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Last active December 11, 2015 07:58
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{
"metadata": {
"name": "just_plot_it_blog_post_part2"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#Part 2 \n",
"\n",
"\n",
"##Getting started\n",
"\n",
"\n",
"OK, let's just dive right in and fill in details as we go. I'll be using Python for this exploration but will focus on the story and not the code. \n",
"\n",
"First things first, let's load the sunspots data, which is easy to find (e.g. [from NOAA](ftp://ftp.ngdc.noaa.gov/STP/SOLAR_DATA/SUNSPOT_NUMBERS/)) and conveniently included in a popular Python package for doing statistical work... "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import statsmodels.api as sm\n",
"import pandas as pd\n",
"data_loader = sm.datasets.sunspots.load_pandas()\n",
"df = data_loader.data"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"`df` is shorthand for \"dataframe\", which we can think of as an Excel-like table of values. Dataframes have various methods that can be called to easily learn about the data contained in them, and we'll step through calling some of these methods. Below, we see that we have 309 pairs of (year, activity) to examine... "
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"df"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 2,
"text": [
"<class 'pandas.core.frame.DataFrame'>\n",
"Int64Index: 309 entries, 0 to 308\n",
"Data columns:\n",
"YEAR 309 non-null values\n",
"SUNACTIVITY 309 non-null values\n",
"dtypes: float64(2)"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can quickly inspect the first and last handful of values to get an idea of what the data look like..."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"df.head()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>YEAR</th>\n",
" <th>SUNACTIVITY</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <td><strong>0</strong></td>\n",
" <td> 1700</td>\n",
" <td> 5</td>\n",
" </tr>\n",
" <tr>\n",
" <td><strong>1</strong></td>\n",
" <td> 1701</td>\n",
" <td> 11</td>\n",
" </tr>\n",
" <tr>\n",
" <td><strong>2</strong></td>\n",
" <td> 1702</td>\n",
" <td> 16</td>\n",
" </tr>\n",
" <tr>\n",
" <td><strong>3</strong></td>\n",
" <td> 1703</td>\n",
" <td> 23</td>\n",
" </tr>\n",
" <tr>\n",
" <td><strong>4</strong></td>\n",
" <td> 1704</td>\n",
" <td> 36</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"output_type": "pyout",
"prompt_number": 3,
"text": [
" YEAR SUNACTIVITY\n",
"0 1700 5\n",
"1 1701 11\n",
"2 1702 16\n",
"3 1703 23\n",
"4 1704 36"
]
}
],
"prompt_number": 3
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"df.tail()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>YEAR</th>\n",
" <th>SUNACTIVITY</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <td><strong>304</strong></td>\n",
" <td> 2004</td>\n",
" <td> 40.4</td>\n",
" </tr>\n",
" <tr>\n",
" <td><strong>305</strong></td>\n",
" <td> 2005</td>\n",
" <td> 29.8</td>\n",
" </tr>\n",
" <tr>\n",
" <td><strong>306</strong></td>\n",
" <td> 2006</td>\n",
" <td> 15.2</td>\n",
" </tr>\n",
" <tr>\n",
" <td><strong>307</strong></td>\n",
" <td> 2007</td>\n",
" <td> 7.5</td>\n",
" </tr>\n",
" <tr>\n",
" <td><strong>308</strong></td>\n",
" <td> 2008</td>\n",
" <td> 2.9</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"output_type": "pyout",
"prompt_number": 4,
"text": [
" YEAR SUNACTIVITY\n",
"304 2004 40.4\n",
"305 2005 29.8\n",
"306 2006 15.2\n",
"307 2007 7.5\n",
"308 2008 2.9"
]
}
],
"prompt_number": 4
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"OK, so the time series of annual values starts in 1700 and goes through 2008. Notice that we have fractional numbers in the more recent observations. This got me wondering when these fractional values started appearing..."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"fractional_nums = df['SUNACTIVITY'].apply(lambda x: x % 1) #Take the modulo of each value with 1 to get the fractional part\n",
"fractional_nums[fractional_nums > 0].head()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 5,
"text": [
"49 0.9\n",
"50 0.4\n",
"51 0.7\n",
"52 0.8\n",
"53 0.7\n",
"Name: SUNACTIVITY"
]
}
],
"prompt_number": 5
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The first fractional value occurs in 1749. I looked into this a bit and (re)learned a few things:\n",
"\n",
"* Galileo first documented sunspots in the early 1600s, using his newly invented _telescope_\n",
"* Reliable sunspot observations begin in about 1700\n",
"* The fractional numbers are probably associated with data coming out of Zurich, Switzerland in 1749 onward\n",
"* The methodology for tallying sunspot counts has evolved, most notably in 1848 with the introduction of the [Wolf number](http://en.wikipedia.org/wiki/Wolf_number) (which is not simply an integer count)\n",
"* There seems to be a [fair bit of debate](http://www.leif.org/research/IAUS286-Mendoza-Svalgaard.pdf) about how accurate the existing data are\n",
"\n",
"With some context in hand regarding the data generating process, let's get back to exploring the data. We can get a quick sense of the distribution of values...\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print df['SUNACTIVITY'].describe()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"count 309.000000\n",
"mean 49.752104\n",
"std 40.452595\n",
"min 0.000000\n",
"25% 16.000000\n",
"50% 40.000000\n",
"75% 69.800000\n",
"max 190.200000\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"...and of course, any time we report statistics we should try to provide an accompanying visualization (and vice versa)..."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"df.plot(x='YEAR', y='SUNACTIVITY', xlim=(1700,2008))"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 7,
"text": [
"<matplotlib.axes.AxesSubplot at 0xada0550>"
]
},
{
"output_type": "display_data",
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7CTWIYvcfsy54qqsV41fstsFT6tZ4gJ3H7oKnBPgVu46oW1oYifILGHXwtKSE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\nc2v6Hj+xUxU7VRDNnMluyAsX0trbYMyY3CR2G8R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}
],
"prompt_number": 7
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Clearly there is a seasonal pattern in activity. If our aim was to fit a model to these data we would want to start looking at the autocorrelation and partial autocorrelation functions..."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"pd.tools.plotting.autocorrelation_plot(df['SUNACTIVITY'])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 8,
"text": [
"<matplotlib.axes.AxesSubplot at 0xaf5e240>"
]
},
{
"output_type": "display_data",
"png": 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rrnRSUhJ27NiBvXv3Yv78+Zg/f77ma6mFgZytMtLLITgaMtLyEKQSVfmqZr0y\nyVq1YitipwC1jv7jD/2VmtIK4mXL6N8LLzh2Iy5fThNuYSHw3nv6svKSUwmtvY+zs20NQmxsLFq1\nUp+I1EIPgHalkZqHoGdklROXNMHpfUbyldbt2pGB0CI2NhabN9Ok3qwZ8MQTwKpV2vJKNmyg+LRE\n/foUnlALa2VmUujN399yTssgyDcdktO2rbo+SoMgxaPVVoIXFpJxkodCAdd5CMoHBL08gtwgAGTI\n9bquFhXFVhh7QD/RLlX8SdgzNgDw+eeUtP76a+B//9OXdTVVmkMICAjAiRMnkGNv+yonuHS9HGLA\ngAEIDQ3FkCFDkJiYaCWTmJiI0aNHo2HDhhg3bhxSdB7PnDEIN+IhOJpU1vIQLl2y/dLolUkqJ8eQ\nEJrs9G7wr7+m8EZ4OJUs+vnZj3lfuwZ8+CHV2r/3HvDii9qtOoSwdAiVo+chqE3wrvIQ5H2MJPTC\ncMrPtHZtuhe0evQUFlKYTxpTWBiNu0Rnwfi33wJjxtDP//gHVQs5Erq7epUmDWUUVuuzVeYEAH2D\noJQFtPMIx46p72Wg5iEowzoS3mAQtAyehDyHAJARPHZMXVbe3hugB7RDh7QfJoSg3eaef552h1u8\nWHscEocP073z9df2ZTMygAceoAeiESOAP//Ulr18mcpkP/mEPFe9tiISdkNGnTt3Rv/+/TF//nws\nXboUS5cuxbJly+z9mSbJyckIlxVGd+rUCXv27LGSSUpKqihzBYAmTZogTeMKu8pDUDMIWjkEZ5LK\nyoSyhNYE9vvvZpvJ1F7YaMsWqqkG6At67720l7EemzfTjd65M00+/foBX36pLvv332QA1Z4GS0tt\nn8zVnkzNZrOqh3DlChkntc9IzSAIoW4Q9DwEZcgI0E9UpqeTEZC8usBAktdKRJvNZuzeDQwYQMdh\nYXQ/OFId9uOP9NSpLLvVMgjKhDKgbRDkmwjJUZswpd3MlDkEQL30VC1cBDhnELRKT11hELQeoK5d\nA06dMlt9Lu3ba/dVUhqExo3pQVGrbHn/frqnBw2iiTstTb+J3/nzNLF37Ag8/TTw3/9qy6al0T3W\nvTuttRg6lLY4lX9vzWYzioqo31iHDhQxMJspgiDtXqj1PQdgv/31woULxQsvvCAWLlxo9e9G2b59\nuxgr60nw/vvvi+eee85KZvz48WLr1q0Vx9HR0SItLc3mtQAIoIsABl//Wfq3TeUcBNBIAN+onP9c\nAONVzk8PqIIJAAAgAElEQVQRwFiV89sEMERxrokAvlWRjRTATyrnkwXQUeX8LAHcrjgXJ4AXVWQh\nAJMAzgugpezcrQI4pCEv/VslgJGy42EC+EBDdogAtmv87h2V8f4igEEqsv7XPzs/2bmWAkjTeO3R\nApimOFdbAJdUZAcJYKnG6+wTQA/FuXgB9NaQHyGAzYpz2wXQS0O+kQByFOfeE8AYO9cAApgngH+q\nnJ96/XfK85ME8LzKZ1KoIjtDAPernH9QAF8pzjURwHcaY5wogNWKcw8IYKGKbEMBnFacCxRAsYrs\nAEH3ttq9OUlxLu76ONTGd0gA3WXHkQI4qCHbUgBrFecGCsCsIf+JALoqzv1PAMM15B8VwOuy439q\nXF/p33gBfHj9506C5pBGKnImASy//rnLz98sgBMC2CSAhwXwkKD5YIMA2ihk/a/L02uooWsQSkpK\nxEMPPeTUhG+PixcvVuyxIAT1TNq8ebOVzNtvvy2WLVtWcdy2bVvV1wIg3nxTiFmzrM+r9TcSgnr5\nq/V3HzVKiI0bbc8vXCjEv/9te75vXyF27rQ+V1REeyoo2bDBei8EiSFDhPjf/2zPh4VRrx4569dT\nL3s1EhOF6NzZ+lxZmRDBwUKcO6f+N2VlQjRrJkR6uuVcaakQLVtaetvLWbqU+jGpMXGi7R4TYWHU\nQ0eNli2FyMy0HCckCHHbbeqyn34qxPjx1ueOHqVe+koOHhSia1f112nWTIjsbOtzEyZQvxw13nyT\n9g+QM2WKEO++qy6/YQP1SpLz7bfqe3LIKS+nz+PIEdvfmc3qn8u4cfS5KGnQwPZ6jxxJ41CSmCiE\nckuT334TIjpafZxbtwpx553W55YvV78nrl2jnkWlpZZzJ09SDyUlO3YI0a+f7fmhQ4X44Qfrcx98\noN6frLxciDp1rPcmuXiRzqn1Idu+XYjYWOtzJ0/SdVBSUmK7T4oQ1N9p0SJbeSFobti+3XK8aZPt\n+0mUlVFPrr17LedmzhRi+nRb2f/8h66P/HOVKCoS4uOPaZ+PDz6w/n5poWUQ7OYQMjIyXJpDkBLS\nCQkJyMjIwPbt2xEdHW0lEx0djQ0bNiA3Nxdr165FhDJ4LcMVISOt1hVaOQS1kFFQECV+lRVPeiEj\nZYhDCHV3Wa/F8Y8/AnfeaX3Oz48qVRSpmQoOHKCKFrmb7e+vHWpKTLSUYCpRhjbKyihEI62jUKLs\naaQWzpFQCxmphYu0ZAEKaeXl2SahpVJGNaStP+XoJZb37AH69rU+N2QI9fHXW3F86BDlMtQqe6TP\nVRmrlrd0kKMWNtLKIUh7EchzHMoeRnLUyoW1CgFq1KD7XR4OVQsXAc6Vs2qFjHJzKaQnr3MJDqbv\no9r9oPaZtGpF94gyPHzyJI2xVi3r81qVRrm5VHzRv7/l3KBBlGBWW0/zyy801h49LOdeeAH46ivr\nhZCnTwPPPAP85z/WxQQSNWvSivrFi4GpU7W/e47g9hwCACxfvhxTp07F4MGDMW3aNDRu3BgrV67E\nypUrAQB9+vTB7bffjl69emHp0qV4/fXXNV/LWYNQXGz7JdPKIWhVGakllU0m9cSylkFQK5O8cAEI\nCDBDue6vXTu6YdVuqj17qG5dSd++9Ds1tmwB7r7b9vx991FyVI4QVBOv9h6ArUHIziZjp1wYKMWj\nlQZBK6EMqE/yaovYAEsOQZnIPXuWfqf8ItnLISgNgl6ceetWs41BqFOH4rV6uZwffqDroEzMAhaj\np9T/+HHnDIJalVFwMN2T8ji4WsmpdM2khXzy743edVPmEfQMgrSdrBwtg6BmwJXrLCS0Eud075mt\nzvn5qedVjhxRT7J37aqeH/r5ZyrqkN/7tWtT3D8+3lZ+3Trg4YdtFwI+8wztgQ3QXDZ+PJWHd+tm\n+xpKqnwdQsuWLTF27FjUrVsXBQUFyM/PR75eFzEHiImJQUpKCo4fP45Zs2YBAKZOnYqpU6dWyCxe\nvBgnTpzAvn37bshDUFup7OdHTxNKeWeb22lVJamVnjrjIZw+bVmdqRx3ly62TyVCqD+dAjdmEAYM\noC+YfILPzKTqGuUEKaEsPdVKZEqEhlo3S9N60gRo4leuZNXyEAID6fO/cMH6vNbr63kIys19AO2m\ncCUlNJmqeVBjxlAJolZFyldfkVemhtTJVH4tLlwgD1TNICoNgtQWQu1+AqiEWP4UqrUGAaAHncBA\n66osraQyQAZBnizWMgjSJlPy6aSkhPRUXmMtD+HUKfUnYq1Ko4wM2wQ+oG7wlQllifBwukeU88iu\nXdbegcSIEVTEIaekhBLIUjGInOnTaZyPPUY7/DVpQlWA7sDuBjkLFy4EAJRcr7mrIfWv9RKkp345\nWh6CJH/1qrUb6OzCNLWVyoC2h6D2RNe4sW3JWHY20L59rOq4pUojqZIFoJumRg1yeZVER1MlQlmZ\n9dPx+fM0Eah11AwIoJ3QFi8G1qyhc5J3oPYUC1DY6cwZKtWsXVs7TCHVR4eGWq/6zc6mSic1JA+h\nvNxS8aO2BkFCMiDySVDLIGgttiovt+3/A9BkeeIEfZHlX4HDh4F27WJt2qED1C753/+mbStHjrT+\n3cGDVJIcE6OuC2BpDSLJSOEitWuhNAjSddC6bp07030gPRioPQ3La9olz076bPVCfY56CIDFS5C6\nB58+TX+v9OgaN6bvlvK7feqU9loLLQ9h4sRYm/NqO7gdOUIPYkqCgsiApKTQKnaJnTsBtc0khw8H\nnn2WwpdSP61ffqFrqfZdCQykdhlLltC1f/hh9VCRGlXeyygtLQ0PPvgg2rVrh3bt2mHs2LFI1yuK\ndzPOhIwA9bUIzjS3u3aNJlm113eFh6D1JVMrPU1MpIlfjUaNaJLYv9/6fHw8xTXVPCiAOjr+8IOl\nLvv776m0TYuAAHqKklxoLYMgoQwZ6T2Z1qxJE4X8c1JbpSyhtpBN6zPVeuLMzqbrpQzbBQXR56mc\nNLQ8NIC+2CtWUOtkpXe3ahXwyCPWCxaVKD0E+eppJVoGQYtOnSwPJFJ7hq5dteXbtLGEmITQf31n\nDIKy9PTvv9UfcPz8SFZpxDMz1T0EvZCRsmwXoM9VuRZBuShNTu/e1h54YSF9nr162cq2akWfX4Js\nU7uPPqLrr0VwMPDKK8DEiRYj4g7sGoRXXnkFI0eORHp6OtLT0zFq1CgsWrTIHWNzCDWDoNXLSEve\nGQ9ByjeoPXlVNoeQnQ2UlppVx62WWP7tN+3JCKBk8/bt1ue2bAHuukv7b0JCgH/9izyF/fvpJp40\nSVseoAS21IM+PV19opBim2FhFoMgBIWbtL50gO1EpxUyAtRDTFoeQrNmZGiULTvU8gcSamsD9uwB\nQkLMmuMfPBh47TVqn7xhA51LSaH48RNPaP6Z6vtpJZQB28/JXuhOHjJKTqYHDqk9g4Q8Hi035GfP\n0oOVck8QCWc9BHliWcsgAOpG3JmQUWkpvVdamtlGXstD0Lo3BwwA5E2f9+4lb0KZgJaYNIkWrAGk\nw48/Ao8+qi5bGao8h7Bv3z6MGzcOAQEBCAgIwJgxY7Bv375KvakrqayHUFZmG0KSUMshqCWUJdQW\npznjIWRlkaFQo1s3+gJLLSyEoNWHUkM0NQYPtjYIZWXkIegZBIB2nTp/np6CFi1SN5ZypPAUQBOk\nVkUSYNmLQAiaKIKCtOPcAE0O8onOXlWSowYhIIA+a+XCKL1JV80g7Npl29JDyUMPUb+iefOoRcXI\nkcDCher9nvTe79gxxw2CPQ+hSxd67cJCCk/ceqv+WOQGQbnSV8mNhIwkXGkQlB5CVhbdI2pRb6WH\nkJ9PuQytsQwYQA9LUn5o2zZ9T/rRR4GffqJwZFwc3RNaBtWT2DUII0aMwJw5c7B//37s27cP8+bN\nw4gRI9wxNodQGoSyMnoS0Ep1KA2CFPtWc93VPAQtbwJQDxmpta4A1D2EU6eAgQNjNV87PJxuPICe\nSOrUsW0nIScmhp7+JB2Sk2lytFeWVqMGTfAlJZTYsodU4pqXR5OGPK4qIcU269Shzy8ry3Y3LzVa\nt7YueVRbqSuh5SFoGRC1xLI9D0GeQM/OJp3VYtJKevaknlS33UatQhzZYyo0lF5f2vxGz9i2akUT\nq5RP06owkggOJu9yyxZtgyCPR8tDRnpGE6hag6Asf9WqMmrVih5q5HODdG3V4uytW9P3sbCQjqUy\nXK2Q3s03U1z/+HEyCt98Y92PSkn9+pRPioqiXENVBVmqPIcwf/58tG/fHgsWLMAzzzyDdu3a4Sl3\nbTLrAEqDIIWLtJJpSnmt/AGgbhC0EsqAcyEjyUOQV6BoPe1IzJ5tSVp9+SWViWrpCZARGTAAWL+e\njjdvVq8uUsPPTz++LadTJ3LFN20ib8FezLNfP9rQxBGDIPcQSkv11zioGQStGDOgXnpqzyDICwGk\nTVkc/Zzq1qXW2HfeqX/dJPz8KPn/44+k1+nT2qWHQUE0SUsGS2q/occDD1CLg127tMuKJeQegj2D\nEBpq2adY8gTVKnsA27yAnkFQbudZVkavreZp+fuToZDvl6zWj0vCz48mecmr+OMPfc/PZCIPfP16\nuieKivQ9Y4A6oP74I3ntlewPWmXYvZWDg4Mxa9YsxMfHIz4+HjNnzkR9L/J1goKsJ3i9cBFg6yHo\nPfGrJZXVWl9LOJNUlrwS6YkEoInv1Cmz5tjHjqUnlylTgC++oEUo9njiCepjUlQEfPyxZRMWV+Lv\nT2GQ2bPVy+4A69jmwIFUZeGsh5CVRZO+MtYtoTQI9pKfah6C2qI0ichICitIpa0JCeSFuWpPZTVG\njqTQ4G+/kSHVqzaRFkyVlNAkZa9u/d57KQz54YfqXpRcrw4d6N4rLdVPbgNkLE6etMTs69XT/o7J\nJ2FA3yAoS0NPnyZPWysaoAwbSXt6aF0vedjIbNa+lyX+9S/qFTR3LoWAHDHyPXtql+u6girPIdx5\n5524KFsRlZeXh6FDh1bqTV2J8onfWYNgz0MoLLR+itczIEoPoayMXl/LgEjbRErjvnTJ0hNfjcBA\ncjeLi8lF1YsRS9x9N02ko0dTBYReJUll+OQTMlRqddVKYmPpSemXX7RLTiXkHoJeuAiwrTK6cIEm\nUDWDDNiWngqhvRgJoIeP226z7HVgNluXAVcFI0dSWGfTJvsTlGQQ/viDPiet+05CWsynF+qQaNiQ\nDOihQ9qL4yRq1iSP4ORJ+0UDyhXgegZBmfg9flzbeEuvLZfX8xAAmqx37KCfzWZ6cNGjY0cKqd58\nM/DSS/qyvoLdgqZz585V7KcMAA0bNsRprV23PcBbby3BpUuzERe3BABw4UIIrl59FHFxb6vKp6eP\nxmefpeDAAfL9MzNb4+LFOxEXp97A3s/vWfz730tQowaVoxw61BUZGe0RF2e7BHXfvh7IymqJuDha\nhVJUVBM1aszCSy+9pvraJtNjiIv7GWFhJ5GX1wC1az+CHTt+xY4d+ntWt21LqyJ//llXrIJ77mmI\nXbv6oVevvYiL09nZvJLUqUOGSgtpL24hgLNnn0KdOunYvXuD5gI6AMjLa4A//ngEcXFv4+DB7rh8\nua3qZw8AOTmN8ddfYxAXR5s7nD7dHDVrjkJc3EpV+QMHInHyZCgCA2lHwMLCWrh6dRbee2+J5tOe\nELdi8eIG+OGHwzhz5h5s2vQO/PxEle4z3rz5aGzbFoK6dTciLk6jxzeAo0c7IDGxD44cSUFgYGvE\nxX1X6feW61W79nAsWJCHQ4f647//fQfbtxdq/l1AwCNYuHAXLlxogMLC5hXfCSXl5Sbk5DyD555b\nAn//MmRnP4tVq16Bv79t7/CyMj+cPLkAzz//Kvz9y7F3b08UFbXQfO3MzJ7YvfsmXLz4PQAgKWku\n4uM/QnDwZdXrlZPTGJ999gjKyz/B+fOT8NVXy+w+9depQ/9eeUVfzp1U6l601wTpoYceEntl3ZeS\nk5PFmDFj7HdPcgMARGGhdVO5P/8UIiJC+28mTqRGUBLx8UIMHqwt37ChEDk5luN33hHiySfVZdet\nE+LBBy3H6enU6E2LRx8VYtUq+vnnn4UYMEBb1mgcOiTE1av25YqKhAgMpEZgcXFCPPustmxenhD1\n61uamn37rXZTQCGouaC8advOnUL07q0/noMHhWjRQohbbxXi/fftj9+dZGYK0by5EI8/LsSKFa5/\n/c8+o8932DD7sk88IcTbb1PjyaVL9WXDw4U4fFiIU6eoEaEeN99saZxo77WTkoTo3p1+zssTom5d\n9YZ3crp1o/lg3Dh9OV9Ha+q3GzKaNWsWxo8fj6FDh2Lo0KEYP3485s2bd+MWyMVIW2hKYR2tthUS\ndetah3X0ksSAbR7h0iXtcjFl2alW/kBCHuOUkp9VGY/2JEq9unbVv04SNWtSCCElxX7IqEEDChFJ\n1Vtai5AklGWMWhvEyOnWjVZyt24NTJhA57zlmrVqRaGaVavsJzgdQalX//50f7/8sv2/lTadsRcy\nAixhowMH7Oc95HmElBT9HFTXrpT3uHrVImsy6V+vuXPpe6m24tgXqOy9aDdkFB0djdTUVOzduxdC\nCPR2xZ3mQvz8KKl07ZolwayXQ6hXz9ogXL6sn/FXVhpplZFKr600CHqv3bYt1acD9iuMqjPSeorj\nx4Fx4/RlpcRg48b2a/HbtqUqFKmlwNGj9g2CyUQ15VWxqKiymEzUWTMxkUqBXU1oKH22eglliQ4d\n6JodOWK/cEAyCBcv2h+33CCkpurnBGrWpHEcPkwFAFqr+uVMmGAx9NURhxZFp6Sk4KeffoLJZEK9\nevWsdjzzNHFxcTCZ/g8LFy5HzZrFOHEiDEVFowDYztpmsxlJSWUoLg5CWdlPAIA9e6JRu3YXALaZ\nLLPZjMuXO+Ctt7bgppso+/jzz8Nx2231AdjOHEeOJOP48dYVMeuUlHCcPdsdZvMZ1frgixf3IyGh\nKeLiPsb33/8DLVqcQc2aewGo1xObzWbV+GBMTIzXy8fGxt7w61+40AmvvjoAV67Uhdn8FmrU6Kcp\nf/VqQ7z+ehq6dz+ErVvHoFu3wzCbm6rKJyebUatWV8yZ8yWaNDmP//53NDp1SoHZ3NhpfdXw5Odv\nMlX+9QH6ft3IeC5froeEhCdw7VogMjJ+Q7t22vLHjvXB7t2NcOFCA/TqtQ9mc3PN109PL0ZyciOc\nPr0NZ848hdWrX8XAgQM05f39g/Hii1k4dKgr+vf/DXFxx73yerlSXvk3etfXBnuxpg8//FD06dNH\nvPbaa2LJkiWib9++4sMPP3R1SOuGkIbftKkQZ87QuU2bhLj7bu2/WbFCiGnTLMcLFwqh2LDNipgY\niu9LjB0rxOefq8umpVnnDFatoo1YtMjOFqJJE/o5KkqIXbu0Zasz588LYTLRtbLH889bNjXq3l2I\n5GR9+fvvF2LtWvq5Sxch9u2r3FgZC5cuOXZPm81CdOggRKNGQmRl6cumplKeZMcOS35Aj2++EaJj\nRyHq1bPd6KY6ozX1280hfPLJJ9i6dSueeuopPP3009iyZQtWrVKvyPEU8tJTvbJQwPmQUd26tjkE\nLXll2aleeAmgVZpXrtCqztRUWsXoLfFoV1MZvRo1ogVUM2fal5Vi1wUF9L9at0o5UqnmuXMUtrMn\nrwZfM3Xq17ffEgOg0t0+fSjka69Gv2NHyv088oh+cziJ+++nDWgGDrS0pzHq9QLcsA4hJCQEubIe\nC3l5eVZlqN6A3CDorSsAbJPKekligCZ/eV5AzyAocwi5ufrrCkwmqmH+/HOaiPRyH9WduXOpFt4e\nUow5KYkWktn7TKUuslIXWK1Fb0zVYTLR4smvv3ZM/uGHyXg48oBgMgGffgp89lnlxlhdsJtDmDt3\nLoYNG1axSU1qamrFzmbegny1sqs9hJAQ653K9OSDgugGLC62bOHXvbv+2B99lHqcTJ5Mx5XtReKt\nuEsvyUNISLDfjgGg67N3L1WpObJASw2+ZpWnbl3HrhdAhmDiRMeNd0CA9UOfUa8XUHnd7BqEO+64\nA0ePHsWePXtgMpkQHR0NP0ebt7gJZzwEpUHQe+IHbA2CPXnJS5A6b2pt5iIxeza1DlDbsIZxnkaN\nKPyweLFjT5yhocDjjwNvvkk96hnvR2/1OVM57M7sd9xxB/z8/NCvXz/ceuut8PPzwx133OGOsTlM\nZQzC5cv2Q0bOGAT5WgRHDEJQEO07MGYMHRs1vulOvdato/CPI0bWZKLOkxcu2G9HrQVfM9/CqHoB\nVbgOoaioCIWFhcjJyUGebDPVc+fOVXpPZVejTCprbaACkEFwNEkM0JOI1PCqvFy/uR1gnVh2xCBI\nY2JcR6NG1P/HGRxZJMcwRkfTIKxcuRJvvfUWsrOz0bNnz4rzoaGhmDNnjlsG5yjyfZVvJGSk5yHI\nQ0b5+fTaeh0n69Wz9K/X291LC6PGN42qF2Bc3Vgv36PKcghz5szBnDlzsGLFCsx0JJ3vQZQhI72k\nslRlJASFC5xJKtszHoBlw49r18ib4Fg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jj+Dn54eUlBRERUUhMzPTwyNlGHXYIDCMi8jJ\nycHjjz+Orl27YtWqVdi2bRsAYNu2bRg/fjxMJhPGjRuHoKAgD4+UYdRhg8AwLmLRokW49dZb8fvv\nv2Px4sUcFmJ8DjYIDOMisrKy0L59e1y9ehVr1qypOD906FCsXbsW5eXl+Oqrr1BcXOzBUTKMNmwQ\nGOYGKCwsROvWrSv+LV++HM888wzmzJmD/v37IzIysqISafLkySgpKUGnTp2QlJSEtm3bqu7CxjCe\nhpvbMUwVc+3aNfj7+8Pf3x8bNmzA+vXrsW7dOk8Pi2FsCPD0ABjG6GRmZmLMmDEoLi5Gr1698Pzz\nz3t6SAyjCnsIDMMwDADOITAMwzDXYYPAMAzDAGCDwDAMw1yHDQLDMAwDgA0CwzAMcx02CAzDMAwA\n4P8DmUwMWVnhMnwAAAAASUVORK5CYII=\n"
}
],
"prompt_number": 8
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"That the blue line goes beyond the horizontal grey lines indicates that this is a non-stationary time series with correlation structure. For my purposes here, I am not interested in fitting a model to the data. Instead, I just want to learn more about the length of the typical sunspot cycle. For this need it helps to view the time series' autocorrelation function in the _frequency_ domain instead of the temporal domain. So, we create an array of frequencies to evaluate the series over..."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import numpy as np\n",
"N2 = df.shape[0] / 2\n",
"freqs = np.linspace(0, 0.5, num=N2, endpoint=False)[1:] #Nyquist range"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"...then, using these frequencies, plot the _periodogram_, which is the frequency domain analog of the autocorrelation plot above. Note that the [Lomb-Scargle method](http://en.wikipedia.org/wiki/Least-squares_spectral_analysis) used below assumes that the frequencies are not in a typical unit like Hertz (cycles per second) but rather as [angular frequencies](http://en.wikipedia.org/wiki/Angular_frequency), which is why we need to multiply the values by $2\\pi$. (The Lomb-Scargle method is flexible in that the time series need not be uniformly sampled.)"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import scipy as sp\n",
"periodogram = sp.signal.lombscargle(df['YEAR'], df['SUNACTIVITY'], freqs * 2 * np.pi)\n",
"plt.plot(freqs, periodogram, color='green')"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "pyout",
"prompt_number": 10,
"text": [
"[<matplotlib.lines.Line2D at 0xafd97f0>]"
]
},
{
"output_type": "display_data",
"png": 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LlizR2q9mYbfslpqDEEIH/YbD3/3d3/GjH/0Is/nSS6uqqsjMzAQgMzOTyspKoP2DPisr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\n+Y77PRqFAAAAAElFTkSuQmCC\n"
}
],
"prompt_number": 10
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We see a big spike in the power of the series at a frequency of just below 0.1. Recall that these are yearly observations, so we can divide this frequency into 1 to get the period of each cycle..."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"freq_index_at_max_power = np.argmax(periodogram)\n",
"print 'Frequency and corresponding time in years at max power: %.2f, %.1f' % (freqs[freq_index_at_max_power], 1 / freqs[freq_index_at_max_power])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Frequency and corresponding time in years at max power: 0.09, 11.0\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The major cycle is about 11 years, which is what the literature states. So, we could have skipped this previous step entirely and just assumed the data had an 11 year cycle like the literature said, but it is always good to sanity check what you are working with, and of course, in many settings one does not already know such things, hence the need for exploration.\n",
"\n",
"At this point, after a handful of lines of code and some internet searches we have a basic handle on:\n",
"\n",
"* The data generating process\n",
"* Distributional information\n",
"* Temporal behavior\n",
"\n",
"There are a lot of things we could dive into further, but now comes the question that ties back to the title of this post: was our basic line plot of the time series data as helpful as it could be? After all, we simply plotted the data using default settings with respect to plot window size and axes scaling."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Optimizing aspect ratio\n",
"\n",
"In the following code segments we'll develop a method for finding _an_ optimal aspect ratio of the plot for the sunspots data (my use of the indefinite article rather than \"the optimal\" is purposeful: we just want to improve upon the default plot size and not necessarily find the truly best size). The code will follow the notation that Cleveland uses in the _The Details of Banking to 45$^\\circ$_ section in [1].\n",
"\n",
"The first thing we do is set up the vertical and horizontal range of the data we'll be plotting..."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"v_data = df['SUNACTIVITY'].max() - df['SUNACTIVITY'].min()\n",
"h_data = df['YEAR'].max() - df['YEAR'].min()\n",
"v_data_diffs = df['SUNACTIVITY'].diff().apply(np.abs)\n",
"vbar_data_diffs = v_data_diffs / v_data \n",
"h_data_diffs = df['YEAR'].diff().apply(np.abs)\n",
"hbar_data_diffs = h_data_diffs / h_data"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 12
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, we'll define our objective function that we want to optimize. This function gets evaluated for each aspect ratio we want to test, and for each evaluation it calls a few supporting functions..."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def objective_fcn(width_height, target):\n",
" dev = setup_device_coords(figsize=width_height)\n",
" lengths = segment_lengths(dev['aspect ratio'], dev['horizontal_device'])\n",
" weighted_avg_banking = np.sum(segment_orientations(dev['aspect ratio']) * lengths) / np.sum(lengths) \n",
" return np.abs(weighted_avg_banking - target)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 13
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The `setup_device_coords` function maps data coordinates to screen coordinates and calculates the vertical and horizontal range of the data in terms of their screen positions..."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def setup_device_coords(figsize=(8,6)):\n",
" h_device, v_device = figsize\n",
" fig, ax = plot_sunspots(figsize)\n",
" device_coords = [ax.transData.transform(data_coords) for data_coords in df.values]\n",
" df_device = pd.DataFrame(device_coords, columns=['YEAR', 'SUNACTIVITY']) \n",
" v_device = df_device['SUNACTIVITY'].max() - df_device['SUNACTIVITY'].min()\n",
" h_device = df_device['YEAR'].max() - df_device['YEAR'].min()\n",
" aspect_ratio = v_device / h_device\n",
" v_conversion = v_device / v_data \n",
" h_conversion = h_device / h_data\n",
" fig.clear()\n",
" return {'aspect ratio': aspect_ratio,\n",
" 'vertical_device': v_device,\n",
" 'horizontal_device': h_device,\n",
" 'vertical conversion': v_conversion,\n",
" 'horizontal conversion': h_conversion}"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 14
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"To do the data-to-screen conversion the `setup_device_coords` function calls a supporting function to render a plot of the data in device memory..."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def plot_sunspots(figsize, color='blue'):\n",
" fig = plt.figure(figsize=figsize)\n",
" fig.canvas.set_window_title('%.1f by %.1f inch window' % (figsize[0], figsize[1]))\n",
" ax1 = fig.add_subplot(111)\n",
" df.plot(x='YEAR', y='SUNACTIVITY', ax=ax1, linewidth=2, color=color)\n",
" fig.tight_layout()\n",
" ax1.set_xlim(right=df['YEAR'].max())\n",
" ax1.set_ylim(top=df['SUNACTIVITY'].max())\n",
" ax1.set_ylabel('Observed Sunspots')\n",
" ax1.set_title('Sunspot Activity Over Time')\n",
" return (fig, ax1)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 15
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Back to the supporting functions called by `objective_fcn`, we need to deteremine the lengths and slopes of each line segment in a given plot. The banking method calculates the average orientation of the line segments, where the averaging is weighted by each line segment's length."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def segment_lengths(aspect_ratio, h_device):\n",
" return h_device * np.sqrt(hbar_data_diffs.dropna()**2 + aspect_ratio**2 * vbar_data_diffs.dropna()**2)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 16
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"def segment_orientations(aspect_ratio):\n",
" return np.arctan(aspect_ratio * vbar_data_diffs / hbar_data_diffs)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 17
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"With the objective function (and its supporting functions) defined, we now need a few lines of code to drive everything. We set our desired average banking of the line segments to be 45 degrees (although the algorithms work in units of radians) and then define a grid of possible plot sizes to evaluate the objective function over. Note that the optimization method is called `brute` for a reason: it is a just a brute-force scan of every possible plot size, where we have defined what is possible. Since I already have experience with these data I am limiting the search to be over plotting windows that are longer than they are tall, and I am only searching over $\\frac{1}{2}$ inch step-sizes in the window dimensions because we are not interested in a super-precise solution. The last line of code unpacks a list of values returned in the `results` variable into individual variables that we can work with directly."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import scipy.optimize as spo\n",
"target = np.radians(45) \n",
"slice_obj = np.s_[20:26:0.5, # widths\n",
" 1:4:0.5] # heights \n",
"results = spo.brute(objective_fcn, slice_obj, args=[target], full_output=True, finish=None)\n",
"optimal_dims, objective_val, search_grid, objective_grid = results"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 18
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"With the optimal plot size determined, let's compare how the time series plot looks using the default aspect ratio versus the optimized one..."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.close('all')\n",
"ax1 = plot_sunspots((8,6))\n",
"print '\\n\\nWeighted-average banking using default 8 x 6 inch plot window: 87.3 degrees (goal is 45 degrees)' "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
"Weighted-average banking using default 8 x 6 inch plot window: 87.3 degrees (goal is 45 degrees)\n"
]
},
{
"output_type": "display_data",
"png": 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sJAeJHYIgCIJIAO7skNhJHhI7BEEQBJEA3Nlp04Y9UoyVHCR2CIIgCCIByNlJDxI7BEEQ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\nDg4ODg4OFY3/B9tV0kH0zUG+AAAAAElFTkSuQmCC\n"
}
],
"prompt_number": 19
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"This is the same plot we saw above, but bigger and with axes labels. The default aspect ratio leaves us with line segments that have an average orientation of _nearly vertical_, so this is a perfect example of the type of problem Cleveland was researching: It is very difficult to perceive patterns in the data when the rates of change over small chunks of time are so extreme. About all we can say is \"there are cycles roughly every 10 years\".\n",
"\n",
"Now let's look at the same data plotted using an aspect ratio that makes the average line segment have an absolute orientation of 45 degrees..."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"ax2 = plot_sunspots(optimal_dims, color='red')\n",
"print '\\n\\nOptimal width and height found to be %.1f by %.1f inches' % (optimal_dims[0], optimal_dims[1]) \n",
"banking = [np.degrees(target - objective_val),\n",
" np.degrees(target + objective_val)] \n",
"print 'Average banking interval at optimized aspect ratio: (%.2f, %.2f)' % (banking[0], banking[1])"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"\n",
"Optimal width and height found to be 25.0 by 1.5 inches\n",
"Average banking interval at optimized aspect ratio: (44.91, 45.09)\n"
]
},
{
"output_type": "display_data",
"png": 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W6fr1lEGumDQJcHenAMnVq87qpT5evAC6dKHbbdvoObO06/Fj4PhxIEMGKidV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\n8zMYPFgSRGqruFiX5V+2rPav52xZWXJvt0yMevxx2V/RZBgyrrUc+02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}
],
"prompt_number": 20
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"(When I run this same code on my laptop I get an optimal width of 22.5 inches by the same 1.5 inch height.)\n",
"\n",
"Ah, now we see something **entirely new**: when there are large spikes in activity the ramp up period is asymmetric with the ramp down period. Specifically, activity ramps up very quickly and tapers off more gradually. In contrast, during weaker cycles the pattern is more symmetric. This nonlinear behavior is interesting and highly studied. But, we might never investigate further had we simply plotted the data in a naive way and moved on to something else."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##Lessons\n",
"1. Even the most pedestrian data task, like plotting an array of values, still requires careful thought if the aim is gaining insight. Without such thought it is remarkably easy to have one's work amount to little more than generating chart porn for PowerPoint decks\n",
"\n",
"2. Default settings in visualization tools are there for expediency. We will encounter plenty of opportunities that warrant going beyond these _defaults_ to instead put _intention_ behind our graphical results"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Extensions\n",
"\n",
"The exploration presented here was a quick first take and there a couple of places we could improve upon. First, the method that Cleveland developed ~ 20 years ago has seen extensions, such as [_multiscale banking_](http://vis.berkeley.edu/papers/banking/). Second, the optimization method was easy to use and understand, but a more general, faster-converging approach is certainly possible."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##About this post \n",
"\n",
"This **entire** post (executable code, results, surrounding text, and text formatting) was created using the [IPython Notebook](http://ipython.org/ipython-doc/dev/interactive/htmlnotebook.html), an amazing extension of IPython[2] that supports highly interactive, collaborative, and reproducible numerical computing. For the many cases in which I want my code to be linked with rich context, it is hard to see _not_ using the Notebook. If your use case is focused more on text, with a bit of code interlaced, then using tools like [Sweave](http://www.stat.uni-muenchen.de/~leisch/Sweave/) in R or [Pweave](http://mpastell.com/pweave/) in Python are excellent options for supporting transparent, reproducible work (John Cook has a nice [blog post](http://www.johndcook.com/blog/2012/12/20/basics-of-sweave-and-pweave/) about this nuanced difference in use cases). In either case, there are no longer excuses for not tightly coupling code, analytical results, and context `:)`\n",
"\n",
"The notebook file can be downloaded directly from a [Gist](https://gist.github.com/4597218) on my GitHub account. If you do not use Python you can still view the file using the free, web-based [IPython Notebook Viewer](http://nbviewer.ipython.org/), which is how you areviewing this part of the post.\n",
"\n",
"If you dabble in building on this exploration, please share it!"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"##References\n",
"\n",
"[1] _The Elements of Graphing Data_, William S. Cleveland, Hobart Press, Summit, New Jersey, 1994\n",
" ISBN: 0-9634884-1-4 \n",
"[2] _IPython: A System for Interactive Scientific Computing_, Fernando P\u00e9rez, Brian E. Granger, Computing in Science and Engineering, vol. 9, no. 3, pp. 21-29, May/June 2007, doi:10.1109/MCSE.2007.53. URL: http://ipython.org"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"**[Back to Part 1](http://ficolabsblog.fico.com/2013/01/a-moment-of-science-just-plot-it.html)**\n",
"\n",
"**[Back to FICO Labs](http://ficolabsblog.fico.com/)**"
]
}
],
"metadata": {}
}
]
}
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