{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:20:36.959984Z",
"iopub.status.busy": "2021-11-16T10:20:36.922843Z",
"iopub.status.idle": "2021-11-16T10:20:37.628578Z",
"shell.execute_reply": "2021-11-16T10:20:37.629483Z"
},
"slideshow": {
"slide_type": "slide"
},
"tags": [
"hide_input",
"hide_output"
]
},
"outputs": [
{
"data": {
"text/html": [
"\n",
" \n",
" \n",
" \n",
" >\n",
" \n",
" \n",
" \n",
" \n",
" \n",
" \n",
" "
],
"text/plain": [
""
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"### BEGIN hide_toggle\n",
"### Update 30/10-'20\n",
"def hide_toggle_code(off=0):\n",
" \"\"\"This function generates HTML code to toggle the display of an input\n",
" cell.\n",
" \n",
" The output of the cell will still be displayed. This can be used\n",
" to hide (from immediate view) some code to generate data or the\n",
" like. It can also be used to hide other notebook explicit\n",
" implementations - e.g., C++ processing, or the like.\n",
" \n",
" Note, calling this function alone will not enable toggling.\n",
" Instead, we must wrap the generated code in an\n",
" `IPython.display.HTML` object and return that as the cell value.\n",
" This will let IPython evaluate the HTML code and pass it on to the\n",
" browser.\n",
" \n",
" If all one wants is to toggle a cell one can use the function\n",
" `hide_toggle` below. However, we can also combine the code\n",
" generated here with other HTML code - for example _style_\n",
" declarations and pass that along embedded in an HTML object.\n",
" \n",
" Parameters\n",
" ----------\n",
" off : int \n",
" Offset of cell to hide relative to the cell calling this function \n",
" \n",
" Returns\n",
" -------\n",
" code : str \n",
" HTML code to enable toggling of the cell\n",
"\n",
" \"\"\"\n",
" from random import randint \n",
" from IPython.display import HTML \n",
" \n",
" jp_cell = 'document.getElementsByClassName(\"jp-Cell jp-mod-selected\")[0]'\n",
" jq_cell = '$(\"div.cell.code_cell.rendered.selected\")'\n",
" toggle_text = 'Please close'\n",
" cell_id = str(randint(1,2**64))\n",
" func_name = f'code_toggle_{cell_id}'\n",
" \n",
" scr1 = f'''\n",
" \n",
" '''\n",
" but = f'''\n",
" \n",
" >\n",
" \n",
" '''\n",
" scr2 = f'''\n",
" \n",
" '''\n",
" return scr1+but+scr2 \n",
"\n",
"def hide_toggle(off=0,cnt=None):\n",
" \"\"\"This will wrap the HTML code returned from the above function\n",
" in an `IPython.display.HTML` object so that the notebook will \n",
" evaluate the HTML code. \n",
" \n",
" This function is what we will use most of the time. However, \n",
" the function `hide_toggle_code` can be combined with other code \n",
" and then be put into an HTML object to let the notebook evaluate\n",
" all the code. \n",
"\n",
" Parameters \n",
" ----------\n",
" off : int \n",
" Cell offset relative to calling cell which we should toggle \n",
" cnt : int or None \n",
" If not None, set the execution count to this number \n",
" (currently broken)\n",
" \n",
" Returns\n",
" -------\n",
" object : IPython.display.HTML \n",
" HTML object wrapping code to toggle cell \n",
" \"\"\"\n",
" from IPython.display import HTML\n",
" if cnt is not None:\n",
" get_ipython().execution_count = cnt\n",
" return HTML(hide_toggle_code(off))\n",
"### END hide_toggle\n",
"\n",
"\n",
"### BEGIN setup_matplotlib\n",
"### Update 30/10-'20\n",
"def _setup_matplotlib():\n",
" \"\"\"Set-up Matplotlib parameters. \n",
" \n",
" We specify that we want both PDF and PNG images, and \n",
" that the default image size should be 8 by 8 inches \n",
" \n",
" We also disable warnings about too many open figures \n",
" \"\"\"\n",
" %matplotlib inline \n",
" from matplotlib import rcParams \n",
" \n",
" rcParams['figure.max_open_warning'] = 0\n",
" rcParams['font.serif'] = ['Palatino'] + rcParams['font.serif']\n",
" rcParams['font.family'] = ['serif']\n",
" rcParams['mathtext.fontset'] = 'dejavuserif'\n",
" rcParams['axes.formatter.use_mathtext'] = True\n",
"\n",
" f = None\n",
" try:\n",
" # IPython >= 7.23 depcrates set_matplotlib_formats\n",
" from matplotlib_inline.backend_inline import set_matplotlib_formats\n",
" f = set_matplotlib_formats\n",
" \n",
" except Exception as e:\n",
" try:\n",
" from IPython.display import set_matplotlib_formats\n",
" f = set_matplotlib_formats\n",
" except Exception as e:\n",
" pass \n",
"\n",
" if f is not None:\n",
" set_matplotlib_formats('png','pdf')\n",
" \n",
"_setup_matplotlib()\n",
"### END setup_matplotlib\n",
"_setup_matplotlib()\n",
"\n",
"### BEGIN css_styling\n",
"### Update 30/10-'20\n",
"def css_styling_code():\n",
" \"\"\"This function returns HTML code to customize the CSS \n",
" of the notebook \n",
" \n",
" - The text font to be Palatino (serif)\n",
" - Headers are oblique (italic)\n",
" - Extra spacing below H1 headers \n",
" - Extra spacing spacing above H1 headers \n",
" - Headers have larger fonts, and is set in normal weight\n",
" - Remove padding around code cells \n",
" - Code uses the fint \"Source Code Pro\" (or monospace)\n",
" - Code background is changed to light yellow \n",
" - Output background is set to lavender\n",
" \n",
" The function combines these CSS declarations with the HTML \n",
" code from `hide_toggle_code` above so what we automatically \n",
" hide this code from the user. \n",
" \"\"\"\n",
" styles = '''\n",
" \n",
" \n",
" '''\n",
" return styles\n",
"\n",
"def css_styling():\n",
" from IPython.display import HTML \n",
" \n",
" return HTML(hide_toggle_code()+css_styling_code())\n",
"### END css_styling\n",
"css_styling()"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en",
"slideshow": {
"slide_type": "-"
},
"tags": [
"title"
]
},
"source": [
"### Christian Holm Christensen \n",
"\n",
"# Ancsombes Quartet \n",
"## or: How I stopped worrying and love ... \n",
"## Version 0.2 - February, 2019 (English)\n",
"\n",
"> Here we will investigate\n",
"> [Anscombes Quartet](https://en.wikipedia.org/wiki/Anscombe%27s_quartet).\n",
"> Francis Anscombe found in 1973 four datasets that give the same linear regression but visually are _distinctly_ different.\n",
">\n",
"> The title of this note is not finished purposely. Here, we will \n",
"> investiage what we can learn from Anscombe's quartet. \n",
">\n",
"> This document is available in many formats at https://cholmcc.gitlab.io/nbi-python\n",
"\n",
"### Niels Bohr Institute "
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:20:37.637708Z",
"iopub.status.busy": "2021-11-16T10:20:37.636613Z",
"iopub.status.idle": "2021-11-16T10:20:38.098319Z",
"shell.execute_reply": "2021-11-16T10:20:38.097202Z"
},
"maxlines": 10,
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"import scipy as sp\n",
"import scipy.optimize\n",
"import scipy.stats"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Data"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en"
},
"source": [
"Here are Anscombe's four datasets"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:20:38.115554Z",
"iopub.status.busy": "2021-11-16T10:20:38.114283Z",
"iopub.status.idle": "2021-11-16T10:20:38.117029Z",
"shell.execute_reply": "2021-11-16T10:20:38.118208Z"
}
},
"outputs": [],
"source": [
"d1 = np.array([[10, 8.04], [ 8, 6.95], [13, 7.58],\n",
" [ 9, 8.81], [11, 8.33], [14, 9.96],\n",
" [ 6, 7.24], [ 4, 4.26], [12, 10.84],\n",
" [ 7, 4.82], [ 5, 5.68]])\n",
"d2 = np.array([[10, 9.14], [ 8, 8.14], [13, 8.74],\n",
" [ 9, 8.77], [11, 9.26], [14, 8.10],\n",
" [ 6, 6.13], [ 4, 3.10], [12, 9.13],\n",
" [ 7, 7.26], [ 5, 4.74]])\n",
"d3 = np.array([[10, 7.46], [ 8, 6.77], [13, 12.74],\n",
" [ 9, 7.11], [11, 7.81], [14, 8.84],\n",
" [ 6, 6.08], [ 4, 5.39], [12, 8.15],\n",
" [ 7, 6.42], [ 5, 5.73]])\n",
"d4 = np.array([[ 8, 6.58], [ 8, 5.76], [ 8, 7.71],\n",
" [ 8, 8.84], [ 8, 8.47], [ 8, 7.04],\n",
" [ 8, 5.25], [19, 12.50], [ 8, 5.56],\n",
" [ 8, 7.91], [ 8, 6.89]])\n",
"data = np.array([d1,d2,d3,d4])\n",
"colors = ['tab:blue', 'tab:orange', 'tab:green', 'tab:red']"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en",
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Visual inspection"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en"
},
"source": [
"We start with a visual inspection of data"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:20:38.132147Z",
"iopub.status.busy": "2021-11-16T10:20:38.130336Z",
"iopub.status.idle": "2021-11-16T10:20:38.133336Z",
"shell.execute_reply": "2021-11-16T10:20:38.134250Z"
}
},
"outputs": [],
"source": [
"def plotQuartet(data,colors):\n",
" \"\"\"Function to draw full quartet\"\"\"\n",
" fig, ax = plt.subplots(ncols=2,nrows=2,figsize=(8,8),\n",
" gridspec_kw=dict(hspace=0,wspace=0),\n",
" sharex=True,sharey=True)\n",
" fig.suptitle(\"Anscombe's Quartet\")\n",
" \n",
" for i,(da,axes,color) in enumerate(zip(data,ax.ravel(),colors)):\n",
" axes.plot(da[:,0],da[:,1],'o',label=f'Data {i+1}',color=color)\n",
" axes.legend()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"caption": {
"da": "De fire datasæt",
"en": "The four data set"
},
"execution": {
"iopub.execute_input": "2021-11-16T10:20:38.165646Z",
"iopub.status.busy": "2021-11-16T10:20:38.164686Z",
"iopub.status.idle": "2021-11-16T10:20:40.833067Z",
"shell.execute_reply": "2021-11-16T10:20:40.832159Z"
},
"label": "fig:anscombe:data",
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
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EZWNvZGUgL0xlbmd0aCAzMDUgPj4Kc3RyZWFtCnicRVDJbcAwDPt7Ci0QwLrteVL01e7/LWm3KJBERCRSpJZNmZIlj+aWrpAOkw8dYYZ/Lt/DdR5kpoJHM2VteQc+mk2uxWJxsN8BQC5wNCZNEqR36OSaFrWWmqBioKLY2SXVS8xNeppYu7QudFxhxwPC89gKvRVLtA6qqeBAsaDh5LQr9qwTJbpPvcaIDA7asX1hfiMM4r+joJQhCb/IGQj2JJdMnAV2E+8TLpmOhrMDu0851rNuBIlTIYUrEn1dxKMCziAsKEBJuQ35Hj0hg1obZnGMB+N/h0cHcZHpe8Q+IHNKpeS/b2RVmK7E1SDPerMSRatwIoHJKdwJ1ilS6EKz8HIJK67tFxkDYcJs/3J0raOiuCtVWe8eIm7mBJ2Qc70dlRSKwvpvlHd8/gATyHR+CmVuZHN0cmVhbQplbmRvYmoKMjMgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzMTEgPj4Kc3RyZWFtCnicPVJJbsQwDLvnFfxAAe2235Oip5n/X0spnR4CErZkUlTyFAQp+FJH1ka641svPxtajvcwW47XZds+zNcwk4CxSvsmAvelJTALKJ/Ukw9m9U0z41eKo2xxLOG5SSIo4Ql/lAj35SpNPARx4BRZ1se7wGfHnv0h7+4rNosp/B6WRpczzocIsas/SE8kq5vgSaNBRqHWEMdXD2iTitFGI0fYT07qHBsq0s33VYWyzlAZx/+8JCYHdWBzxdl2z6tR6OFMlO05Mo332Gr2GHTm9LBoIc4dTqRS5CRBW7HomqKx+Q7rG5mo5TA9ixUF5Rc12sla7kmDtb0Lp5fdcR8Z8moSp3esphyG3UlU4iZax2B0n8zK/MzvYrUG29Nz4nwhlS6cOuv0ephDhGPWdAyfdd3Xzy9+enflCmVuZHN0cmVhbQplbmRvYmoKMjQgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyNTggPj4Kc3RyZWFtCnicTVFJbsQwDLvnFfrAANZm2e9J0VP6/2tJeboACcRYMhdlxpAhtuWlLrmH1BzyoZdqSpp8Naix5Lkw9AcwBTDyHwrvpplEgTJCYodYmaQOuXFtgzLFHUp4vU69r/BqFAsTAxgKkYVOTiCewJmHdrVJNiKtJZxQtb4zjWQgwTc5mYkqrPdFXSL6eGUb27QFo4aHvpcwyFIeA4wT9l2wjudnLyexeWBDRFoqpgVh8MPnboqJ2dV6YbCfLPCBJkBgFUgSsWUzasCo9hJAt1bXE5XInWtFnDX7SlhnBUdAoimrjkbVe9lE9BBztKmw7sCm88fAtkd1NSjcv5Ge6/Mbjshj9gplbmRzdHJlYW0KZW5kb2JqCjI1IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMjM4ID4+CnN0cmVhbQp4nD1RSXIEMQi7+xX6QKrACGy/p1Nzmvz/GuGp5NLIoMW4swyGNHx5IJ3ICHz7aOhZ+BlpDjcD10JukI4wPIOWEFSrpSFW12fMmRd5aS6pH5Srv9TSWVHeToZZbSMQnNCUti+bsnxGy1Odtus7dUDXZ4S+t1OFnAdxjmpHMMRRNEt72ATPAvfqiVAk8R5k/qHYV8spRYjdS+ZN0AW5qItRevHbS1XLad5oeiml4EeT+bmvEo6WS/GDt342bORbHTFc3NacHrRJTrSnBB2ionTaPS/XY8uTqG7TF+TC6HdMjeb9Qc//r3qP1y/wn1WSCmVuZHN0cmVhbQplbmRvYmoKMjYgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyNDQgPj4Kc3RyZWFtCnicRVExbkUxCNtzCl+gUgyEJOf5Vaff+681vFadcCywDVnXMLEmPuhYYVju+OQoaKK/B9dq9H5Q5C/iTjAPaA7ewNl4DTOJUf0XHnCyymu45ut9DBGIeZBLdMjrLIQmyESk6iqZClHoPRYvOCdCOUXECtitUSoBPKOD+7SuFSAbUQYs2QupvsYWpbdycO8qlrOMKpdhW4cijxyOeKauIcbsuYjd7KpVdjQKX90RkotHS15B9ccj+nfC2jM74reQrpByM7ajX037bV1pZp1Ny+oo5VhVK2nnZpSlOnjl6p1y1zG3lp2tWt9SPv+O7/H1AwOOWW0KZW5kc3RyZWFtCmVuZG9iagoyNyAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDM4MSA+PgpzdHJlYW0KeJw1UkGSBCEIu88r+MBWCYLoe2Zrb/P/6yax59BFWiEJ4JrLhq22H59W61hn2K+/ci3zc+wjFOWWNS0OYrTNGPZ+5XCbeWyuvJ9vxfcr2oViljJinKfG92XxHmJlpA5uiLKNGT6WarpJBpLcJs5HhBpSTKMJ3NKVsmmT5WoAdN9GcJPLCrefiw7uUL9mWHrYKlbPfWxtCNW2da4aI1u6KFDLjIh8agIOyOJniFUROmiJaMA6PfZUTSa9kCXxR1aqU4cRDuo5gRNmEN8auiWL3IP12w9qzkT+VmeYzh6WhwuAeoAp6LK0vrtjDp7xzkVo4gTTgp0akKGTZL3Ns/U26JCR+7ivxbtw75wf06HPEbW4GEQOQLUdEncSyY5nyqDvluHI2wKHBnSwtMKInAJoJ7kCp7MOQ2+Fx8Gg9gGW4ynh40YcegtnpHLrKJC33jV7aJmlFBGJmZE7n5p69lpZYmW8MkLQremyUaMeY9lHVjNd1r/7eL/+/gHaP6EQCmVuZHN0cmVhbQplbmRvYmoKMjggMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyNTMgPj4Kc3RyZWFtCnicTVFJbsQwDLvnFfrAANZuv2eKOaX/v5ZU0KKHgIxNSaRcXrJkp7zUJfNI25EvvXL50O9hFUfuS+v8YxGLDKWRJraAtcRsA0vel+WSaNx0AVN8xeD78m3DInCSLnGgXAc3CTdeOUZ81aC58gZMoaXiPCXJc/bY4n0mgJ0axPSy5wR+XihFzYt6zZYSNRXdjO00BNRupkGmX+aijr/ccgLikF7sq/BaYoGhMfMAiBRN4rtoKzTYm+5MVLGrxMzqwSfPMDSmwvGFwkvXbAc6THGMCOuZQWSmhxlcBhIYIoROKmoWMqGDMw33V9yDag+7h/FF77+3va/PD3JSX4oKZW5kc3RyZWFtCmVuZG9iagoyOSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDEwNSA+PgpzdHJlYW0KeJxFjrsRwDAIQ3umYASbn5N9cqnw/m2A+OwG3gFCMjZsyD2KXoZDCJ8OLDeSDJxFxooOvbWa+d46qEkIJxBTdK+utE429Dv14bGB5ErQVoYOEt8Ord8R59Avze2hMsgIGzLD+wGqbCiwCmVuZHN0cmVhbQplbmRvYmoKMzAgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAyODkgPj4Kc3RyZWFtCnicRZJLlsUgCETnWQVLQL66nvTp0ev9T7tAXzIwVUqUC7psEpMGPksGuSr9jMvHJMP4u1ydzIPck2waeQ02uq8Y+F2UwqS3Rc7W+0rdK5lKPoImM/YKIlOCDBmnIec6qlwROBf6XE3xNQyNlEc7kM6vUeGvQzzBYoMpK89mwczcKSbqiATtagU/b+fgNh+7QuS8UXOArjCglq0yV0XgOnWgBY8pAvX5aAdM4zWKPh2X4JDqruyh1Utd0V3WHM2k6odS1nYS1pRieihFpCkFpxRl6aYs16ll8WuKzsZXenmIvMZiFn+8xseqvXXa40yyXFUQRYMezkmCqpyjKuE62/pW6w1o6HkVxtvtxkArwh1Z9T5qVjeBxp7Xd1+//5lxfkYKZW5kc3RyZWFtCmVuZG9iagozMSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDE5MSA+PgpzdHJlYW0KeJxNkDEWwzAIQ3efgiNggbF9nvR1Su+/VtC06RCjPIH1TbiLigWP6CHDTB69eef/K8uAnK0Dt/CYVJz4idE3BTr+lCNNYLGtC4aKryWY7NaQo5nmlS7GwAy12FWP5vhgeCzex5g9OOt0RqYPMmW4alUzTScpErDe8BVaeOtXy3CPWyTFpYIpRlrllzmGZCGrD7pzF4+5Vj0a9iqFyA4IuMeco8PTNt/MLZjPqlg7nX6tEVtvkXS177M93z8RSuoKZW5kc3RyZWFtCmVuZG9iagozMiAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDIxNiA+PgpzdHJlYW0KeJw1UMltxDAM/KsKNhBAPCXV42B/2/83M5QDGOBY5BxkTZMpOeVHXTJN0l1+dfhU8ZDv8DgEvhMtCZ1yVJ4ReFM7ErFE0WO1muwAObqc8DObErbRoUZUCSUDmB6szzBKA5lWT+ixl6O1WkUzW5X1+hDRmRNMQk5Howj0qMkId5GnN+KS32GWjbTAVnxHisSFJ/zjGLoWyzUC8DBZiDQ3JrZE3miBoS2U49VowAor0oHCV0/E9peTPBleeGmKsr4uQG3LVVSbU/fSiympydD/azzj8wdFYFIZCmVuZHN0cmVhbQplbmRvYmoKMzMgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA4MyA+PgpzdHJlYW0KeJxNzbENwDAIBMCeKRgBY/zE+0Sp7P3bAIqSNHBC+gcdLNxUY9o0dlM+GzXLw649lBcp5geMI5Shgf4I6qEuUhUh+E8Vzf4Xkrn6sui6AayDGa0KZW5kc3RyZWFtCmVuZG9iagozNCAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDEyNCA+PgpzdHJlYW0KeJwtTskNwzAM+2cKLhBAlO04mqdFf93/W1IpYIAGL3HwRqAmTg5kTpAX3jzELOJrvAqMwG0tURuvgzaG+Bkd4KpGKXs/TGU7MtYTSW5X+IQKDeoXrc/QZal6di+3KH2a2b3L9UYJOtiMYjZoUPu1T3GNHYn6V39+aDooVwplbmRzdHJlYW0KZW5kb2JqCjM1IDAgb2JqCjw8IC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggNTIgPj4Kc3RyZWFtCnicMzI3VTBQsLRQMDG1UDA0N1MwN7JUSDHkgjFzwSyQZA4XVBWYAZLLgavK4UoDAAY2DlkKZW5kc3RyZWFtCmVuZG9iagozNiAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDE3NCA+PgpzdHJlYW0KeJxFkDGyAzEIQ/s9BUcwQjb2eZJJlX//9gsy2RRevTFYaGFuGxZLHwpnhD39asSwv6Y4w94XsW6i0ZdOGmMahw63Pa44MC75ZUjTgqdVleoRId043UC9hasCRPvCof7Vin2qIprQwNCwGzqBf6WvHfgB167O9YPpR9BuNxFZhMoXBiWiZiKPzfHJm7KkEnkvJfZH6x9nE71uvJ0mKi8ZouwN1NvvFh/X6x9sHkORCmVuZHN0cmVhbQplbmRvYmoKMzcgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzNDEgPj4Kc3RyZWFtCnicPZJLbsQwDEP3OYUuMID1i+3zTNHV9P7bPjpFFwEFKZZISu1pw/q2F0HdYZ1pX36RiW0/Qu9hn8vH+o+2ubt5uK0wr7I77X35Pa3SYrhlWdQteF+xTpBOlUou60k6e9sMyzls1wEPdTlRtSVc/KZS03wuVZKZO+C1GTKZAJ43vjSvxS3J0dlVn9PWPL+/L7hlDI1WQ8Fy0gQVy2ahvU3Kigl0RFT7PvPkSHQdlBw/UTrdsChLGH/M29tq8GaAqK6tKYoSDZ8rV/xHAz8w5GZmPrQKt+kTvJ0NcXCBIgkyG0aKfPOWLj798IZvE/F5Bd3+cJwKUa4kA1dplKd9NNIh5RebzWDfZNOPElyNrV0nKwq5Iz8bPiiO1D+aFvJLe5KW+zkFKkSstLgF9IhFnPWxgsGA59SCUxJK1JPREl84DovXWSrrSluoLHuu8X19/wJjjH96CmVuZHN0cmVhbQplbmRvYmoKMzggMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCA3NyA+PgpzdHJlYW0KeJxNzLsNgDAMhOHeU9wIifEj3gdRmf1bbCQimruv+u0wDCypURM4B85JTfPATVw7kMTD3hdfMInSlPmTaqs6G51K+qK5m0nXAyaTFskKZW5kc3RyZWFtCmVuZG9iagozOSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDMzMCA+PgpzdHJlYW0KeJw1UsttJTEMu7sKNbCA9bfrmUVOSf/XkJoXYABx9KUol5dsqZZ/6pLt0mHyX5dbi4f8LIcPIPaR3BLuckKeFdmieiR6i1aNNd+MEF0XZnjolHgnI+gR+wpbhpVwBu2z7OxBFjEZZhtZjYhe5MGrmGq3X+usIdJWYYaaokblTLNISfwfJfHPIsgvTlespJfTUkxTAr0tyHZK0S+Q59uwEYr9jAV33YMYjTQM2KPJsxJ/XjHi+c6xrxJEir4J4UA9GfTR7gpUuHdEd/OxJK6DFJsrPgjXnHAu8OWRDMvUK+uzAMgGUiegYuvyV7KW3kjGMrymI0r7LL/vfQPyNjpGHNg5TRfQHo4NQglvDymiRN33Chzpg5BdEDDKpfgq0LOKVANHqJPCSXUhIB4BLZb7eCxQyycC8cvsc8iEtDxQ7i1/h3rW1y8JfnzrCmVuZHN0cmVhbQplbmRvYmoKNDAgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxNyA+PgpzdHJlYW0KeJwzNrRQMIDDFEMuABqUAuwKZW5kc3RyZWFtCmVuZG9iago0MSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDE3MSA+PgpzdHJlYW0KeJxNkEsOAzEIQ/c5hS9QKUDI5zxTdTW9/7Z2Ru10xYsJlqFVR4UvPCwQq6HPiqcVqxOtD7wLe4JTkLYI6t2kAdL6p6sbHLvpMlH3JosvrYAzSm9wM6TjKM7RxmyRCMo5VShP228ZkSpTJeXg774QnliUvcNcLtpJxBDUR0OMKdvgFEf4IRwPp9/YN/Csux47lsi6scKUxaQbDShz9+m7aI3jd7KzvD5QfEA6CmVuZHN0cmVhbQplbmRvYmoKNDIgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAzNDYgPj4Kc3RyZWFtCnicPVLLrRwxDLtPFWzgAdbXdj0bvNOm/2tI7SKHgWjJpkRqOhoLu/FjgWrHTscfe+5G34O/j0Vhm8O2YXvAV2OH4fV4MhMHvnNexaqJryfIJ5RBPm/kdrI1K0Wm7kKx0u4Tq48qQp4oO8izkXchS5XkVOnMsnuug9iBuFMJonPJfxG9IfYITVBZcGqQIi+faDyzIuSXnS+22pBUajJ5m2w+Tvj9OEKVnGEyvvBzYSd5ZN7yoGFy5sg/2vR6GI2kb7pm/1FOP6uFS7h5e4mXPmbD+fGGUw8DrcsBIQco2VpDajo+1YsiU37jOCrkRRGZM3UaX7sqwVGjqIn6gj1d50/vOIPeg9IHjctCYXdQKEMdMZuQvNRu6LV8L/aZ2P7dRC9m3NCxZz/da/6FRNNVTdE3ZyuKcjY+GbL2CerhzWEzzta8b9VoW4zc4Eyulc7g3//z/fz+A6Zmg/YKZW5kc3RyZWFtCmVuZG9iago0MyAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDIyMiA+PgpzdHJlYW0KeJxFUblxBDEMy1UFShB/qp7zODr3nxrUes7BLjAiBQJUWmIjm7+wRrniS5ZoIyLws8oueQ/JHiK7UNsgbC0pSPGaFl5LxVBWUH+EtPXia1k8Jy7Ta/BUqs2d2IkMDufE3A+G3QqZZ8Cpb71hRG0ZtdpQ+jFWldYtheisSBXY+l7Oxg+RGjbx/tlgfiCMqH0o62RGA6bKkfyS/NDybg5wcbgfuNLY0YuP3cs6GZHR1Gl5gt3wOQtmAHbk8RtikAszv0wOw3NZMkuOM0G8kHwaMaptRvh7kNf6/gVtdFHbCmVuZHN0cmVhbQplbmRvYmoKNDQgMCBvYmoKPDwgL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxODEgPj4Kc3RyZWFtCnicTZBLEsMgDEP3nEIX6Az+YThPOl2l999WOP1toocdbInhjg5N3MQweiJk4S7NwgufLVSLzouUUP99oFPd9KtrN1wCkbBlMIGNBMcfzVxwc5Z67dMcpUdTmUWSAX59woJlUcG+2yeEFkrn2g2Ss3M2Wv/CZVPW/COVfJMEN/bgJAbm4Jl7sSUG68N3Iusl2+ioc+beb2uBA47mvCbK1cwpaaXKgEclv3zsl/vRZeTxAiUhQ2AKZW5kc3RyZWFtCmVuZG9iago0NSAwIG9iago8PCAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDIxMSA+PgpzdHJlYW0KeJw1UMlxxDAM+6sKNJAZUbykepzZ3/b/DUE5L8EmLjI0MBGBH1F4TqQt/MpQ2VDDd2g0sOkIgemESOAZ5gYpvkViufarYZwUsixJMdyzNSGLE5pUFj3jGBjC9xnr/bPILcaa8WpkS7tInHble3OImEwGm1Bzu7WLYN3q7ypP78Q1v0W4SJJREF3YFO4N8cVzLDN0UwoL2FbU1EtAdlh3q6+cG7Tj3RiQPdGTjcxPM3zqq3HLduGtacr3phAxlgy2oGbfUx+2pCdL/6/xjM8faopTGgplbmRzdHJlYW0KZW5kb2JqCjE4IDAgb2JqCjw8IC9CYXNlRm9udCAvRGVqYVZ1U2VyaWYgL0NoYXJQcm9jcyAxOSAwIFIKL0VuY29kaW5nIDw8Ci9EaWZmZXJlbmNlcyBbIDMyIC9zcGFjZSAzOSAvcXVvdGVzaW5nbGUgNDYgL3BlcmlvZCA0OCAvemVybyAvb25lIC90d28gL3RocmVlIC9mb3VyCi9maXZlIC9zaXggL3NldmVuIC9laWdodCA2NSAvQSA2OCAvRCA4MSAvUSA5NyAvYSAvYiAvYyAxMDEgL2UgMTA5IC9tIC9uIC9vCjExNCAvciAvcyAvdCAvdSBdCi9UeXBlIC9FbmNvZGluZyA+PgovRmlyc3RDaGFyIDAgL0ZvbnRCQm94IFsgLTc3MCAtMzQ3IDIxMDYgMTExMCBdIC9Gb250RGVzY3JpcHRvciAxNyAwIFIKL0ZvbnRNYXRyaXggWyAwLjAwMSAwIDAgMC4wMDEgMCAwIF0gL0xhc3RDaGFyIDI1NSAvTmFtZSAvRGVqYVZ1U2VyaWYKL1N1YnR5cGUgL1R5cGUzIC9UeXBlIC9Gb250IC9XaWR0aHMgMTYgMCBSID4+CmVuZG9iagoxNyAwIG9iago8PCAvQXNjZW50IDkyOSAvQ2FwSGVpZ2h0IDAgL0Rlc2NlbnQgLTIzNiAvRmxhZ3MgMzIKL0ZvbnRCQm94IFsgLTc3MCAtMzQ3IDIxMDYgMTExMCBdIC9Gb250TmFtZSAvRGVqYVZ1U2VyaWYgL0l0YWxpY0FuZ2xlIDAKL01heFdpZHRoIDEzNDIgL1N0ZW1WIDAgL1R5cGUgL0ZvbnREZXNjcmlwdG9yIC9YSGVpZ2h0IDAgPj4KZW5kb2JqCjE2IDAgb2JqClsgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAKNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCA2MDAgNjAwIDYwMCAzMTggNDAyIDQ2MCA4MzggNjM2Cjk1MCA4OTAgMjc1IDM5MCAzOTAgNTAwIDgzOCAzMTggMzM4IDMxOCAzMzcgNjM2IDYzNiA2MzYgNjM2IDYzNiA2MzYgNjM2IDYzNgo2MzYgNjM2IDMzNyAzMzcgODM4IDgzOCA4MzggNTM2IDEwMDAgNzIyIDczNSA3NjUgODAyIDczMCA2OTQgNzk5IDg3MiAzOTUKNDAxIDc0NyA2NjQgMTAyNCA4NzUgODIwIDY3MyA4MjAgNzUzIDY4NSA2NjcgODQzIDcyMiAxMDI4IDcxMiA2NjAgNjk1IDM5MAozMzcgMzkwIDgzOCA1MDAgNTAwIDU5NiA2NDAgNTYwIDY0MCA1OTIgMzcwIDY0MCA2NDQgMzIwIDMxMCA2MDYgMzIwIDk0OCA2NDQKNjAyIDY0MCA2NDAgNDc4IDUxMyA0MDIgNjQ0IDU2NSA4NTYgNTY0IDU2NSA1MjcgNjM2IDMzNyA2MzYgODM4IDYwMCA2MzYgNjAwCjMxOCAzNzAgNTE4IDEwMDAgNTAwIDUwMCA1MDAgMTM0MiA2ODUgNDAwIDExMzcgNjAwIDY5NSA2MDAgNjAwIDMxOCAzMTggNTExCjUxMSA1OTAgNTAwIDEwMDAgNTAwIDEwMDAgNTEzIDQwMCA5ODkgNjAwIDUyNyA2NjAgMzE4IDQwMiA2MzYgNjM2IDYzNiA2MzYKMzM3IDUwMCA1MDAgMTAwMCA0NzUgNjEyIDgzOCAzMzggMTAwMCA1MDAgNTAwIDgzOCA0MDEgNDAxIDUwMCA2NTAgNjM2IDMxOAo1MDAgNDAxIDQ3MCA2MTIgOTY5IDk2OSA5NjkgNTM2IDcyMiA3MjIgNzIyIDcyMiA3MjIgNzIyIDEwMDEgNzY1IDczMCA3MzAKNzMwIDczMCAzOTUgMzk1IDM5NSAzOTUgODA3IDg3NSA4MjAgODIwIDgyMCA4MjAgODIwIDgzOCA4MjAgODQzIDg0MyA4NDMgODQzCjY2MCA2NzYgNjY4IDU5NiA1OTYgNTk2IDU5NiA1OTYgNTk2IDk0MCA1NjAgNTkyIDU5MiA1OTIgNTkyIDMyMCAzMjAgMzIwIDMyMAo2MDIgNjQ0IDYwMiA2MDIgNjAyIDYwMiA2MDIgODM4IDYwMiA2NDQgNjQ0IDY0NCA2NDQgNTY1IDY0MCA1NjUgXQplbmRvYmoKMTkgMCBvYmoKPDwgL0EgMjAgMCBSIC9EIDIxIDAgUiAvUSAyMiAwIFIgL2EgMjMgMCBSIC9iIDI0IDAgUiAvYyAyNSAwIFIgL2UgMjYgMCBSCi9laWdodCAyNyAwIFIgL2ZpdmUgMjggMCBSIC9mb3VyIDI5IDAgUiAvbSAzMCAwIFIgL24gMzEgMCBSIC9vIDMyIDAgUgovb25lIDMzIDAgUiAvcGVyaW9kIDM0IDAgUiAvcXVvdGVzaW5nbGUgMzUgMCBSIC9yIDM2IDAgUiAvcyAzNyAwIFIKL3NldmVuIDM4IDAgUiAvc2l4IDM5IDAgUiAvc3BhY2UgNDAgMCBSIC90IDQxIDAgUiAvdGhyZWUgNDIgMCBSIC90d28gNDMgMCBSCi91IDQ0IDAgUiAvemVybyA0NSAwIFIgPj4KZW5kb2JqCjMgMCBvYmoKPDwgL0YxIDE4IDAgUiA+PgplbmRvYmoKNCAwIG9iago8PCAvQTEgPDwgL0NBIDAgL1R5cGUgL0V4dEdTdGF0ZSAvY2EgMSA+PgovQTIgPDwgL0NBIDEgL1R5cGUgL0V4dEdTdGF0ZSAvY2EgMSA+PgovQTMgPDwgL0NBIDAuOCAvVHlwZSAvRXh0R1N0YXRlIC9jYSAwLjggPj4gPj4KZW5kb2JqCjUgMCBvYmoKPDwgPj4KZW5kb2JqCjYgMCBvYmoKPDwgPj4KZW5kb2JqCjcgMCBvYmoKPDwgL00wIDEyIDAgUiAvTTEgMTMgMCBSIC9NMiAxNCAwIFIgL00zIDE1IDAgUiA+PgplbmRvYmoKMTIgMCBvYmoKPDwgL0JCb3ggWyAtOCAtOCA4IDggXSAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDEzMSAvU3VidHlwZSAvRm9ybQovVHlwZSAvWE9iamVjdCA+PgpzdHJlYW0KeJxtkEEOhCAMRfc9RS/wSUtFZevSa7iZTOL9twNxQEzdNNC+PH5R/pLwTqXA+CQJS06z5HrTkNK6TIwY5tWyKMegUS3WznU4qM/QcGN0i7EUptTW6Hijm+k23pM/+rBZIUY/HA6vhHsWQyZcKTEGh98LL9vD/xGeXtTAH6KNfmNaQ/0KZW5kc3RyZWFtCmVuZG9iagoxMyAwIG9iago8PCAvQkJveCBbIC04IC04IDggOCBdIC9GaWx0ZXIgL0ZsYXRlRGVjb2RlIC9MZW5ndGggMTMxIC9TdWJ0eXBlIC9Gb3JtCi9UeXBlIC9YT2JqZWN0ID4+CnN0cmVhbQp4nG2QQQ6EIAxF9z1FL/BJS0Vl69JruJlM4v23A3FATN000L48flH+kvBOpcD4JAlLTrPketOQ0rpMjBjm1bIox6BRLdbOdTioz9BwY3SLsRSm1NboeKOb6Tbekz/6sFkhRj8cDq+EexZDJlwpMQaH3wsv28P/EZ5e1MAfoo1+Y1pD/QplbmRzdHJlYW0KZW5kb2JqCjE0IDAgb2JqCjw8IC9CQm94IFsgLTggLTggOCA4IF0gL0ZpbHRlciAvRmxhdGVEZWNvZGUgL0xlbmd0aCAxMzEgL1N1YnR5cGUgL0Zvcm0KL1R5cGUgL1hPYmplY3QgPj4Kc3RyZWFtCnicbZBBDoQgDEX3PUUv8ElLRWXr0mu4mUzi/bcDcUBM3TTQvjx+Uf6S8E6lwPgkCUtOs+R605DSukyMGObVsijHoFEt1s51OKjP0HBjdIuxFKbU1uh4o5vpNt6TP/qwWSFGPxwOr4R7FkMmXCkxBoffCy/bw/8Rnl7UwB+ijX5jWkP9CmVuZHN0cmVhbQplbmRvYmoKMTUgMCBvYmoKPDwgL0JCb3ggWyAtOCAtOCA4IDggXSAvRmlsdGVyIC9GbGF0ZURlY29kZSAvTGVuZ3RoIDEzMSAvU3VidHlwZSAvRm9ybQovVHlwZSAvWE9iamVjdCA+PgpzdHJlYW0KeJxtkEEOhCAMRfc9RS/wSUtFZevSa7iZTOL9twNxQEzdNNC+PH5R/pLwTqXA+CQJS06z5HrTkNK6TIwY5tWyKMegUS3WznU4qM/QcGN0i7EUptTW6Hijm+k23pM/+rBZIUY/HA6vhHsWQyZcKTEGh98LL9vD/xGeXtTAH6KNfmNaQ/0KZW5kc3RyZWFtCmVuZG9iagoyIDAgb2JqCjw8IC9Db3VudCAxIC9LaWRzIFsgMTAgMCBSIF0gL1R5cGUgL1BhZ2VzID4+CmVuZG9iago0NiAwIG9iago8PCAvQ3JlYXRpb25EYXRlIChEOjIwMjExMTE2MTEyMDQwKzAyJzAwJykKL0NyZWF0b3IgKE1hdHBsb3RsaWIgdjMuMy40LCBodHRwczovL21hdHBsb3RsaWIub3JnKQovUHJvZHVjZXIgKE1hdHBsb3RsaWIgcGRmIGJhY2tlbmQgdjMuMy40KSA+PgplbmRvYmoKeHJlZgowIDQ3CjAwMDAwMDAwMDAgNjU1MzUgZiAKMDAwMDAwMDAxNiAwMDAwMCBuIAowMDAwMDEzOTI1IDAwMDAwIG4gCjAwMDAwMTI2MjggMDAwMDAgbiAKMDAwMDAxMjY2MCAwMDAwMCBuIAowMDAwMDEyODAyIDAwMDAwIG4gCjAwMDAwMTI4MjMgMDAwMDAgbiAKMDAwMDAxMjg0NCAwMDAwMCBuIAowMDAwMDAwMDY1IDAwMDAwIG4gCjAwMDAwMDAzOTQgMDAwMDAgbiAKMDAwMDAwMDIwOCAwMDAwMCBuIAowMDAwMDAzMjc5IDAwMDAwIG4gCjAwMDAwMTI5MDkgMDAwMDAgbiAKMDAwMDAxMzE2MyAwMDAwMCBuIAowMDAwMDEzNDE3IDAwMDAwIG4gCjAwMDAwMTM2NzEgMDAwMDAgbiAKMDAwMDAxMTI0NSAwMDAwMCBuIAowMDAwMDExMDQ1IDAwMDAwIG4gCjAwMDAwMTA1OTEgMDAwMDAgbiAKMDAwMDAxMjMwMCAwMDAwMCBuIAowMDAwMDAzMzAwIDAwMDAwIG4gCjAwMDAwMDM0ODQgMDAwMDAgbiAKMDAwMDAwMzcyMyAwMDAwMCBuIAowMDAwMDA0MTAxIDAwMDAwIG4gCjAwMDAwMDQ0ODUgMDAwMDAgbiAKMDAwMDAwNDgxNiAwMDAwMCBuIAowMDAwMDA1MTI3IDAwMDAwIG4gCjAwMDAwMDU0NDQgMDAwMDAgbiAKMDAwMDAwNTg5OCAwMDAwMCBuIAowMDAwMDA2MjI0IDAwMDAwIG4gCjAwMDAwMDY0MDIgMDAwMDAgbiAKMDAwMDAwNjc2NCAwMDAwMCBuIAowMDAwMDA3MDI4IDAwMDAwIG4gCjAwMDAwMDczMTcgMDAwMDAgbiAKMDAwMDAwNzQ3MiAwMDAwMCBuIAowMDAwMDA3NjY5IDAwMDAwIG4gCjAwMDAwMDc3OTMgMDAwMDAgbiAKMDAwMDAwODA0MCAwMDAwMCBuIAowMDAwMDA4NDU0IDAwMDAwIG4gCjAwMDAwMDg2MDMgMDAwMDAgbiAKMDAwMDAwOTAwNiAwMDAwMCBuIAowMDAwMDA5MDk1IDAwMDAwIG4gCjAwMDAwMDkzMzkgMDAwMDAgbiAKMDAwMDAwOTc1OCAwMDAwMCBuIAowMDAwMDEwMDUzIDAwMDAwIG4gCjAwMDAwMTAzMDcgMDAwMDAgbiAKMDAwMDAxMzk4NSAwMDAwMCBuIAp0cmFpbGVyCjw8IC9JbmZvIDQ2IDAgUiAvUm9vdCAxIDAgUiAvU2l6ZSA0NyA+PgpzdGFydHhyZWYKMTQxNDIKJSVFT0YK\n",
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plotQuartet(data,colors)"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en",
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"The four datasets are obviously very different."
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en",
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Statistics "
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en"
},
"source": [
"Let us calculate the average $\\bar{x}$, $\\bar{y}$ and the variables $s_x^2$, $s_y^2$ for each data set and plot it"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:20:40.846012Z",
"iopub.status.busy": "2021-11-16T10:20:40.844307Z",
"iopub.status.idle": "2021-11-16T10:20:40.847130Z",
"shell.execute_reply": "2021-11-16T10:20:40.847939Z"
}
},
"outputs": [],
"source": [
"def drawTable(cells,columns,colors,title=''):\n",
" \"\"\"Function to draw a table of values per data set\"\"\"\n",
" rows = np.arange(1,len(cells)+1)\n",
"\n",
" fig, ax = plt.subplots(1,1,figsize=(1.5*len(columns),4))\n",
" fig.suptitle(title)\n",
" \n",
" tab = ax.table(cellText=cells,\n",
" colLabels=columns,\n",
" rowLabels=rows,\n",
" rowColours=colors,\n",
" bbox=[0,0,1,1])\n",
" tab.auto_set_column_width(range(len(columns)))\n",
" tab.set_fontsize(15)\n",
" ax.axis('tight')\n",
" ax.axis('off')"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:20:40.860850Z",
"iopub.status.busy": "2021-11-16T10:20:40.859784Z",
"iopub.status.idle": "2021-11-16T10:20:41.899614Z",
"shell.execute_reply": "2021-11-16T10:20:41.898824Z"
},
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"application/pdf": 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\n",
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"cells = np.round(np.hstack((data.mean(axis=1), data.var(axis=1))),2)\n",
"cols = [r'$\\bar{x}$',r'$\\bar{y}$',r'$s_x^2$',r'$s_y^2$']\n",
"drawTable(cells, cols, colors,'Statistics on Anscombe\\'s Quartet')"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en",
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Linear regression "
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en"
},
"source": [
"We will perform a [simple linear regression](https://en.wikipedia.org/wiki/Simple_linear_regression) on each of the data sets. Linear regression consists of determining the line\n",
"\n",
"$$y = ax + b\\quad,$$\n",
"\n",
"with"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\\begin{align*}\n",
" a &= \\frac{c_{xy}}{s_x^2} \n",
" = \\frac{\\tfrac1{N-1}\\sum_{i=1}^N (x_i-\\bar{x})(y_i-\\bar{y})}{\n",
" \\tfrac1{N-1}\\sum_{i=1}(x_i-\\bar{x})^2}\\\\\n",
" b &= \\bar y - a\\bar x\\quad,\n",
"\\end{align*}"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en"
},
"source": [
"where $c_{xy}$ is the covariance between $x$ and $y$ and $s_x^2$ is the variance of $x$. "
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en",
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"The correlations coefficient"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$r = \\frac{c_{xy}}{\\sqrt{s_x^2 s_y^2}}\\quad,$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en"
},
"source": [
"tells us how correlated $x$ and $y$ are - or naively how close to a line the points fall. "
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en",
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"The uncertainty on $a$ is given by"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"source": [
"\\begin{align*}\n",
" \\delta_a &= \\sqrt{(1-r^2)\\frac1{\\nu}\\frac{s_y^2}{s_x^2}}\\quad.\n",
"\\end{align*}"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en",
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Here the $s_y^2$ is the variance of $y$, and $\\nu=N-2$ is the number of degrees of freedom ($N$ from data, $-2$ corresponding to the two parameters $a$ and $b$). The uncertainty on $b$ is given by "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\\delta_b = \\delta_a \\sqrt{\\frac1N\\sum_{i}^{N} x_i^2}\\quad.$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en",
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"The probability of the value $a$, given our points and with $\\nu$ degrees of freedom is given by a [$t$-distribution](https://en.wikipedia.org/wiki/Student's_t-distribution) where"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\\begin{align*}\n",
" t &= r \\sqrt{\\frac{\\nu}{(1+r)(1-r)}}\\quad,\n",
"\\end{align*}"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en"
},
"source": [
"and"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\\begin{align*}\n",
" P(t|(x,y),\\nu) &= 1-\\int_{-\\infty}^t \\mathrm{d}t' f_t(t';\\nu)\\quad.\n",
"\\end{align*}"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en",
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"The probability function of a $t$ distributed random variable $X\\sim T$ is"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$f_t(t;\\nu) = \\frac{\\Gamma\\left(\\tfrac{\\nu+1}{2}\\right)}{\\sqrt{\\nu\\pi}\\Gamma\\left(\\tfrac{\\nu}{2}\\right)}\n",
"\\left(1+\\frac{x^2}{\\nu}\\right)^{-\\frac{\\nu+1}{2}}\\quad.$$"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en",
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"We can now perform the linear regression on each of our data sets. We will also calculate $\\chi^2$ and determine the probability $P(\\chi^2|\\nu)$ with"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$\\chi^2 = \\sum_{i=1}^N (y_i-b-ax_i)^2\\quad.$$"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:20:41.915514Z",
"iopub.status.busy": "2021-11-16T10:20:41.914017Z",
"iopub.status.idle": "2021-11-16T10:20:41.916662Z",
"shell.execute_reply": "2021-11-16T10:20:41.917480Z"
}
},
"outputs": [],
"source": [
"def linregOne(data,xrange,color,axes,label):\n",
" \"\"\"Function do and draw linear regression on one data set\"\"\"\n",
" a,b,r,p,ea = sp.stats.linregress(data)\n",
" eb = ea * np.sqrt((data[:,0]**2).mean())\n",
" chi2 = np.sum((data[:,1]-b-a*data[:,0])**2)\n",
" pchi2 = sp.stats.chi2.sf(chi2,len(data[:,0])-2)\n",
" axes.plot(data[:,0],data[:,1],'o',color=color,label=label)\n",
" axes.plot(xrange,b+a*xrange,'--',color=color,\n",
" label=label.replace('Data','Line'))\n",
" \n",
" return [a,b,r,ea,eb,p*100,chi2,pchi2*100]"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:20:41.932080Z",
"iopub.status.busy": "2021-11-16T10:20:41.930265Z",
"iopub.status.idle": "2021-11-16T10:20:41.933447Z",
"shell.execute_reply": "2021-11-16T10:20:41.934275Z"
}
},
"outputs": [],
"source": [
"def linregQuartet(data,colors):\n",
" \"\"\"Function to do and draw linear regression on full quarted\"\"\"\n",
" fig, ax = plt.subplots(ncols=2,nrows=2,figsize=(8,8),\n",
" gridspec_kw=dict(hspace=0,wspace=0),\n",
" sharex=True,sharey=True)\n",
" fig.suptitle('Linear regression on Anscombe\\'s Quartet')\n",
" result = np.empty((0,8))\n",
"\n",
" xrange = np.array([data[...,0].min()-1,data[...,0].max()+1])\n",
" for i,(da,axes,color) in enumerate(zip(data,ax.ravel(),colors)):\n",
" res = linregOne(da,xrange,color,axes,f'Data {i+1}')\n",
" result = np.vstack((result,res))\n",
" axes.legend()\n",
" \n",
" return result"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"caption": {
"da": "Lineær regression",
"en": "Linear regression"
},
"execution": {
"iopub.execute_input": "2021-11-16T10:20:41.946212Z",
"iopub.status.busy": "2021-11-16T10:20:41.945192Z",
"iopub.status.idle": "2021-11-16T10:20:44.007691Z",
"shell.execute_reply": "2021-11-16T10:20:44.008368Z"
},
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
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\n",
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"result = linregQuartet(data,colors)"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en",
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"Off-hand, the four lines look pretty similar. Fortunately, we have some numbers to look at. "
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"execution": {
"iopub.execute_input": "2021-11-16T10:20:44.027877Z",
"iopub.status.busy": "2021-11-16T10:20:44.016420Z",
"iopub.status.idle": "2021-11-16T10:20:45.415168Z",
"shell.execute_reply": "2021-11-16T10:20:45.415731Z"
},
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"application/pdf": 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\n",
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"cells = np.round(result,2)\n",
"cols = [r'$a$',r'$b$',r'$r$',r'$\\delta_a$',r'$\\delta_b$',\n",
" r'$P(a)$ (%)',r'$\\chi^2$', r'$P(\\chi^2)$ (%)']\n",
"drawTable(cells,cols,colors)"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en",
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"From the table above we see that we _cannot_ distinguish the four data sets from each other:\n",
"\n",
"- In all four cases we find the same line\n",
"\n",
"$$y = (3.0\\pm1.1) + (0.50\\pm0.12)x$$\n",
" \n",
"- The probabilities of these are all equally bad\n",
"- All $\\chi^2$ comes to the same value with the same probability."
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en",
"slideshow": {
"slide_type": "subslide"
}
},
"source": [
"So where are we now? We cannot use a linear regression to distinguish these four datasets from each other. If we only had the values from the analysis, we would in all cases assume that the model\n",
"\n",
"$$y=b+ax$$\n",
"\n",
"was adequate. On the other hand, we can visually very easily distinguish the data sets from each other."
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en",
"slideshow": {
"slide_type": "fragment"
}
},
"source": [
"- Data set 1 (blue) looks like something we would expect from a linear dependence and $y$ values normally distributed around the line.\n",
"- In data set 2 (orange) there is a clear dependence between $x$ and $y$ which, however, is not linear. In fact, it looks like $y$ has a square dependence on $x$.\n",
"- There is a clear linear dependency between $x$ and $y$ in the third data set (green) _except_ at one point. The rest of the points lie on a straight line, though not with the slope found.\n",
"- In the last data set (red), there is _no_ dependence between $x$ and $y$, but as above, there is one point that pulls in the linear regression."
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en",
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Conclusion"
]
},
{
"cell_type": "markdown",
"metadata": {
"lang": "en"
},
"source": [
"In his article, Anscombe does not indicate any other way of distinguishing the four datasets from each other than by visual inspection. Nor is it obvious that there _is_ another quantitative way of doing this. The main point of Anscombe's article is to say that we must _also_ use graphic representations in our statistical work. In 1973, when Anscombe published his article, computers were not as powerful as they are today, and a point for Anscombe was that we had to work to solve _that_ problem."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"> Unfortunately, most persons who have recourse to a\n",
"> computer for statistical analysis of data are not much\n",
"> interested either in computer programming or in sta-\n",
"> tistical method, being primarily concerned with their\n",
"> own proper business. Hence the common use of library\n",
"> programs and various statistical packages. Most of\n",
"> these originated in the pre-visual era. The user is not\n",
"> showered with graphical displays. He can get them\n",
"> only with trouble, cunning and a fighting spirit. It's\n",
"> time that was changed."
]
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"Today we have good opportunities to easily and quickly make graphic representations of high quality, as illustrated in this note using _Python_, _NumPy_, _SciPy_ and <_> MatPlotLib <_>. Let us finish where we started and finish the title of this note:\n",
"\n",
"> **Ancsombes Quartet, or: How I stopped worrying and love a good plot**"
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"# References"
]
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"- [Anscombe, Francis J. Graphs in statistical analysis. _The American Statistician_, **27**, 17–21](https://doi.org/10.2307/2682899)"
]
}
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