1S1\nfOolm0B54UAzlfWdfGltMbFRdrRvJnbPyrkkxUbxyKu1TpdipsCfI/6rgVpVrVPVIeApYP05bdYD\n/6pjtgNpIjI7wLWaAOofGuXB31VRmpvMh660Wysa/6TERfPZNQv4/f5m9jZ0Ol2OuUT+BH8eUO/z\nvMG7zd82CrwsIrtEZMOlFmoC69HXjtDY2c//+MBlRLntVI/x3xeuW8CshGh++EKN06WYSzQTv/Fr\nVHUFY8NB94nI9eM1EpENIlIhIhWtrTZrYDrVd5zmn187wvuXz2FVYYbT5ZgQkxwXzX03FfPG4Ta2\n1bY5XY65BP4EfyPge+Yv37vNrzaqeuZzC7CRsaGj86jqY6parqrlWVm2ZMB0UVW+++x+3CJ86/ZS\np8sxIerjq+YxJzWOH7xQY3foCkH+BP9OoEREFohIDHA3sOmcNpuAT3pn96wCulT1hIgkikgygIgk\nArcC+wNYv5mkJ3fU82pNK39z2yJmp8Y7XY4JUXHRbr526yIq6zt5Zlf9xB1MUJkw+FV1BLgfeAGo\nAp5W1QMicq+I3OttthmoA2qBXwBf9G7PAbaKSCWwA3heVf8Q4O/B+Omd9j4eev4gq4sz+NQ1850u\nx4S4v7wij6sXpPN3m6tp6x10uhwzCX6t1aOqmxkLd99tj/o8VuC+cfrVAcunWKMJgOFRD199uhK3\nS/jhh5bjctlCbGZqRIS/u3Mp6376Og/97iAP33250yUZP9l0jgjx0O8OsuudUzx0xxLmpNkQjwmM\n4uwk/uuNxfx2TxOv1rQ4XY7xkwV/BHjireP86s13+MJ1C2z1TRNwX7yxiEU5yXz96UpOdg84XY7x\ngwV/mPtTbRvffXY/Ny7K4oF1i50ux4ShuGg3j3zsck4PjfLlJ3czMupxuiQzAQv+MLbtSBuf+9VO\nCrMS+YeQ6LflAAAKcklEQVR7Lsdt4/pmmhRnJ/PQHUt462gHD7982OlyzATsRixhalttG5/91U7m\npifwxBdWkRIX7XRJJsx98Mp8dhzt4B9frSV/Vjx3Xz3X6ZLMBVjwB4FA3ikJoOJYB89WNpGRGMOH\nrizgxQMnA/r6xlzIQ3cuobl7gG9t3EdGUiy3lOU4XZIZhw31hJGRUQ+bKpv4ze5GFmQmsuH6QpJi\n7f92M3Oi3S7+6WNXsDQvlfufeNtm+gQpC/4wcbzjNP/4ai3b69pZU5zJp66ZT0KMhb6ZeYmxUfzL\nZ66mODuJL/yqgl/vanC6JHMOC/4Q190/zG/3NPLz144wOOLhU9fM4/als+1ErnFUemIMT21YxcrC\ndL72TCUPv3yIUVvTJ2jYIWGIOnV6iDePtLO9rh2PKisLM7i1LMdun2iCRnJcNL/89FV889f7ePjl\nw7xV18HDd68gJyXO6dIingV/CBnxeDh8speKd05RfaIbgBUFady8OIf0xBiHqzPmfLFRbn78keWs\nKsrgvz97gPc+/Dp//d5F3H3VXPur1EEW/EFuYHiU2pZeak72cLCpm/7hURJj3NywMIurF6STlmCB\nb4KbiPCR8gKumDuLb2/cx7c37ueJt47z9fcu4saFWYjYfwAzzcb4g8C3Nu5797Gq0tI9wBuHW3n8\njToeev4gT+w4zoGmLhblJvOpa+bxwLrF3HpZ7nmh7/s6ga5rvG1nHp/b7lsb91203Xj9zn3s2+ZC\nr3Xux8X6X0rbieoZ7/O5fS+2fby+F3ofz30Nf/Zd6Hvwx4X+bS/V/Aeepzg7iac2rOJn91zOqb4h\nPvMvO1n30zd4pqKe3sGRgHydc7+mGZ8d8QeJ6uZuapp7OHSyh1OnhwHITYljTXEWi3KTmZueYH8a\nm5AnIrx/+Rzee1kumyqb+PlrR/jr/9zLf3t2P7eW5XLz4mzWFGeSkRTrdKlhzYLfIcfbT/NqTcu7\n85z/9c13iHG7KMpO4oaF2SzMSbJhHBN0pnKx4Xh9P33tfI53nGZ3fScvV51kU2UTAmQlx5I/K4E5\naXFkJMaQnhjLrIRouz90gFjwz5ChEQ87j3XwavVY2B9p7QOgMDMRgM+sns+CjET7wTYRRUSYl5HI\nvIxEPrB8Dk2d/Rxu6eV4+2lqmrt5+/ipP7cFUuOjSUuIISU+ipS4aFLiokiOj/7z47hoYqLsd2gi\nFvzTqLlrgD/WtPBKdQt/qm2jb2iUmCgXqwoz+Piqedy0KJv5mYnMf+B5SrKTnS7XGEe5RMiflUD+\nrARg7HxX7+AIHX1DtPcN0eH96Dw9TOOpfqoGuhkePf/agLhoF8netam++h97yE9PoCQ7iZKcJBZk\nJhIbZVOeLfgDaGTUw+76Tu9RfStV3imXeWnx3HF5HmtLs7mmKMOuqDXGDyJCclw0yXHRzMtIPG+/\nqjIw7KF7YJiegZGxz/3DdHsft/YMsr2uneY9jZy5dsztEualJ1A2J4Xl+Wksy09lSV4qiRG2tElk\nfbcBpqocbetj25F23qxrZ+vhNrr6h3G7hPJ5s/jmulJuKs2mJDvJpqwZE2AiQnyMm/gYNzkp5+//\n1sZ9bPvmzQwMj3K0rY9DJ3uobenl0Mkedh/v5Hd7TwDgEijJTmZZfirLCtJYnp/KotzksP7LwK/g\nF5HbgJ8CbuBxVf3+OfvFu/924DTwaVV925++oWRoxENNcw97GzvZdewU24600+y941BuShy3lOWw\ntjSbNSWZtgyyMUEiLtrN4tkpLJ599v8OrT2D7GvsZE99F3sbOtlS3cIz3nWFot1CaW4KS/JSWZaf\nytK8VBbmJIfN+YMJg19E3MAjwC1AA7BTRDap6kGfZuuAEu/HSuCfgZV+9g06w6MeGk71c6ytj6Nt\nfdS29rK/sYvqEz0Mee8ulJEYw6qiDK4tyuDaokzmZyTYUb0xISQrOZa1pTmsLR1bOlpVaTjVz77G\nLvY2dLG/sYvn9zbx5I6x2UgxbhcLc5MoykqiMDOJouxECjOTmJeREHJDRf5UezVQq6p1ACLyFLAe\n8A3v9cC/qqoC20UkTURmA/P96Bswp4dGGB5VRkY9jHh07GPUM7bN42Fg2EPf4Ai9gyP0eT/a+4Zo\n6x2krWfsc0vPII2d/WctKJUcF8XSvFQ+s2Y+y/LGxgXzZ8Vb0BsTRkSEgvQECtITuH3pbGDsP4Pj\nHafZ19jFvoYuDp7opuLYKTZVNqE+55WTY6PISY0jNyWO3NQ40hNjSI2PJiU+euxzXBRx0W5iolzE\nuF3ERrmIjfI+j3LhdgkuGTsHMRPnAP35CnlAvc/zBsaO6idqk+dn34C54sGXGBie/P0+0xKiyUqK\nJTMplhUFaXxg+Zyx2TYZCczPTCQjMcZC3pgI5Dvd9H3L5ry7/cx5gyOtvTSc6qe5a2Dso3uArYfb\nOHV6iMGRyWdRZlIMFd+5JZDfwrhE9eJLpYrIh4DbVPXz3uefAFaq6v0+bX4HfF9Vt3qfbwG+wdgR\n/0X7+rzGBmCD9+kioGZq39oFZQJt0/Taocrek7PZ+3E+e0/OF2zvyTxVzfKnoT9H/I1Agc/zfO82\nf9pE+9EXAFV9DHjMj3qmREQqVLV8ur9OKLH35Gz2fpzP3pPzhfJ74s8p6p1AiYgsEJEY4G5g0zlt\nNgGflDGrgC5VPeFnX2OMMTNowiN+VR0RkfuBFxibkvlLVT0gIvd69z8KbGZsKmctY9M5P3OxvtPy\nnRhjjPGLX6ePVXUzY+Huu+1Rn8cK3OdvX4dN+3BSCLL35Gz2fpzP3pPzhex7MuHJXWOMMeElPC5D\nM8YY47eIDX4R+ZqIqIhkOl2L00TkhyJSLSJ7RWSjiKQ5XZNTROQ2EakRkVoRecDpepwmIgUi8qqI\nHBSRAyLyFadrChYi4haR3d7p7CElIoNfRAqAW4FLv6tEeHkJWKKqy4BDwDcdrscRPkuMrAPKgHtE\npMzZqhw3AnxNVcuAVcB99p686ytAldNFXIqIDH7g74G/AewEB6CqL6rqmZuebmfseotI9O7yJKo6\nBJxZYiRiqeqJMwsuqmoPY0GX52xVzhORfOAvgMedruVSRFzwi8h6oFFVK52uJUh9Fvi900U45EJL\njxhAROYDlwNvOVtJUHiYsYPHya/LEARCa0k5P4nIy0DuOLu+DXyLsWGeiHKx90RVn/W2+TZjf9r/\n+0zWZoKfiCQBvwb+SlW7na7HSSLyPqBFVXeJyI1O13MpwjL4VfU9420XkaXAAqDSu+haPvC2iFyt\nqs0zWOKMu9B7coaIfBp4H3CzRu4cX3+WJ4k4IhLNWOj/u6r+xul6gsBq4AMicjsQB6SIyL+p6scd\nrstvET2PX0SOAeWqGkwLLc04781yfgLcoKqtTtfjFBGJYuzk9s2MBf5O4KORfLW59yZLvwI6VPWv\nnK4n2HiP+L+uqu9zupbJiLgxfjOufwSSgZdEZI+IPDpRh3DkPcF9ZomRKuDpSA59r9XAJ4C13p+N\nPd4jXRPCIvqI3xhjIpEd8RtjTISx4DfGmAhjwW+MMRHGgt8YYyKMBb8xxkQYC35jjIkwFvzGGBNh\nLPiNMSbC/H+drfGCtzpGagAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1180243c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = load_data_norm(100)\n",
    "axis = sns.distplot(x, kde=True, rug=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7.3 Violin Plots (combined: boxplot + kde)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* boxplot summarizes quantiles\n",
    "* kernel density estimation, non-parametric"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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qUzkg4XCYF154gaeefpramhrS+b2J9JtIOq+n09FEuhRXpJZA5fu467ZRVFTM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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1186810b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = load_data_norm(1000)\n",
    "fig, axis = plt.subplots(figsize=(8,4))\n",
    "axis = sns.violinplot(x, ax=axis)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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x0y03MXr0aBRF4cv536td0sUxWiAspuZnIi5MTk4O7733Lhs2bKRhpI9Hryin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\nhRBCoyTghRBCoyTghRBCo/4f0Dq9l6JqRAkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1186fdcf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "sns.set_style(\"whitegrid\")\n",
    "tips = sns.load_dataset(\"tips\")\n",
    "ax = sns.violinplot(x=\"time\", y=\"tip\", data=tips,\n",
    "                     order=[\"Dinner\", \"Lunch\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 8. Modeling Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.1 Transition from Descriptive to Inferential"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* we almost never have \"all the data\"\n",
    "* we have a subset, a \"sample\" of the total data, the \"population\"\n",
    "* \"Inference\" is just asking \"what can the sample tell us about the population\"?\n",
    "* This can be seen as a modeling problem: select the sample as a model for the population, and then bootstrap resample to estimate the (center and spread of the) distribution of a population parameter."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.2 Modeling the Distribution (single variable)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Steps in modeling:\n",
    "1. Pick a general model (with unknown parameters) that you like (people often pick a gaussian, but doesn't have to be)\n",
    "2. Find the optimal parameters to plug in that make a specific model that best fits the data\n",
    "3. Determine the uncertainty or variation in the parameter value, e.g. by repeating 1 & 2 for another measurement of the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# get data\n",
    "x = load_data_norm(1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8.3 Example: Find the best parameters (mu, sigma) to use in a parametric model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# use an optimization method to find the model parameters that best fit the data\n",
    "from scipy.stats import norm\n",
    "(mu, sigma) = norm.fit(x)\n",
    "\n",
    "# predict values for the model using these paramters\n",
    "bins = np.linspace(-4, +4, 51)\n",
    "model = norm.pdf(bins, mu, sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PB6yu8Acg9nYVCnnicUNVnToBXbtKG/fvlycYIidi4iVqCdvebkSEOFSGmk6h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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118753358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the model and the data together\n",
    "fig, axis = plt.subplots(figsize=(8,4))\n",
    "data_opts = dict(rwidth=0.8, color='black', alpha=0.25)\n",
    "model_opts = dict(linewidth=4, color='red', alpha=0.5, linestyle='-', )\n",
    "\n",
    "count, bins, patches = axis.hist(x, bins, normed=True, cumulative=False, label='data', **data_opts)\n",
    "line = axis.plot(bins, model, label='model', **model_opts)\n",
    "axis.legend()\n",
    "title = axis.set_title('Guassian model, mu = {:0.3f}, sigma = {:0.3f}'.format(mu, sigma))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1lnl4eOgeR0REICIiosG4Z8cQ0pSiqxehevwQA0cYz02gn4dAKMSgEUE4k/YTHjx4gM6d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\nISaCCp0QQkwEFTohhJgIKnRCCDER/x9JmmrjZR0e8QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118024ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "import seaborn as sns\n",
    "\n",
    "x = load_data_norm(1000)\n",
    "ax = sns.distplot(x, fit=norm, kde=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 9. Models and Parameter Estimation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* The goal is to \"estimate\" parameters of a model that fits the data\n",
    "* Part of that is asking what is the \"optimal\" value of the parameter (center)\n",
    "* Part of that is asking how uncertain is the parameter estimate (spread)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 9.1 Method of Moments"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* You've probably already done this before and maybe didn't realize it.\n",
    "* \"The moments of the sample and equal to the moments of the model\" (usually mean and standard deviation)\n",
    "* Find the model parameters so that the sample moments match the model moments.\n",
    "    * e.g. For a gaussian distribution, the moments are the same as the model parameters:\n",
    "        * `mean = param1, std=param2`\n",
    "    * e.g. For a gamma distribution, the moments are **NOT** the same as the parameters:\n",
    "        * `mean = param1*param2`, `var = param1*(param2**2)`\n",
    "* first moment = compute the mean of the sample and assume that is equal to the population parameter mu\n",
    "* second moment = compute the standard deviation of the sample and assume that is equal to the population parameter sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "x = load_data_norm(100)\n",
    "mu = np.mean(x)\n",
    "sigma = np.std(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CocDdd9/tjLiJ5HdjliGFyWQuEgoFCkaOdK/ey/VU0rEj8mNipNG5KhkMwP/+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\nH6WAbk2ig4OwAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118f660f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.linspace(-4, +4, 51)\n",
    "model = norm.pdf(bins, mu, sigma)\n",
    "\n",
    "fig, axis = plt.subplots(figsize=(8,4))\n",
    "data_opts = dict(rwidth=0.8, color='black', alpha=0.25)\n",
    "model_opts = dict(linewidth=4, color='red', alpha=0.5, linestyle='-', )\n",
    "\n",
    "count, bins, patches = axis.hist(x, bins, normed=True, cumulative=False, label='data', **data_opts)\n",
    "line = axis.plot(bins, model, label='model', **model_opts)\n",
    "axis.legend()\n",
    "title = axis.set_title('Guassian model, mu = {:0.3f}, sigma = {:0.3f}'.format(mu, sigma))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 9.2 Method of Maximum Likelihood"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Easy to do computationally, hard or impossible to do analytically\n",
    "* Pick a parameterized distribution (e.g. guassian, gamma, poisson, whatever)\n",
    "* guess at a range of values for the model parameters\n",
    "* For each value in the range, take many samples, compute the likelihood for each sample\n",
    "* \"Given these data, how likely is this model with this parameter value?\"\n",
    "* Likelihood(param): compute product of model(param, sample) over all samples\n",
    "* alternate: LogLikelihood(param): compute sum of log(model(param, sample)) over all samples\n",
    "* Repeat for all param values\n",
    "* Pick the param that reulted in the maximum likelihood"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 10. Parameter Variation and \"Uncertainty of the Estimate\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10.1 Sampling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Population (noun) = all the data, the \"underlying\" data, nature\n",
    "* Sample (noun) = a datum or a small portion taken from the population, a data set collected during a measurement\n",
    "* Sample (verb) = take act of taking a sample from the population at random\n",
    "* Statistic (noun) = a summary value computed from a sample or sample distribution (e.g. mean, std, slope) often used as an approximation of a parameter in a model for the population distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10.2 Resampling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Resample (verb) = sample again and again\n",
    "* Resample with Replacement = sample again and again, but \"replace\" or \"put back\" the thing you took out so that it might be drawn again on future draws.\n",
    "* Bootstrap Resampling = assume the sample is a model for the population and resample with replacement from the sample to generate many samples.\n",
    "* Resampling with Shuffling = computational method to test hull hypothesis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10.3 Sample Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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r4nQJYCY6dOiQli9frs2bN6e6lQE7f/68Fi5cqD/++EOhUEizZs3SY489luq2BuTChQta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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1190d6f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "population = load_data_norm(1000)\n",
    "bins = np.linspace(-4, +4, 51)\n",
    "\n",
    "fig, axis = plt.subplots(figsize=(8,4))\n",
    "opts_pop = dict(rwidth=0.8, color='green', alpha=0.25)\n",
    "count, bins, patches = axis.hist(population, bins, normed=True, cumulative=False, label='data', **opts_pop)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sample1 = np.random.choice(population, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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mcTMWmOQYvPX19RoYGJizrKmp6ZL1Dhw4ULquAACoUdxAAwAAgwheAAAM4ksSAMAB70dA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\nm38CPcUPBbYAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1187caba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.linspace(-4, +4, 51)\n",
    "\n",
    "fig, axis = plt.subplots(figsize=(8,4))\n",
    "opts_pop = dict(rwidth=0.8, color='green', alpha=0.25)\n",
    "opts_s1  = dict(rwidth=0.8, color='red', alpha=0.25)\n",
    "count, bins, patches = axis.hist(population, bins, normed=True, cumulative=False, label='data', **opts_pop)\n",
    "count, bins, patches = axis.hist(sample1, bins, normed=True, cumulative=False, label='data', **opts_s1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10.4 Sampling Variance"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Because you are RANDOMLY drawing, each sample will differ from another, due to random chance. So any satistics computed from a sample will vary from sample to sample."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sample2 = np.random.choice(population, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XudFLYe+8Atxkpfy1Te5lbOnZPPuf2/iFdeY6bleDZVlT3pPxjhVsty80Pt0abXuYzh09\nNqZoNHpxLxdqzDNFpT69eO5XpmL2EgqF8o7Znmr2+XwaGhqSJIXDYTU0NEwZb29v19mzZ7Vnz57s\nKWcAAJCb7RFvc3OzhoeHFQwGlclk1N3drb6+PiUSCV1zzTV65pln9NGPflQbNmyQJLW2tqq5ubnk\nhQMAUI1sg9fhcKizs3PKsvr6+uzPf/7zn4tfFVAsg4O5lzc1mayirAbDi3Iuv4R+BUBF4QO3AAAY\nRPACAGAQwQsAgEEELwAABhG8AAAYRPACAGAQwQsAgEEELwAABhG8AAAYRPACAGAQwQsAgEEELwAA\nBhG8AAAYRPACAGAQwQsAgEEELwAABrnKXQAqWKVfRD5ffVK2RtuLwOeYozYalbzeuVSGGch3H0kz\neKiFw3kmaJzYx67c402bGt8uYjD/3NMoIt/8k/cxeRfRaK3GxqY9PeYZjngBADCI4AUAwCCCFwAA\ng2yDN51Oq729XYFAQOvXr1c0Gr1onf/+978KBoM6efJkSYoEAGC+sA3e/v5+pVIp9fb2qq2tTT09\nPVPG//jHP2rdunX6+9//XrIiAQCYL2yDNxQKye/3S5IaGxsViUSmjKdSKe3evVvLli0rTYUAAMwj\nth8nisVi8ng82dtOp1Pj4+NyuSY2Xb58+bR2ZFnWLEucKplMFm2ucqv0XmpzvKwgSYkcNZeil2i0\nNu+YZSXy1if9v8bR0dE820+M55ojlUplx+22n+34hXXmOm5XQzKZ1Ojo2Ky3LzQ+3RqL0WNtNKpU\nKnXRS13TvZ9n8zh45z4KmU4Pkx/Pk3uxrITt/JWs0v+OzYSpXmyD1+PxKB6PZ2+n0+ls6M6Et0if\ni7Qsq2hzlVvF9zKW+w92rs+4lqKXfLvPlmC7gjS29GyeYW/enUSjUV09ze1nO35hnbmO29VgWZaW\nLl066+0LjU+3xmL0qLExRaNR1dXVvXOFgjVOt8fpPJYKmdb9NGkXk3up5D8B01Hxf8dmoJi9hEKh\nvGO2p5p9Pp+GhoYkSeFwWA0NDUUpCgCAS5HtoWtzc7OGh4cVDAaVyWTU3d2tvr4+JRIJBQIBEzUC\nADBv2Aavw+FQZ2fnlGX19fUXrXfo0KHiVQUAwDzFF2gAAGAQwQsAgEEELwAABhG8AAAYRPACAGDQ\nzL8JA5Iq/xrxtuZ44e+ilGB38fB8FzeXshc4x6VhMLxIo6NJnTqzaMryqnm+SVMezwtGR6UzZyZu\nTPOxnO/50rTp7e1t/ihVwFMeb+OIFwAAgwheAAAMIngBADCI4AUAwCCCFwAAgwheAAAMIngBADCI\n4AUAwCCCFwAAgwheAAAMIngBADCI4AUAwCCCFwAAg2yDN51Oq729XYFAQOvXr1c0Gp0yfvToUa1Z\ns0aBQEBPPfVUyQoFAGA+sA3e/v5+pVIp9fb2qq2tTT09Pdmxc+fOadu2bdq/f78OHTqk3t5evf76\n6yUtGACAamYbvKFQSH6/X5LU2NioSCSSHTt58qSuuuoqvfe975Xb7dby5cv1u9/9rnTVAgBQ5Woy\nmUym0Arf+ta3tGrVKq1cuVKS1NTUpP7+frlcLh0/flyPP/64du3aJUn69re/rSuvvFJf+MIXpswR\nCoVKVD4AAJVp+fLlOZe77Db0eDyKx+PZ2+l0Wi6XK+dYPB7X5ZdfPu2dAwBwqbE91ezz+TQ0NCRJ\nCofDamhoyI7V19crGo3q3//+t1KplI4fP67rr7++dNUCAFDlbE81p9NpdXR06MSJE8pkMuru7tYr\nr7yiRCKhQCCgo0ePavfu3cpkMlqzZo3WrVtnqnYAAKqObfBWqpMnT2rt2rX69a9/rQULFpS7nFlJ\nJBJqa2vTW2+9pXe9613avn27rrjiinKXNSv/+c9/dPfddysWi+ncuXO69957q/7sx5EjR/TCCy9o\n586d5S5lRi78szwyMiK3262uri7V1dWVu6w5efnll7Vjxw4dOnSo3KXM2rlz57Rlyxa99tprSqVS\nuvPOO/XpT3+63GXNyvnz53Xffffp1KlTqqmp0f333z/lbGg1euONN3TLLbdo//79qq+vL+m+qvIL\nNGKxmLZv3y63213uUubkqaee0kc+8hE98cQTuvnmm/Xoo4+Wu6RZO3DggD72sY/p8ccf17Zt29TZ\n2Vnukuakq6tLO3fuVDqdLncpM1boI4DV6NFHH9V9992ns2fPlruUOXn++ee1aNEiPfnkk/rBD36g\nBx54oNwlzdrAwIAk6fDhw9q0aZMefvjhMlc0N+fOnVN7e7ve/e53G9lf1QVvJpPR1q1btXnzZi1c\nuLDc5czJHXfcoTvvvFOS9I9//EPvec97ylzR7N1xxx0KBoOSJv4brtazEBf4fD51dHSUu4xZKfQR\nwGp01VVX6ZFHHil3GXP22c9+VnfddZekib9jTqezzBXN3o033pj9x6Ha/3ZJ0vbt2xUMBvX+97/f\nyP5s39VcTk8//bQee+yxKcuuvPJKtbS06MMf/nCZqpqdXL10d3fr2muvVWtrq06cOKEDBw6UqbqZ\nKdTL6dOndffdd2vLli1lqm5m8vXS0tKiY8eOlamquYnFYvJ4PNnbTqdT4+Pj2U8jVJvPfOYzevXV\nV8tdxpxddtllkibun6997WvatGlTmSuaG5fLpXvuuUdHjhzRd77znXKXM2vPPvusFi9eLL/fr337\n9hnZZ9W9xtvc3KylS5dKmniX9bXXXqsnnniizFXN3cmTJ7Vx40b19/eXu5RZGxkZ0ebNm/WNb3wj\n+7nvanbs2DEdPny46k6jbdu2Tdddd51aWlokSZ/4xCeyn0yoVq+++qo2b95c9V9L+89//lNf+cpX\ndNttt+nWW28tdzlFcfr0aa1du1Y/+9nPVFtbW+5yZmzdunWqqalRTU2NLMvSBz/4Qe3du1dLliwp\n2T6r7l/gI0eOZH/+1Kc+pf3795exmrn5/ve/ryuuuEKrV6/WZZddVtWnnv7617/qrrvu0q5du6ru\nbMR84/P5NDAwoJaWlos+Aojyef311/WlL31J7e3tWrFiRbnLmZPnnntOY2Nj2rhxoxYuXKiamho5\nHFX3yqUkTTlwW79+vTo6OkoaulIVBu98smbNGt1zzz368Y9/rPPnz6u7u7vcJc3azp07lUql9OCD\nD0qa+HKVvXv3lrmqS1Nzc7OGh4cVDAazHwFE+X3ve9/TW2+9pT179mjPnj2SJt44ZuoNPcW0atUq\nffOb39S6des0Pj6uLVu2VGUf5VJ1p5oBAKhm1XluAACAKkXwAgBgEMELAIBBBC8AAAYRvAAAGETw\nAgBgEMELAIBBBC8AAAb9D9rVkZyGY40MAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1187baa58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.linspace(-4, +4, 51)\n",
    "\n",
    "fig, axis = plt.subplots(figsize=(8,4))\n",
    "opts_s1 = dict(rwidth=0.8, color='red', alpha=0.25)\n",
    "opts_s2  = dict(rwidth=0.8, color='blue', alpha=0.25)\n",
    "count, bins, patches = axis.hist(sample1, bins, normed=True, cumulative=False, label='data', **opts_s1)\n",
    "count, bins, patches = axis.hist(sample2, bins, normed=True, cumulative=False, label='data', **opts_s2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean1 = 0.054, std1 = 0.919\n",
      "mean2 = 0.006, std2 = 0.937\n"
     ]
    }
   ],
   "source": [
    "mean1 = np.mean(sample1)\n",
    "std1  = np.std(sample1)\n",
    "mean2 = np.mean(sample2)\n",
    "std2  = np.std(sample2)\n",
    "print(\"mean1 = {:0.3f}, std1 = {:0.3f}\".format(mean1, std1))\n",
    "print(\"mean2 = {:0.3f}, std2 = {:0.3f}\".format(mean2, std2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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tFqLk0Gw0ZzXExMiiqmYyZAj4+MCBgxpFccPVjTLdLLyUJF4hLkJJCWRnq7U/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\nQgjRiiTxCiGEEK3o/wNUDG14hr8ERwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118c949b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "# predict values for the model using these paramters\n",
    "bins = np.linspace(-4, +4, 51)\n",
    "model1 = norm.pdf(bins, mean1, std1)\n",
    "model2 = norm.pdf(bins, mean2, std2)\n",
    "\n",
    "fig, axis = plt.subplots(figsize=(8,4))\n",
    "opts_model1 = dict(linewidth=2, color='red', alpha=0.5)\n",
    "opts_model2 = dict(linewidth=2, color='blue', alpha=0.5)\n",
    "\n",
    "label1 = 'mean1={:0.3f}, std1={:0.3f}'.format(mean1, std1)\n",
    "label2 = 'mean2={:0.3f}, std2={:0.3f}'.format(mean2, std2)\n",
    "\n",
    "line1 = axis.plot(bins, model1, label=label1, **opts_model1)\n",
    "line2 = axis.plot(bins, model2, label=label2, **opts_model2)\n",
    "vl1 = axis.axvline(mean1, **opts_model1)\n",
    "vl2 = axis.axvline(mean2, **opts_model2)\n",
    "leg = axis.legend(loc=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10.5 Resampling from the Population"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x118181898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "population = load_data_norm(1000)\n",
    "bins = np.linspace(-4, +4, 51)\n",
    "\n",
    "fig, axis = plt.subplots(figsize=(8,4))\n",
    "opts_pop = dict(rwidth=0.8, color='green', alpha=0.25)\n",
    "count, bins, patches = axis.hist(population, bins, normed=True, cumulative=False, label='data', **opts_pop)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "pmean mean = 0.032, pmean std = 0.100\n",
      "pstd mean = 0.992, pstd std = 0.073\n"
     ]
    }
   ],
   "source": [
    "sample_means = np.zeros(1000)\n",
    "sample_stds = np.zeros(1000)\n",
    "for n in range(1000):\n",
    "    sample = np.random.choice(population, 100)\n",
    "    sample_means[n] = np.mean(sample)\n",
    "    sample_stds[n] = np.std(sample)\n",
    "\n",
    "mean_mean = np.mean(sample_means)\n",
    "mean_std = np.std(sample_means)\n",
    "std_mean = np.mean(sample_stds)\n",
    "std_std = np.std(sample_stds)\n",
    "print('pmean mean = {:0.3f}, pmean std = {:0.3f}'.format(mean_mean, mean_std))\n",
    "print('pstd mean = {:0.3f}, pstd std = {:0.3f}'.format(std_mean, std_std))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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QqJ511lnaunVrsmsBACCtMVMFAMAQQhUAAEP4mcJ+itumAYB5zFQBADCEUAUAwBAO/wJA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\nAgBgCKEKAIAhhCoAAIYQqgAAGPJ/u3gHULLPMPUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117f6ba58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.linspace(-0.3, +0.3, 51)\n",
    "fig, axis = plt.subplots(figsize=(8,4))\n",
    "opts_pop = dict(rwidth=0.8, color='black', alpha=0.25)\n",
    "count, bins, patches = axis.hist(sample_means, bins, normed=True, cumulative=False, label='sample means', **opts_pop)\n",
    "leg = axis.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 10.6 Spread of the Estimate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Confidence Interval = the width of the 90th percentile of the parameter resample distribution\n",
    "* Standard Error = the standard deviation of the parameter resample distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IoQoAgCGEKgAAhhCqAAAYQqgCAGAIoQoAgCF8Sw2yprW1Ne5yvjkEduO9CLswUgUAwBBC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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119172b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.linspace(1-0.3, 1+0.3, 51)\n",
    "fig, axis = plt.subplots(figsize=(8,4))\n",
    "opts_pop = dict(rwidth=0.8, color='black', alpha=0.25)\n",
    "count, bins, patches = axis.hist(sample_stds, bins, normed=True, cumulative=False, label='sample stds', **opts_pop)\n",
    "leg = axis.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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5/T/VadOm6a233pIknTx5UgkJCYNeFAAAocjry7897/49ffq0LMvSxo0bNWHCBH/VBwBA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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118e05668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.linspace(-1, +1, 51)\n",
    "\n",
    "fig, axis = plt.subplots(figsize=(8,4))\n",
    "opts_pop = dict(rwidth=0.8, color='black', alpha=0.25)\n",
    "count, bins, patches = axis.hist(sample_means, bins, normed=True, cumulative=False, label='sample means', **opts_pop)\n",
    "leg = axis.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 11. Modeling 2-variable Data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* at first glance, just another optimization problem\n",
    "* at closer inspection, it's parameter estimation again!\n",
    "* this time, there are 3 parameters:\n",
    "    * y = a0 + a1*x + e, parameters intercept=a0, slope=a1, spread=var(e)\n",
    "    * intercept\n",
    "    * slope\n",
    "    * variance of underlying randomness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PPaadO3f63a7EcJo94vQPILNNgGRKGWOMly9euHBBg4OD6u/vV29v77K/n5iYWDZbYqXK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\nwhoALEBYA4AFCGsAsMD/AFGUR7IzbgyPAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118dda6d8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y = load_data_line(npts=50)\n",
    "data_opts = dict(color='black', linestyle=' ', marker='o')\n",
    "line = plt.plot(x, y, **data_opts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def model_predict(x, a0, a1):\n",
    "    return a0 + a1*x"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 11.1 Tune the parameter values to make the model fit the data..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "xd, yd = load_data_line(npts=50)\n",
    "xm = xd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PA9vl/RlFJCxEXFjXO+T27oV77oGbboItWxyPt2oF8+aZDxnvuqtm9aGzHWEy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\nRURCgMJaRCQEKKxFRELA/wNiP5svhsFWvQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1187bae48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ym = model_predict(xm, a0=0.3, a1=0.9)\n",
    "\n",
    "fig, axis = plt.subplots()\n",
    "data_opts = dict(color='black', linestyle=' ', marker='o')\n",
    "model_opts = dict(color='red', linestyle='-', linewidth=4)\n",
    "\n",
    "ld = axis.plot(xd, yd, **data_opts)\n",
    "lm = axis.plot(xm, ym, **model_opts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 11.2 Linear Regression as Optimization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import optimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def sum_sqrs(theta, x, y):\n",
    "    model = theta[0] + theta[1]*x\n",
    "    data = y\n",
    "    residuals = model - data\n",
    "    rss = np.sum( residuals**2 )\n",
    "    return rss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "34.9225964518\n"
     ]
    }
   ],
   "source": [
    "x, y  = load_data_line()\n",
    "theta = [0, 1]\n",
    "rss = sum_sqrs(theta, x, y)\n",
    "print(rss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 28.545638\n",
      "         Iterations: 36\n",
      "         Function evaluations: 70\n",
      "0.025042275433 1.01070230882\n"
     ]
    }
   ],
   "source": [
    "x, y  = load_data_line()\n",
    "theta_guess = [0,1]\n",
    "a0, a1 = optimize.fmin(sum_sqrs, theta_guess, args=(x,y))\n",
    "print(a0, a1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "28.5456381462\n"
     ]
    }
   ],
   "source": [
    "theta = [a0, a1]\n",
    "rss = sum_sqrs(theta, x, y)\n",
    "print(rss)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def model_fit(x,y, cost_function=sum_sqrs):\n",
    "    theta_guess = [0,1]\n",
    "    a0, a1 = optimize.fmin(cost_function, theta_guess, args=(x,y))\n",
    "    return a0, a1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 26.047050\n",
      "         Iterations: 41\n",
      "         Function evaluations: 77\n",
      "-0.0513221759177 1.00928950881\n"
     ]
    }
   ],
   "source": [
    "x, y = load_data_line()\n",
    "a0, a1 = model_fit(x, y)\n",
    "print(a0, a1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def model_predict(x, a0, a1):\n",
    "    return a0 + (a1*x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MGdPmtSLiorCOU/4CMC8vz1V06eqrKQBSvK6rBX7WqxccOABDh/rc11+L3R9/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\nlu+tLgy5HAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118704240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "line_dots = plt.plot(x,y, linestyle=\" \", marker=\"o\", color=\"black\")\n",
    "line_red  = plt.plot(x, model_predict(x,a0,a1), color=\"red\", linewidth=4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_data_and_fit(xd, yd):\n",
    "    a0, a1 = model_fit(xd, yd)\n",
    "    rss = sum_sqrs([a0, a1], xd, yd)\n",
    "    fig, ax = plt.subplots()\n",
    "    ax.plot(x, y, linestyle=\" \", marker=\"o\", color=\"black\")\n",
    "    ax.plot(x, model_predict(x,a0,a1), color=\"red\", linewidth=4)\n",
    "    title_text=\"a0={:0.2f}, a1={:0.2f}: RSS = {:0.2f}\".format(a0, a1, rss)\n",
    "    fig.axes[0].set_title(title_text)\n",
    "    return fig, rss"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Optimization terminated successfully.\n",
      "         Current function value: 30.769160\n",
      "         Iterations: 46\n",
      "         Function evaluations: 86\n"
     ]
    },
    {
     "data": {
      "image/png": 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IslWrHGqr7JEo7CXrWQuPV2Y7cZ87B1OmwMaNmkH6Z2ACpnQ9srKIiIhwqKcs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\nvIAEayGE8AISrIUQwgtIsBZCCC/w/wHu061+NbQZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117f3eb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y = load_data_line()\n",
    "fig = plot_data_and_fit(x, y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 11.3 Linear Regression, Analytic Solution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* these is an exact analytic solution to the optimization problem for least-squares\n",
    "* using RSS as the cost function is equaivalent to finding the maximum likelihood estimator\n",
    "* we can implement the analytic solution in numpy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def load_data(num_pts=101, a0=-4, a1=2, mu=0, sigma=1):\n",
    "    x = np.linspace(0,10,num_pts)\n",
    "    e = np.array([np.random.normal(mu,sigma) for n in range(num_pts)])\n",
    "    y = a0 + (a1*x) + e\n",
    "    return x,y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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HMHmoQCgUYk02lR0DmzzN7uIVtUoPhVr4a1WGTE9Pq7bBmmwqJQY2eZrVxStqlR5qCsNf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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117ba3b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x, y = load_data()\n",
    "\n",
    "fig, axis = plt.subplots()\n",
    "opts_data  = dict(label='data', color='black', linestyle=\" \", marker=\"o\")\n",
    "line = axis.plot(x, y, **opts_data)\n",
    "leg = axis.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def model_predict(x, a0, a1):\n",
    "    return a1*x + a0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def model_fit(x, y):\n",
    "    X_bar = np.sum(x)/len(x)\n",
    "    Y_bar = np.sum(y)/len(y)\n",
    "    a1 = np.sum( (x - X_bar)*(y - Y_bar) )/np.sum( (x - X_bar)**2 )\n",
    "    a0 = Y_bar - (a1*X_bar)\n",
    "    return a1, a0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_model_and_data(xd, yd, xm, ym):\n",
    "    fig, axis = plt.subplots()\n",
    "    opts_data  = dict(label='data', color='black', linestyle=\" \", marker=\"o\")\n",
    "    opts_model = dict(label='model', color='red', linestyle=\"-\")\n",
    "    ld = axis.plot(xd, yd, **opts_data)\n",
    "    lm = axis.plot(xd, ym, **opts_model)\n",
    "    leg = axis.legend()\n",
    "    return fig"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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snDlhAsUjRmC+5RaOZGfzdVISfPABtGzp1ufb2yruzBpprYAveW8R6CRgi0pc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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x118c86400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xd, yd = load_data()\n",
    "\n",
    "a1, a0 = model_fit(xd, yd)\n",
    "xm = xd\n",
    "ym = model_predict(xm, a0, a1)\n",
    "\n",
    "fig = plot_model_and_data(xd, yd, xm, ym)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 11.4 Resampling to Visualize Uncertainty in Parameter Estimates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a1 mean = 1.992, a1 std = 0.118\n",
      "a0 mean = -3.910, a0 std = 0.687\n"
     ]
    }
   ],
   "source": [
    "def model_fit(x, y):\n",
    "    X_bar = np.sum(x)/len(x)\n",
    "    Y_bar = np.sum(y)/len(y)\n",
    "    a1 = np.sum( (x - X_bar)*(y - Y_bar) )/np.sum( (x - X_bar)**2 )\n",
    "    a0 = Y_bar - (a1*X_bar)\n",
    "    return a1, a0\n",
    "\n",
    "size_population = 1000\n",
    "size_sample = 10\n",
    "num_samples = 100\n",
    "\n",
    "xp, yp = load_data(size_population)\n",
    "ip = list(range(size_population))\n",
    "\n",
    "a1_bs = np.zeros(num_samples)\n",
    "a0_bs = np.zeros(num_samples)\n",
    "for n in range(num_samples):\n",
    "    isample = np.random.choice(ip, size_sample, replace=True)\n",
    "    xs = np.take(xp, isample, axis=0)\n",
    "    ys = np.take(yp, isample, axis=0)\n",
    "    a1s, a0s = model_fit(xs, ys)\n",
    "    a1_bs[n] = a1s\n",
    "    a0_bs[n] = a0s\n",
    "\n",
    "a1_mean = np.mean(a1_bs)\n",
    "a1_std  = np.std(a1_bs)\n",
    "a0_mean = np.mean(a0_bs)\n",
    "a0_std  = np.std(a0_bs)\n",
    "\n",
    "\n",
    "print('a1 mean = {:0.3f}, a1 std = {:0.3f}'.format(a1_mean, a1_std))\n",
    "print('a0 mean = {:0.3f}, a0 std = {:0.3f}'.format(a0_mean, a0_std))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.7222758334457471, 2.2528531446830433)"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a1_bs.min(), a1_bs.max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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V1NQkx3GUkpIS5XTxqb2Z1dfXa/jw4erXr59SU1N13333af/+/TFIGF+mTZuml156SdK/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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117ba6470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.linspace(a1_bs.min(), a1_bs.max(), 21)\n",
    "fig, axis = plt.subplots(figsize=(8,4))\n",
    "opts_pop = dict(rwidth=0.8, color='black', alpha=0.5)\n",
    "count, bins, patches = axis.hist(a1_bs, bins, normed=True, cumulative=False, label='a1_bs', **opts_pop)\n",
    "leg = axis.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+cAzerq4uRaNRdXZ2qrm5WR0dHYmxv//+W2vWrNGrr76qTZs2qbOzU7/++mtGCwYAIJc5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\nRQQvAAAWEbwAAFj0fxhPMibz+Om9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11875c7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bins = np.linspace(a0_bs.min(), a0_bs.max(), 21)\n",
    "fig, axis = plt.subplots(figsize=(8,4))\n",
    "opts_pop = dict(rwidth=0.8, color='black', alpha=0.5)\n",
    "count, bins, patches = axis.hist(a0_bs, bins, normed=True, cumulative=False, label='a0_bs', **opts_pop)\n",
    "leg = axis.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x117f3e3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes  = plt.subplots(ncols=2)\n",
    "box_dict = axes[0].boxplot(a0_bs)\n",
    "ylabel   = axes[0].set_ylabel('Intercept')\n",
    "box_dict = axes[1].boxplot(a1_bs)\n",
    "ylabel   = axes[1].set_ylabel('Slope')\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GK4oibG1tYWlpiScXKauD/OQkSZBlGVfY1F3S6XTYp7ZtG51OB7VaDUmSoN1uw3Vd3r9o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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11922f7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axis = plt.subplots()\n",
    "opts = dict(linestyle=\" \", marker=\"o\", alpha=0.005, color='black')\n",
    "xd, yd = load_data(100)\n",
    "for n in range(len(a1_bs)):\n",
    "    axis.plot(xd, model_predict(xd, a0_bs[n], a1_bs[n]), **opts)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 12. Linear  Regression in Practice"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12.1 Linear Regression with scipy.optimize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def model_predict(x, a0, a1):\n",
    "    return a1*x + a0\n",
    "\n",
    "def model_fit(x, y, model=model_predict):\n",
    "    param_opt, param_cov = optimize.curve_fit(model, x, y)\n",
    "    a0 = param_opt[0]\n",
    "    a1 = param_opt[1]\n",
    "    std_err = numpy.sqrt(numpy.diag(param_cov))\n",
    "    e0 = std_err[0]\n",
    "    e1 = std_err[1]\n",
    "    return a0, a1, e0, e1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BRouFbx5+mLOXXUbx22+zqEUL1k+eDDfdVKt2yPZYQrgmwVpU6tWCLVCri7u9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\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1193cd278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xd, yd = load_data()\n",
    "\n",
    "a0, a1, e0, e1 = model_fit(xd, yd, model_predict)\n",
    "\n",
    "xm = xd\n",
    "ym = model_predict(xd, a0, a1)\n",
    "\n",
    "fig = plot_model_and_data(xd, yd, xm, ym)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12.2 Linear Regression with statsmodels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/vestuto/anaconda/envs/jlab/lib/python3.6/site-packages/statsmodels/compat/pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
      "  from pandas.core import datetools\n"
     ]
    }
   ],
   "source": [
    "import statsmodels.api as sm\n",
    "\n",
    "def model_fit(x, y):\n",
    "    X_const   = sm.add_constant(x)\n",
    "    model     = sm.OLS(y, X_const)\n",
    "    model_fit = model.fit()\n",
    "    a0        = model_fit.params[0]\n",
    "    a1        = model_fit.params[1]\n",
    "    return a0, a1, model_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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OH5PJpOv6JpNJ9QaVC0qBehdUG1CxsbG6vwiUks/ZU65ipwyJCBGC9Gwc4FORI7OZOWYz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\nESL+DzDZzFUholB9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1193cd5f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xd, yd = load_data()\n",
    "\n",
    "a0, a1, mf = model_fit(xd, yd)\n",
    "\n",
    "xm = xd\n",
    "ym = model_predict(xm, a0, a1)\n",
    "\n",
    "fig = plot_model_and_data(xd, yd, xm, ym)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.971</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.971</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   3353.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 27 Mar 2018</td> <th>  Prob (F-statistic):</th> <td>3.64e-78</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>18:21:41</td>     <th>  Log-Likelihood:    </th> <td> -144.72</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   101</td>      <th>  AIC:               </th> <td>   293.4</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    99</td>      <th>  BIC:               </th> <td>   298.7</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</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>const</th> <td>   -4.1605</td> <td>    0.202</td> <td>  -20.564</td> <td> 0.000</td> <td>   -4.562</td> <td>   -3.759</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    2.0240</td> <td>    0.035</td> <td>   57.902</td> <td> 0.000</td> <td>    1.955</td> <td>    2.093</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 1.310</td> <th>  Durbin-Watson:     </th> <td>   2.141</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.519</td> <th>  Jarque-Bera (JB):  </th> <td>   1.368</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td>-0.215</td> <th>  Prob(JB):          </th> <td>   0.504</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.625</td> <th>  Cond. No.          </th> <td>    11.7</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.971\n",
       "Model:                            OLS   Adj. R-squared:                  0.971\n",
       "Method:                 Least Squares   F-statistic:                     3353.\n",
       "Date:                Tue, 27 Mar 2018   Prob (F-statistic):           3.64e-78\n",
       "Time:                        18:21:41   Log-Likelihood:                -144.72\n",
       "No. Observations:                 101   AIC:                             293.4\n",
       "Df Residuals:                      99   BIC:                             298.7\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "const         -4.1605      0.202    -20.564      0.000      -4.562      -3.759\n",
       "x1             2.0240      0.035     57.902      0.000       1.955       2.093\n",
       "==============================================================================\n",
       "Omnibus:                        1.310   Durbin-Watson:                   2.141\n",
       "Prob(Omnibus):                  0.519   Jarque-Bera (JB):                1.368\n",
       "Skew:                          -0.215   Prob(JB):                        0.504\n",
       "Kurtosis:                       2.625   Cond. No.                         11.7\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mf.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12.3 Linear Regression with statsmodels and pandas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import statsmodels.formula.api as smf\n",
    "import pandas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Tp7NjxQreN5mw+3gOmfMsRAD5PFnQj7mEzYnEeZvdu3fXfY61s4bzrUeBOmww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\nSGALIUSI+P+LcQLktgsK5QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x117fc07f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xd, yd = load_data()\n",
    "df = pandas.DataFrame(dict(x=xd, y=yd))\n",
    "xm = xd\n",
    "\n",
    "model = smf.ols(formula=\"y ~ x\", data=df).fit()\n",
    "ym = model.predict(df)\n",
    "\n",
    "fig = plot_model_and_data(xd, yd, xm, ym)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.966</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.966</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   2822.</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Tue, 27 Mar 2018</td> <th>  Prob (F-statistic):</th> <td>1.41e-74</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>18:21:42</td>     <th>  Log-Likelihood:    </th> <td> -150.42</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>   101</td>      <th>  AIC:               </th> <td>   304.8</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    99</td>      <th>  BIC:               </th> <td>   310.1</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</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>   -3.8390</td> <td>    0.214</td> <td>  -17.934</td> <td> 0.000</td> <td>   -4.264</td> <td>   -3.414</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x</th>         <td>    1.9647</td> <td>    0.037</td> <td>   53.122</td> <td> 0.000</td> <td>    1.891</td> <td>    2.038</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 0.036</td> <th>  Durbin-Watson:     </th> <td>   1.939</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.982</td> <th>  Jarque-Bera (JB):  </th> <td>   0.042</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.030</td> <th>  Prob(JB):          </th> <td>   0.979</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.920</td> <th>  Cond. No.          </th> <td>    11.7</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.966\n",
       "Model:                            OLS   Adj. R-squared:                  0.966\n",
       "Method:                 Least Squares   F-statistic:                     2822.\n",
       "Date:                Tue, 27 Mar 2018   Prob (F-statistic):           1.41e-74\n",
       "Time:                        18:21:42   Log-Likelihood:                -150.42\n",
       "No. Observations:                 101   AIC:                             304.8\n",
       "Df Residuals:                      99   BIC:                             310.1\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept     -3.8390      0.214    -17.934      0.000      -4.264      -3.414\n",
       "x              1.9647      0.037     53.122      0.000       1.891       2.038\n",
       "==============================================================================\n",
       "Omnibus:                        0.036   Durbin-Watson:                   1.939\n",
       "Prob(Omnibus):                  0.982   Jarque-Bera (JB):                0.042\n",
       "Skew:                           0.030   Prob(JB):                        0.979\n",
       "Kurtosis:                       2.920   Cond. No.                         11.7\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 12.4 Linear Regression with scikit-learn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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1kJQEBw/CQw9Bo0ZOrZqXlJQUkrMSvUECthBBpL5TtqunVO4G9gPPlJXxqUZjnqG4ZAlc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\nQPw/kAAa4Y73R3IAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11a696a58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xd, yd = load_data()\n",
    "df = pandas.DataFrame(dict(x=xd, y=yd))\n",
    "xm = xd\n",
    "xdf = df.x.values.reshape(len(df.y),1)\n",
    "ydf = df.y.values.reshape(len(df.y),1)\n",
    "\n",
    "model = LinearRegression(fit_intercept=True)\n",
    "model.fit(xdf, ydf)\n",
    "a1 = model.coef_[0][0]\n",
    "a0 = model.intercept_[0]\n",
    "\n",
    "ym = model.predict(xdf)\n",
    "\n",
    "fig = plot_model_and_data(xd, yd, xm, ym)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "a0 = -4.104, a1 = 2.039\n"
     ]
    }
   ],
   "source": [
    "print('a0 = {:0.3f}, a1 = {:0.3f}'.format(a0, a1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 13. The End"
   ]
  }
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