ipython notebook for demonstrating chi^2 test for goodness of fit, some confidence intervals

chi-squared test, confidence intervals.ipynb

{
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  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Setup, as usual"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import scipy.stats as sps"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import matplotlib.pylab as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Define some x values, and a set of uncertainties which range between 0.1 and 0.3."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = np.linspace(0,3,1000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "unc_y = sps.uniform(loc=0.1,scale=0.3).rvs(size=1000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": true,
     "input": [
      "unc_y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "array([ 0.10216633,  0.27018913,  0.15767724,  0.10862438,  0.20397054,\n",
        "        0.15794319,  0.31282561,  0.23260152,  0.10627931,  0.13797688,\n",
        "        0.35922886,  0.25488782,  0.14191069,  0.34295542,  0.2901974 ,\n",
        "        0.33960413,  0.3970181 ,  0.32316568,  0.11548779,  0.10818265,\n",
        "        0.11329229,  0.34133473,  0.30629405,  0.25978934,  0.1186692 ,\n",
        "        0.35960511,  0.38003277,  0.29779231,  0.22528064,  0.33568386,\n",
        "        0.34430634,  0.14801682,  0.25696423,  0.12529844,  0.13494679,\n",
        "        0.1473631 ,  0.31049867,  0.33041936,  0.19650345,  0.185577  ,\n",
        "        0.12282243,  0.35645973,  0.26782032,  0.13302257,  0.28419825,\n",
        "        0.19109748,  0.39052839,  0.18127591,  0.10623178,  0.26546022,\n",
        "        0.11589029,  0.17601353,  0.22647002,  0.29785132,  0.17721078,\n",
        "        0.35751718,  0.31205948,  0.10711282,  0.36275372,  0.16044644,\n",
        "        0.38877817,  0.11102063,  0.27325703,  0.20242968,  0.10435264,\n",
        "        0.25106182,  0.12835407,  0.25806447,  0.31336911,  0.37713357,\n",
        "        0.38952205,  0.25249316,  0.19637402,  0.11401988,  0.39714709,\n",
        "        0.17918303,  0.18392369,  0.1516111 ,  0.13667847,  0.12959539,\n",
        "        0.31088653,  0.28270477,  0.20000458,  0.39430247,  0.39581787,\n",
        "        0.30556208,  0.13796356,  0.35154574,  0.365855  ,  0.12757876,\n",
        "        0.12054907,  0.17855238,  0.14918736,  0.22007669,  0.24044694,\n",
        "        0.16237772,  0.38862363,  0.2713936 ,  0.16554684,  0.38819659,\n",
        "        0.39176455,  0.22219396,  0.23921399,  0.32467068,  0.31575573,\n",
        "        0.14664254,  0.20153573,  0.30327224,  0.23489666,  0.19545848,\n",
        "        0.23247625,  0.39260066,  0.2962883 ,  0.11181117,  0.16363184,\n",
        "        0.19449927,  0.33099907,  0.10857431,  0.3051965 ,  0.35708196,\n",
        "        0.39380706,  0.21003524,  0.12224448,  0.35833533,  0.13879131,\n",
        "        0.37794588,  0.19966205,  0.30123757,  0.28174149,  0.34622543,\n",
        "        0.30826817,  0.35081861,  0.34923455,  0.23115029,  0.12673497,\n",
        "        0.1419739 ,  0.16104715,  0.3307849 ,  0.3111381 ,  0.27354794,\n",
        "        0.36035595,  0.22478714,  0.26914919,  0.11295718,  0.11445527,\n",
        "        0.24760119,  0.39127459,  0.15761869,  0.21767269,  0.16882438,\n",
        "        0.36967279,  0.29764255,  0.29689861,  0.10693595,  0.26059926,\n",
        "        0.19246536,  0.24473801,  0.37835071,  0.11461481,  0.16794682,\n",
        "        0.2883325 ,  0.16859477,  0.17380515,  0.29921635,  0.18826106,\n",
        "        0.30855608,  0.20609633,  0.37747386,  0.3217377 ,  0.19335866,\n",
        "        0.32690712,  0.14589037,  0.20806287,  0.10659596,  0.32278226,\n",
        "        0.34488796,  0.37803566,  0.27356921,  0.1134985 ,  0.19433613,\n",
        "        0.26615752,  0.19436959,  0.10343824,  0.16068046,  0.17278822,\n",
        "        0.35513613,  0.39719759,  0.24323729,  0.18635771,  0.24111237,\n",
        "        0.32192754,  0.14855111,  0.3593992 ,  0.36976639,  0.10459432,\n",
        "        0.18821851,  0.18523542,  0.10870044,  0.34629036,  0.26794838,\n",
        "        0.38746875,  0.14459198,  0.34111735,  0.13778403,  0.25199204,\n",
        "        0.2376846 ,  0.12702275,  0.32818263,  0.10576627,  0.25396912,\n",
        "        0.16152364,  0.11702018,  0.28661078,  0.39595912,  0.22267044,\n",
        "        0.29649901,  0.21743668,  0.18867033,  0.22057456,  0.17003509,\n",
        "        0.38415417,  0.23690885,  0.37560807,  0.25772663,  0.13436604,\n",
        "        0.38330209,  0.11673201,  0.29971122,  0.17856444,  0.22628696,\n",
        "        0.18777478,  0.1227442 ,  0.28868283,  0.10148671,  0.29356233,\n",
        "        0.14997073,  0.21714682,  0.20800176,  0.13233819,  0.21974258,\n",
        "        0.16811936,  0.2170017 ,  0.27417101,  0.12824934,  0.21408775,\n",
        "        0.20711986,  0.21003473,  0.1343599 ,  0.33317334,  0.21599612,\n",
        "        0.32833885,  0.29696145,  0.33175003,  0.32171223,  0.16123364,\n",
        "        0.14059047,  0.13568597,  0.21157371,  0.10667258,  0.31761534,\n",
        "        0.330646  ,  0.35584755,  0.33067774,  0.35437266,  0.16383071,\n",
        "        0.22650126,  0.19654719,  0.32146466,  0.24603149,  0.37625707,\n",
        "        0.32986537,  0.15448412,  0.31770562,  0.1778612 ,  0.31715566,\n",
        "        0.20164348,  0.17481247,  0.23149658,  0.26519164,  0.37461814,\n",
        "        0.10964821,  0.16361225,  0.22727194,  0.20683167,  0.32708794,\n",
        "        0.38056997,  0.1961193 ,  0.12508951,  0.36162854,  0.34885374,\n",
        "        0.30551375,  0.23597909,  0.17557257,  0.15261475,  0.17551676,\n",
        "        0.11509012,  0.22281376,  0.23057391,  0.31713701,  0.33623237,\n",
        "        0.36509189,  0.30758553,  0.38871875,  0.12976454,  0.19916754,\n",
        "        0.14695487,  0.16679594,  0.28390751,  0.10487015,  0.26943428,\n",
        "        0.21131173,  0.1443201 ,  0.24727235,  0.24530377,  0.11526088,\n",
        "        0.21323279,  0.30946065,  0.20145398,  0.27139897,  0.278367  ,\n",
        "        0.399504  ,  0.2275028 ,  0.25715113,  0.15188205,  0.18120528,\n",
        "        0.24474742,  0.12600401,  0.18865647,  0.23380324,  0.37780435,\n",
        "        0.25672111,  0.24377577,  0.10701229,  0.25698709,  0.39716363,\n",
        "        0.30790086,  0.24249628,  0.13827744,  0.15421689,  0.17008871,\n",
        "        0.27741007,  0.16968371,  0.26264967,  0.19029066,  0.37798698,\n",
        "        0.30087851,  0.33283946,  0.12579653,  0.17711353,  0.19698711,\n",
        "        0.13096917,  0.18190778,  0.17976255,  0.29369162,  0.14600906,\n",
        "        0.35445285,  0.23363128,  0.16057466,  0.3468681 ,  0.10245169,\n",
        "        0.24450778,  0.17798933,  0.1130744 ,  0.38093145,  0.1263928 ,\n",
        "        0.21624316,  0.23603977,  0.32895615,  0.34031726,  0.36475026,\n",
        "        0.23819533,  0.21199272,  0.35956773,  0.13543314,  0.24986284,\n",
        "        0.31342983,  0.25032047,  0.39773985,  0.22867729,  0.28863817,\n",
        "        0.29972447,  0.38743254,  0.23682356,  0.28999799,  0.27397988,\n",
        "        0.19813397,  0.10230899,  0.31991158,  0.32595785,  0.2974383 ,\n",
        "        0.38830327,  0.21889493,  0.13467741,  0.15219898,  0.13492315,\n",
        "        0.30838694,  0.26526918,  0.21402426,  0.10675591,  0.29318912,\n",
        "        0.30091388,  0.23370861,  0.15820059,  0.39582245,  0.2592133 ,\n",
        "        0.36859404,  0.21442448,  0.15636554,  0.33908164,  0.22398963,\n",
        "        0.3822394 ,  0.29847309,  0.38057105,  0.3686075 ,  0.10571254,\n",
        "        0.3010516 ,  0.19744859,  0.38269655,  0.21891424,  0.12464287,\n",
        "        0.23879442,  0.27448557,  0.24659881,  0.17705558,  0.1518335 ,\n",
        "        0.34054801,  0.33786196,  0.38114314,  0.12449498,  0.14820551,\n",
        "        0.3626601 ,  0.32410391,  0.37516477,  0.16201114,  0.22453493,\n",
        "        0.15924012,  0.22619   ,  0.23428093,  0.16674686,  0.19982069,\n",
        "        0.21061346,  0.24655907,  0.1531913 ,  0.28970768,  0.31703387,\n",
        "        0.28849491,  0.22646674,  0.17039888,  0.28693393,  0.17510345,\n",
        "        0.37939939,  0.24516453,  0.16428944,  0.25812735,  0.23731367,\n",
        "        0.20030906,  0.20721686,  0.30151963,  0.25331299,  0.28671249,\n",
        "        0.38861415,  0.1035103 ,  0.2097175 ,  0.13309142,  0.2133482 ,\n",
        "        0.35702505,  0.2598072 ,  0.27792883,  0.38619256,  0.34993462,\n",
        "        0.29281688,  0.33873627,  0.2297547 ,  0.22678195,  0.36676181,\n",
        "        0.39557604,  0.36092058,  0.39164456,  0.32491895,  0.31383022,\n",
        "        0.30303544,  0.34374   ,  0.31213074,  0.14690526,  0.36436743,\n",
        "        0.22428017,  0.2032013 ,  0.34779925,  0.22627841,  0.23223619,\n",
        "        0.15023201,  0.33963992,  0.25906486,  0.34580742,  0.39608577,\n",
        "        0.14794137,  0.25913681,  0.17861085,  0.2777828 ,  0.39336454,\n",
        "        0.35528396,  0.11977524,  0.32960942,  0.26739443,  0.30230507,\n",
        "        0.16498064,  0.34582172,  0.14793272,  0.35547603,  0.14525994,\n",
        "        0.39395659,  0.2351164 ,  0.23221217,  0.17376561,  0.15996013,\n",
        "        0.21084839,  0.3091015 ,  0.33245587,  0.11718564,  0.37974225,\n",
        "        0.18049999,  0.35060156,  0.32409177,  0.16527033,  0.28077022,\n",
        "        0.3018639 ,  0.12084235,  0.30007243,  0.30189788,  0.38058679,\n",
        "        0.10338151,  0.22854673,  0.21469799,  0.16835349,  0.18667345,\n",
        "        0.36147984,  0.21965372,  0.3382954 ,  0.14348932,  0.19863664,\n",
        "        0.36693865,  0.26375978,  0.29760092,  0.11637781,  0.1608433 ,\n",
        "        0.34564013,  0.32417463,  0.26999063,  0.35804686,  0.39635298,\n",
        "        0.39444167,  0.36926296,  0.13842855,  0.37787463,  0.17788669,\n",
        "        0.10302373,  0.24393119,  0.27850217,  0.26871045,  0.22576524,\n",
        "        0.29379901,  0.22085757,  0.3404364 ,  0.33357274,  0.20494995,\n",
        "        0.33181   ,  0.18359492,  0.18748317,  0.17804734,  0.30384045,\n",
        "        0.24820528,  0.38345672,  0.23721871,  0.32453356,  0.33078216,\n",
        "        0.22446706,  0.24407489,  0.14262553,  0.11599013,  0.21618143,\n",
        "        0.20485365,  0.34429157,  0.27584406,  0.13558521,  0.14203792,\n",
        "        0.38565862,  0.30867264,  0.38419795,  0.15247763,  0.19952685,\n",
        "        0.35121241,  0.15297364,  0.19373766,  0.20329829,  0.22044481,\n",
        "        0.16686817,  0.25027309,  0.18546786,  0.30649268,  0.25169693,\n",
        "        0.28736937,  0.37895169,  0.24860315,  0.16637796,  0.33613481,\n",
        "        0.15494636,  0.31897446,  0.31188006,  0.19882412,  0.39185577,\n",
        "        0.18003989,  0.36566127,  0.16871583,  0.10350172,  0.13609504,\n",
        "        0.20715992,  0.27097587,  0.3145615 ,  0.34095472,  0.30212541,\n",
        "        0.21470399,  0.32129115,  0.36258179,  0.16518316,  0.2861407 ,\n",
        "        0.37458068,  0.23368475,  0.25604307,  0.35647373,  0.23900799,\n",
        "        0.12627724,  0.22674048,  0.19299677,  0.1358254 ,  0.39082263,\n",
        "        0.1791159 ,  0.38442271,  0.10207492,  0.39715196,  0.10563008,\n",
        "        0.23668715,  0.15898158,  0.11681998,  0.33685718,  0.198436  ,\n",
        "        0.2385814 ,  0.28339774,  0.39841903,  0.26840484,  0.15029317,\n",
        "        0.2079926 ,  0.10259596,  0.130469  ,  0.20096308,  0.31124508,\n",
        "        0.28744003,  0.33840283,  0.2339559 ,  0.36191636,  0.2711472 ,\n",
        "        0.28130672,  0.37762148,  0.37178646,  0.34857662,  0.38235039,\n",
        "        0.29002587,  0.35041043,  0.19460427,  0.2907768 ,  0.15064311,\n",
        "        0.17517755,  0.2160362 ,  0.3887027 ,  0.30514667,  0.16980671,\n",
        "        0.2071928 ,  0.2606598 ,  0.31103409,  0.3939855 ,  0.38463655,\n",
        "        0.23598314,  0.3652801 ,  0.34497568,  0.29124982,  0.21367899,\n",
        "        0.26884074,  0.1506642 ,  0.26563296,  0.1108866 ,  0.3587183 ,\n",
        "        0.30578383,  0.27883748,  0.10714645,  0.36019695,  0.10999835,\n",
        "        0.12694862,  0.32229108,  0.17909211,  0.35084355,  0.32260322,\n",
        "        0.28985127,  0.23550736,  0.15341639,  0.31403561,  0.10679103,\n",
        "        0.16430414,  0.33742098,  0.2572022 ,  0.20092487,  0.26544923,\n",
        "        0.24017329,  0.11844626,  0.33527564,  0.35515421,  0.36321436,\n",
        "        0.271829  ,  0.19889525,  0.18750882,  0.16278652,  0.33871035,\n",
        "        0.31492848,  0.22948874,  0.32900863,  0.16014988,  0.19167827,\n",
        "        0.36780778,  0.12601528,  0.26941834,  0.39428293,  0.22329245,\n",
        "        0.31771602,  0.3390305 ,  0.36615209,  0.22485527,  0.3978946 ,\n",
        "        0.28162887,  0.23164543,  0.35669204,  0.39161483,  0.29550148,\n",
        "        0.35290135,  0.2624819 ,  0.2471617 ,  0.19414942,  0.32400739,\n",
        "        0.30911663,  0.1621781 ,  0.16840543,  0.28765315,  0.27579714,\n",
        "        0.25285476,  0.32599712,  0.29130607,  0.24871366,  0.33465746,\n",
        "        0.20421532,  0.37434971,  0.1657448 ,  0.3306844 ,  0.15041635,\n",
        "        0.2464842 ,  0.29373483,  0.35307196,  0.36033971,  0.25169828,\n",
        "        0.18779335,  0.30835264,  0.23948144,  0.16786354,  0.30784149,\n",
        "        0.28473428,  0.35594696,  0.3335274 ,  0.32944167,  0.15261086,\n",
        "        0.19101073,  0.23750254,  0.16905325,  0.30477939,  0.27724524,\n",
        "        0.14227323,  0.1398323 ,  0.33684891,  0.20817088,  0.28431742,\n",
        "        0.28487678,  0.10336459,  0.20661938,  0.18734408,  0.23308794,\n",
        "        0.35351373,  0.3366583 ,  0.16646037,  0.38941225,  0.13599997,\n",
        "        0.19998264,  0.15105074,  0.12358299,  0.36201896,  0.23448871,\n",
        "        0.3624609 ,  0.35370796,  0.35350612,  0.33061298,  0.2156524 ,\n",
        "        0.35430353,  0.35627314,  0.14520813,  0.35333252,  0.16855564,\n",
        "        0.24224702,  0.31526557,  0.28313767,  0.12597074,  0.39138112,\n",
        "        0.17091154,  0.22339999,  0.20813049,  0.38204337,  0.21959071,\n",
        "        0.10496859,  0.25060809,  0.14597185,  0.25978525,  0.10366627,\n",
        "        0.27352521,  0.31218123,  0.36450579,  0.14959596,  0.35694   ,\n",
        "        0.26834759,  0.24449994,  0.10642313,  0.22570474,  0.26697354,\n",
        "        0.23943506,  0.36383802,  0.17007361,  0.33414029,  0.32160824,\n",
        "        0.23402833,  0.2609669 ,  0.13477352,  0.21305318,  0.25783002,\n",
        "        0.16263967,  0.32499355,  0.33308919,  0.33458817,  0.19871411,\n",
        "        0.24175848,  0.15822576,  0.14131776,  0.32776462,  0.12098002,\n",
        "        0.28577323,  0.1329814 ,  0.27191495,  0.39296191,  0.15261976,\n",
        "        0.25868986,  0.12738732,  0.27439573,  0.39866968,  0.14409122,\n",
        "        0.26710253,  0.37013807,  0.18372909,  0.25816965,  0.27417157,\n",
        "        0.36431489,  0.33173384,  0.14168343,  0.18145311,  0.34521754,\n",
        "        0.2609733 ,  0.27071476,  0.22855587,  0.38091694,  0.17776344,\n",
        "        0.19991766,  0.31882936,  0.26916117,  0.35649475,  0.34834285,\n",
        "        0.17698963,  0.29800569,  0.36950623,  0.24340534,  0.11068308,\n",
        "        0.28365613,  0.27928989,  0.27192234,  0.38258579,  0.14366749,\n",
        "        0.25944218,  0.24895615,  0.27102612,  0.30372553,  0.29857935,\n",
        "        0.1460041 ,  0.21472302,  0.28737954,  0.30237195,  0.28178164,\n",
        "        0.27767067,  0.10709559,  0.25868996,  0.30574929,  0.15428077,\n",
        "        0.21879852,  0.36929945,  0.22203102,  0.30782217,  0.20829953,\n",
        "        0.36932411,  0.2599584 ,  0.3384736 ,  0.29240485,  0.32741621,\n",
        "        0.23204238,  0.20300657,  0.2177195 ,  0.10102198,  0.16333067,\n",
        "        0.32427046,  0.12101149,  0.10865063,  0.20088362,  0.3433798 ,\n",
        "        0.30860291,  0.18504418,  0.18363774,  0.11827423,  0.16442836,\n",
        "        0.22317332,  0.21984757,  0.34347464,  0.15781435,  0.25485548,\n",
        "        0.18802379,  0.28066855,  0.21200021,  0.11545208,  0.22743913,\n",
        "        0.34623492,  0.28692769,  0.24262119,  0.21003974,  0.2788029 ,\n",
        "        0.27118531,  0.36454918,  0.33035862,  0.35100626,  0.3362381 ,\n",
        "        0.24674463,  0.35499656,  0.37873248,  0.27691058,  0.25396415,\n",
        "        0.24926708,  0.30544084,  0.1523637 ,  0.37925957,  0.33147782,\n",
        "        0.20835153,  0.24082885,  0.2605738 ,  0.32250431,  0.35284778,\n",
        "        0.36829249,  0.19054867,  0.30217355,  0.16591617,  0.30385605,\n",
        "        0.26165679,  0.12220822,  0.1407073 ,  0.20928168,  0.31925692,\n",
        "        0.33395132,  0.2722996 ,  0.32849942,  0.33041904,  0.24909779,\n",
        "        0.21829847,  0.19310255,  0.35259712,  0.18396   ,  0.23453159,\n",
        "        0.22379394,  0.19364272,  0.35983352,  0.3404507 ,  0.21999996,\n",
        "        0.35135984,  0.21628367,  0.39382172,  0.39325562,  0.38964229])"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now, define our y offsets as being drawn from the probability distribution characterized by the individual uncertainties "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "delta_y = sps.norm(loc=0,scale=unc_y).rvs(size=1000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "delta_y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As we expect, delta y has a larger spread where unc_y is also larger"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(unc_y,delta_y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "[<matplotlib.lines.Line2D at 0x10703af10>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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t3udpmUlPR7r++SgebLe3t8eIVwIdGzH5m/K/+tWvhBBCvPjii+53zz//vBBC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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10731e550>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now our observed y-values are the \"model\" values plus the offset"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y_obs = x+delta_y"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(x,y_obs)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "[<matplotlib.lines.Line2D at 0x10706ac90>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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aoIgQklTCoY4TZvuadU0115ETl9WwKp5jrN71TrS0k2SZ/ErcwTgTDvNI3LDE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\ntvrWs6dX8gAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107049ad0>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Define weights as 1/uncertainty^2"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "weight = 1/unc_y**2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Do a weighted linear fit"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.polyfit(x,y_obs,1,w=weight)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 96,
       "text": [
        "array([ 0.98652246,  0.02398974])"
       ]
      }
     ],
     "prompt_number": 96
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def yfit(x):\n",
      "    return(-0.03202+1.01978*x)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Compute the chi^2 value for the fit"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def compute_chi2(x,y_obs,y_unc,f):\n",
      "    chi = (y_obs-f(x))/y_unc\n",
      "    chi2 = chi**2\n",
      "    return(chi2.sum())\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "compute_chi2(x,y_obs,unc_y,yfit)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 97,
       "text": [
        "1042.7009691145925"
       ]
      }
     ],
     "prompt_number": 97
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now compute the p-value: \"sf\" = \"survival function\" = 1-cumulative distribution function of chi2, for given number of degrees of freedom"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pval = sps.chi2.sf(978.3111,998)\n",
      "print pval"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "0.665922872474\n"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Let's look at the probability distribution function of chi^2 in general:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "generic_x = np.arange(0,200,1)\n",
      "pdf_chi=sps.chi2.pdf(generic_x,100)\n",
      "plt.plot(generic_x,pdf_chi)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 39,
       "text": [
        "[<matplotlib.lines.Line2D at 0x107d968d0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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0MZMhIiLdMJMhCvs2jXDbX4omzGSIiEg3DDJEYUpEvLYbKaU4XoaWHYMMERHphm0yRBHT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\nIt0wyBARkW4YZIiISDcMMkREpJv/B7ARk2Qs77wUAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1073f1ad0>"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def badfit(x):\n",
      "    return(7-0.2*x)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "compute_chi2(x,y_obs,unc_y,badfit)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "sps.chi2.sf(697320.3,998)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now set up a grid of slopes and intercepts"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "slope_vals = np.linspace(0.8,1.2,100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 120
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "intc_vals = np.linspace(-0.2,0.2,100)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 42
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "and compute the chi^2 value at each point on the grid"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def compute_chi2_linfit(x,y_obs,y_unc,slope,intc):\n",
      "    chi = (y_obs-(intc+slope*x))/y_unc\n",
      "    chi2 = chi**2\n",
      "    return(chi2.sum())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 43
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "chi2_grid = np.zeros((len(slope_vals),len(intc_vals)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 44
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for i,slope in enumerate(slope_vals):\n",
      "    for j,intc in enumerate(intc_vals):\n",
      "        chi2_grid[i,j]=compute_chi2_linfit(x,y_obs,unc_y,slope_vals[i],intc_vals[j])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 117
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "compute the p-value associated with each chi^2 value on the grid"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "chi2_pval = sps.chi2.sf(chi2_grid,9998)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 119,
       "text": [
        "0.66592287247437953"
       ]
      }
     ],
     "prompt_number": 119
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "and make a plot of the reduced chi^2 as a function of grid position"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "delta_chi2 = chi2_grid - chi2_grid.min()\n",
      "red_chi2_grid = chi2_grid/9998"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 47
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.contour(slope_vals,intc_vals,delta_chi2,inline=True,levels=(1,10,20,50),fontsize=12)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 48,
       "text": [
        "<matplotlib.contour.QuadContourSet instance at 0x107d6ad40>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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GqN699X0f1xFNGkpZ5NjevXw7eTI7Fy6k3UMP0fnpp009EHE3JbzJUdZQzP00\n4GF88afigQy7DlbMd/xnPQzrCX/s73zO4+efc3n00cUcOFDAwIGxPPhgG+Ljm5y3TXm5naVL9zJr\n1k9s2JDNzJl3c+edzWuss7QM/i8VXv8MzpTDxIfh3tsr7hE5g/AVRcwgjxPYGU0j7qL+RZNHeVkZ\n2//v//j+b39D7Ha6vvgiMX37avK4DmjSUMpiJzIzWfvGG/z0/vu0vOcebnv2WRq3anXRcgco5X3y\nWchx7sSbEfgSdXbe4MDhil/8s5dCjw7w/+6DTk6q3LnzKJ999jOzZ28iONibp5/uTJ8+0VVGH199\nlcYjjyzit7+N5OWXuxEcXPO5MJGKeY+Js8Eu8OJD0KdLxchDEL6lmGkcpYBy/ng2edS5SPIQEXZ/\n+SXfvPwyZ06fpsuECbQaMACbi/PJdnX1aNJQqpacys9n/TvvsO7NNwmOj6fTmDFE3HHHRd+cl085\nc8nnQ/JphQcP0pDu1MMFg8JieH8JTP0cmvjBI7+D33er+dTVmTN2vvhiJ6+99gMHDhynS5dQOnYM\npkOHIKKj/fD3r0tRUSmPPfYlixfvIjPzaXx9nc9RiFScNkv6AMrt8M8xcPtNZ9chrDmbPPIo5880\n5rfUwzCRPPYuXco3kyZx6tgxur38Mq0GDNCRxzVIk4ZStazs1Cm2fvwx/502DfuZM3QaPZq2Q4de\n9HLd09j5kkKSySeHMwzBh/tpiA8unDkD/15bMVn97RYYdAc80RdahdVc3+7deaxdm8mGDYfYsCGb\nvXuPcezYKRo3rsupU2VMntyDUaM6mm6XCHy2Cp55GxLbw19HQfA5rxdZTRGvcgRvbIzD39SEuYiw\n76uvWDl+PPbychKTkmhx1136itpriCYNpX4hIsL+1FT++8YbZPzwAx1GjKDDyJE0MPFstG2c5gPy\n+Q+F9MKb+2lIOzwwMMg6Au8tqrjiqVVYxdzHvbdDAxOvMC8rKycn5yQiQtOmF7/yqzpFxRWT9jMW\nw58egD/dD5Vnl8oRUjjOVI7SBg8m4E8oF39Kroiwc+FCVk+ciIubGz2mTCGiR4/Lik9ZS5OGUldB\n3u7drH/7bbbMnUuzhARufvJJwrp1u+gv6iOc4XOO8ykFuGNwHw3pQ30aUYfSMljwLXz8FaRuqpj7\nGHRHxRVP7r/A08zTs+GRv1VMnH80HsKD/7euBDuzyGcmx3j07A2O7ibeKC12O9tTUvj6+efxbd6c\nO6ZMIbAPr9IfAAAcqUlEQVRdu1pshboYTRpKXUWlRUVs/ugj1r/1FgDxTz7JTYMH416/vtNydoR1\nnOJTCviaIhKoy3005Jaz78rIL4SF38JH/4EtaXBf94oE0rnV/0YBtcFur7jK6q/JFaerhv/u/PUZ\nlPIyueymhJcIoDsmhkNAeWkpG2bM4JtJkwjv3p0ekyfTMCzM+gaoi9KkodQ1QETYv2oV699+m31f\nf01Mv350eOwxmnTqdNHRx3HKmc9xUjhOLuXcS336Up9WeACw/1BF8vhsFeTmw123wj23wW86gpdH\n7bRn2z7o/0JFskoaXnF57rm+4STjOUwX6jIBf7xMjDoASgoL+eH111n35pvE/+EP3PbnP+s7zX9h\nmjSUusYU5eSwec4cNsyYgVu9enQcNYo2gwfj7u3k1vCz9lLCAk6wkON440I/6nMv9QnAFYB92RWX\nzX6xBjbsgjtvhgEJ0KszeF/8MVqXJDcf7nwGuraFqU9WfWPhCcp5mVzWUczfCKIz5gM4fvAgK557\njoPffkuPV1+lzaBBeqXVL0SThlLXKLHb2ff11/w4fTrpK1cSfe+9tHv4YZp17XrRA2Tl6asUjrOc\nQlriTi+86YU3QWcTyNEC+OI7+DwVvtsKN0VUXAWV2A5uawN1zb311qmCQujyR5j0aMXkfHVWUMg4\ncngMXx7B56KX554r4/vvWTZmDHU8PbnrvfdoHBNz5UErpzRpKHUdKMrJYcvcuWyaPZszp07Rdtgw\n2g0bZuqO8xLsfE8xSyhkBYU0x53fnU0ggWcTSPFpWPtzxQT6qp/gpz3QPgq6x1UkkU6tLv9U1mvz\nYHcmvPdMzdtkUcajZNIODyYSYGqSvJK9vJwfp09ndVISHR9/nC7jxlHHo5bOuylNGkpdT0SE7B9/\nZNPs2WybN48m8fHcNGQI0X37mjq3X4qwhpN8yQlWUEQEbnSnHj2oRwzujl/5J0/Bmq0VCSR1U8Vk\nequwikQSGwbRzSA6FEIa1zyxLgI7DsDbC2DVRtj+kfPYiijnGQ5RgJ05hFxS4gA4kZXFstGjydm6\nlT4ffEDTW2+9pPLKHE0aSl2nyoqL2bVoEZs//JCM778n+t57uWnIEMK6dTP1GI5ShHUUs5IivqaI\nUoTu1KM79bgVLzzPOWgXn64YfWzaU5EIdhyAnQfhSAEENYKm/uDvA3VcKj7l5fD9top5jDtvhhF3\nQbyJM0d2hCfJxhWDNwi6pFNVlXYsWMC/n3iCtkOHkpiUpKMOi2nSUOoGUJSTw7ZPPmHLRx9RlJND\nm0GDaH3//QS2b2/qbmpB2EcpX59NID9Tws140oW63EpdWuBW7QG8pBSyjkLmkYoEcqa8ImEI0LEl\ntGha9cqpizmNnQc4yG/w5gkaXVrhs07m5vLlqFHk7d5N/08+IaBNm8uqR1Xl9NhZ4zv9LlFpaalM\nnDhRwsPDxdXVVZo0aSJPPfVUja9ivZyyle8Rv/AzYcKEauu1sHlKXVNytm2Tr8eNk2kREfJmVJSs\nfOEFyd2+/ZLqKJAzskiOy58lW7rIXomT3fK4ZMocOSa75bTYTbz+9Upsk1PSXdIuvqETdrtdfvrg\nA/mbn59sfP99iyJTzo6dlo00hgwZQnJyMi4uLkRFRZGWlkZZWRkJCQmsXLnS6S8hs2VtZ68mad++\nPe7u/3s/wMMPP8yIESOq1KsjDXWjk7PzH9s++YSfP/0Ur8aNaf3AA7QaMADfyMhLqiuLMv5LMT+c\n/ZzGTme8uBkv2uBBDO6OtxBaoRyhHXv4mgjHY+Iv15Ht2/lswACa3Hwzd737rp6uukK1PtLYsGGD\n41f/22+/LSIiixcvdnw3f/58S8oahiE2m00OHDhgKi6LmqfUdaH8zBlJX7VKFo8cKX8PCJDpbdtK\nalKS5P7882XVlyGl8pnky7OSLb1kn7SUnXKn7JOnJEvelaOSKoWSJaWXNSLZJyXypGRKnOyWXCm7\nrPguVFJUJJ///vfy/u23S3FeniV1/lo5O3ZaMtJ45ZVXeOGFFzAMg+zsbAICArDb7dStW5eSkhJG\njBjBe++9d8VlK0cavr6+FBcXEx4ezpAhQ3j66adxc6v64B0daahfK3t5ORlr1rBj/nx2pKTgVq8e\nrQYMIKZ/fwLatr2sJ8qWYGcXJew8+9lOCWmUUIwQiRvhuBGCKyG4Ekwd6uOCNza8sFGOcJRyjnCG\nVRSxjCIewYeH8XW8ydAKYrfz1bPPsmfJEgYvXaqPIblMzo6dVzYmPCsjI8Ox7O/vD1Qc4P38/MjK\nyjpv/ZWW9fX1JTQ0lAMHDrBjxw7GjRvHpk2bmDdvXrX1T5w40bGcmJhIYmLipTZPqeuOzcWFZl27\n0qxrV+58/XWy1q1jR0oKn/brh9jttLjrLlrecw/NEhKo4179q2Av5I6Nm/Dkpgsef36cctIoZT+l\nZFLGT5zi35RRiJ1C7BRhpw7QiDr44UIsHqwigoZY/4Asw2bjt//4B/WbNuWDxEQe+f57vIODL17w\nVy41NZXU1FRzGzsboowfP77GyefKT2pqqowaNcpx6shu/99QtUmTJmIYhvTq1avGfYwcOdJ02XXr\n1jmWi4uLpUePHo44MjIyLmmIpdSvkd1ul5ytW+WbyZPlX7fcIq82aCCfDRwomz78UE4ePXq1w7PU\nN5MnyzutW+upqsvg7NjpdKTRoUMHhg0b5jTpBAYG0vScO1ZzcnIIDAzEbreTl5cHQKiTdwmcu+5i\nZePj4x3Lnp6e9OnTxzFRnpmZSUhIiNNYlfq1MwwD/9at8W/dmi7PP8/J3Fx2f/klO+fPZ+mTT+Lf\npg3Ne/Wi+Z13EhQXd10/6+n2557jVF4en/brx0MrV17XbbmmWJGVzp3Mfuutt0REZNGiRY7vFixY\nICIimZmZ0rJlS4mOjnZ8Z7bst99+K19++aVjNHLq1Cm54447HKOU7OzsS8qWSqnzlRYXy55ly2TZ\nU0/JWzEx8jc/P/m/+++Xn2bPlhPV/Pd1PbCXl8vMTp1kw7/+dbVDua44O3ZadlQdNGiQGIYhLi4u\nEh0dLa6urmIYhiQkJDi2SU9PdySDOXPmXFLZ2bNni2EYUq9ePWnTpo34+Pg46nrkkUeqb5wmDaUu\nW8HBg7LhX/+SzwYMkCkNG8q77drJV88+K7uXLJFTBQVXOzzTsjdulL81biyn8vOvdijXjV8kaZSV\nlclLL70k4eHh4u7uLk2aNJExY8acd4NeZdKw2WznJQ0zZffu3SuPP/64xMbGSv369cXHx0fi4+Nl\nxowZUl5eXn3jNGkoZYnysjI58N13smriRPmgWzd5pW5deS8uTpaNHSs7Fi685ucNZnftKmkrVlzt\nMK4bzo6d+hgRpdQlO1NSQvb69exfvZoDq1eT+cMP+ERE0KxrV0K7dCHklluoHxJyWZf21oYljz+O\nX6tWdPrjH692KNcFffaUUqpWlZeVcWjjRg588w0Z331H5tq1YBg0iY8nqGNHgs9+6gUE/OKxlZw4\nwcybb6b7pEm0GjDgF9//9UiThlLqFyUinMjIIGv9erLXr+fQhg1kb9iAq5cXwR06ENi+PUFxcQS2\na0f9pk1rbUQiInzWvz91/f256913a2UfNyJNGkqpq05EKEhPJ3vDBg7/9FPFZ/NmSo4fxzcqikZR\nUfhERtIwLIyG4eE0bNYM7+Bg3Ly9LymplJw4QebatRz87jt2LliAZ6NGPLh8uembGJUmjasdhlLK\niZITJzi2dy95u3eTv28fBenp5Kenc/zAAQqzs8Ew8A4OxqtRIzwaNsSjYUNcvbzAMDBsNsRu51Re\nHiePHOFkbi6F2dkEd+hA6O23E37HHYQlJl4zcyvXC00aSqnrkohQWlhIYXY2p/LzOV1QwOmCAsqK\ni0EEsdvBMPD09aWuvz91GzfGJyICl2qeRafM06ShlFLKNGfHTr2vXimllGmaNJRSSpmmSUMppZRp\nmjSUUkqZpklDKaWUaZo0lFJKmaZJQymllGmaNJRSSpmmSUMppZRpmjSUUkqZpklDKaWUaZYljbKy\nMpKSkoiIiMDNzY2QkBDGjh1LUVHRRcvOmDGDhIQEvL29sdls2Gw2Vq9eXWW7nJwchg8fjr+/P+7u\n7sTGxvLPf/7TqiYopZS6iDpWVTR8+HCSk5NxcXEhKiqKtLQ0pk2bxqZNm1i5cqXTRxMvXbqUDRs2\nEBQURFpaGoZhVNn+5MmTJCQksHv3bry8vAgPD2fHjh2MGTOGo0ePkpSUZFVTlFJK1cCSkcbGjRtJ\nTk4GYNq0aWzfvp2UlBQAVq9ezcKFC52Wf+eddzhx4gRvvPFGjdu899577N69G5vNxtq1a9m5cydP\nP/00AFOmTCE3N9eKpiillHLCkqSxdOlSoOJxuv379wegd+/euJ99U9ayZcuclg8KCsJmszl9jHnl\nPqKiomjdujWAY19lZWV8/fXXV9YIpZRSF2XJ6amMjAzHsr+/PwA2mw0/Pz+ysrLOW3+l+6is/8Ll\nmvYxceJEx3JiYiKJiYlXHItSSt1IUlNTSU1NNbWt06QxYcIEJk+e7LSCVatW1ThfUdsvQDJT/7lJ\nQymlVFUX/qB2NkfsNGl06NCBYcOGOd1ZYGAgTZs2dfydk5NDYGAgdrudvLw8AEJDQ02E7VxoaCi7\nd+8+b+7i3GUr9qGUUso5p0mjb9++9O3b96KV9OzZkwkTJiAipKSk8Ic//IElS5ZQUlLiWA+QlZVF\njx49MAyDV199lT59+tRY54WjiJ49e7JixQp2797N1q1badOmjWOy3c3NjR49elw0TqWUUldILDJo\n0CAxDENcXFwkOjpaXF1dxTAMSUhIcGyTnp4uhmGIYRgyZ84cx/fPPvusREZGSlBQkGN9cHCwREZG\nyptvvikiIkVFRdKiRQsxDEO8vLwcyzabTSZMmFBtTBY2TymlfjWcHTstu7lvzpw5vPjii4SGhpKe\nno6/vz+jR4/myy+/rLLthXMgubm5pKenk5OT47hH4/Dhw6Snp5Ofnw9A3bp1Wb16NQ899BD16tXj\nwIEDREdHM3XqVP7yl79Y1QyllFJOGGezyg3JMIxan4xXSqkbjbNjpz57SimllGmaNJRSSpmmSUMp\npZRpmjSUUkqZpklDKaWUaZo0lFJKmaZJQymllGmaNJRSSpmmSUMppZRpmjSUUkqZpklDKaWUaZo0\nlFJKmaZJQymllGmaNJRSSpmmSUMppZRpmjSUUkqZZlnSKCsrIykpiYiICNzc3AgJCWHs2LEUFRVd\ntOyMGTNISEjA29sbm82GzWZj9erVVYM9u+7CzwsvvGBVM5RSSjlRx6qKhg8fTnJyMi4uLkRFRZGW\nlsa0adPYtGkTK1eurPKK13MtXbqUDRs2EBQURFpamuOVrzVp37497u7ujr9DQ0OtaoZSSiknLHnd\n68aNG+nYsSMAb731Fk888QRffvkl99xzDwApKSn07du3xvKHDh0iICCApUuXcvfdd2MYBqtWraJr\n167nbWez2TAMg/T0dFOJQl/3qpRSl67WX/e6dOlSx4769+8PQO/evR2jgWXLljktHxQUhM1mM3WA\nFxHi4uLw8vIiNjaWKVOmUFpaeoUtUEopZYYlSSMjI8Ox7O/vX1GxzYafn1+V9VfK19eX0NBQPD09\n2bFjB+PGjWPo0KGW1a+UUqpmTuc0JkyYwOTJk51WsGrVqhrnH6w+NfTf//6X+Ph4AE6dOsXdd9/N\nypUr+eyzz/jHP/5BSEhIlTITJ050LCcmJpKYmGhpTEopdb1LTU0lNTXV1LZOk0aHDh0YNmyY0woC\nAwNp2rSp4++cnBwCAwOx2+3k5eUB1k1UVyYMAE9PT/r06eOYZM/MzLxo0lBKKVXVhT+ok5KSatzW\nadLo27ev0wnsSj179mTChAmICCkpKfzhD39gyZIllJSUONYDZGVl0aNHDwzD4NVXX6VPnz411nnh\nKGXNmjUUFBTQu3dvDMPg9OnTfPHFF471zZo1u2icSimlrpBYZNCgQWIYhri4uEh0dLS4urqKYRiS\nkJDg2CY9PV0MwxDDMGTOnDmO75999lmJjIyUoKAgx/rg4GCJjIyUN998U0REZs+eLYZhSL169aRN\nmzbi4+Pj2PaRRx6pNiYLm6eUUr8azo6dlt2nMWfOHKKiovjwww9JT0/H39+fAQMGMGnSpCrbXjgH\nkpubS3p6+nnrDh8+DEB+fj4AXbp0YdSoUXzzzTccOHAAFxcXOnbsyIgRI3jkkUesaoZSSiknLLlP\n41ql92kopdSlq/X7NJRSSv06aNJQSillmiYNpZRSpmnSUEopZZomDaWUUqZp0lBKKWWaJg2llFKm\nadJQSillmiYNpZRSpmnSUEopZZomDaWUUqZp0lBKKWWaJg2llFKmadJQSillmiYNpZRSpmnSUEop\nZZomDaWUUqZZljTKyspISkoiIiICNzc3QkJCGDt2LEVFRU7LFRUVMXbsWDp27Ejjxo3x9PQkKiqK\np59+mqNHj563bU5ODsOHD8ff3x93d3diY2P55z//aVUTlFJKXYxVLyJ/8MEHxTAMqVOnjsTExIib\nm5sYhiGJiYlit9trLJeeni6GYYibm5u0bdtWgoODxTAMMQxD2rZt6yhbVFQkLVu2FMMwpG7duo5l\nwzDkxRdfrLZuC5tXq1atWnW1QzBF47TW9RDn9RCjiMZpNWfHTktGGhs3biQ5ORmAadOmsX37dlJS\nUgBYvXo1CxcurLGsp6cnf/3rX8nNzWXTpk0cPHiQvn37ArBlyxa2bNkCwHvvvcfu3bux2WysXbuW\nnTt38vTTTwMwZcoUcnNzrWjKVZGamnq1QzBF47TW9RDn9RAjaJy/JEuSxtKlS4GKl5H3798fgN69\ne+Pu7g7AsmXLaiwbEBDAn/70Jxo0aACAi4sLiYmJjvoq66jcR1RUFK1btwZw7KusrIyvv/7aiqYo\npZRywpKkkZGR4Vj29/evqNhmw8/Pr8r6iyksLGTGjBkAdO3alejo6PPqqKz/wuVL2YdSSqnL5Oy8\n1vjx4x3zBjV9UlNTZdSoUWIYhthstvPmL5o0aSKGYUivXr1MnUfLzMyU9u3bi2EY0rp1a8nJyXGs\nq5zD6Nq1q+O7PXv2OOL461//Wu15Of3oRz/60c+lf2pSByc6dOjAsGHDnG1CYGAgTZs2dfydk5ND\nYGAgdrudvLw8AEJDQ53WARXzInfffTeHDh3i9ttv54svvsDHx8exPjQ0lN27d583d3HucnX7qMgb\nSimlLGNqCHARGzZscPzif+utt0REZNGiRY7vFixY4BhJtGzZUqKjox3fiYjMnz9fvLy8xDAMGTJk\niJSUlFTZx2uvveYYzWzZskVERJ5++mkxDEPc3d0lNzfXiqYopZRywhCx5uf44MGD+eSTT7DZbERF\nRZGWlsaZM2fo2rWr44qB/fv3ExERAcAHH3zA0KFDyc7OJiQkBKiYBO/YsaNjhGAYBu+88w7t27fn\n5MmTxMXFsWfPHjw9PQkJCWHPnj0YhsG4ceP4y1/+YkUzlFJKOWNV9ikrK5OXXnpJwsPDxd3dXZo0\naSJjxoyRwsJCxzaV92TYbDaZM2dOle/O/VR+t3r1avnkk0+kffv24u7uLm5ubo7/jYmJkWnTplUb\nT25urowcOVLCwsLE09NTvL29pU2bNvLKK69IeXm5Y7vS0lKZOHGihIeHi6urqzRp0kSeeuqp8+I2\nqzJODw8P8fHxkQEDBsjevXudljEbZ0JCQrVzSrfffnutx1hUVCQvv/yyREdHi6enpzRu3Fgeeugh\nyc7OPm+7q92XZuO0qi9Xr14tv/vd78Tf399Rx8SJEy1rnxX9WdsxXu2+NFvOqn+btR2nVf1Zm675\nu9/+9a9/OTouMjJSGjZsKIZhSEBAgBw+fLjGcr/5zW8c5Vq3bi1hYWGOv1999VXHdpd7U+IvHWfl\nP6bmzZvLLbfc4viMGjWq1mPs3r27GIYhLi4u0rZtW/Hz8xPDMCQiIkJOnDjh2O5q96XZOK3oSxGR\nqVOnSp06daRVq1aOeJOSkixrnxX9WdsxXu2+NFvOqn+btR2nVf1Zm67ppFFSUuL4D3/gwIEiIpKd\nnS3169cXwzBk9OjRNZaNjo4WwzCkZ8+ejrq8vb3FMAx5/PHHReT8uZi3335bREQWL17s+G7+/PnX\nRJwi//vHVDlCu1SXG+PPP//s6I+pU6eKiEh+fr5jDmrKlCkicvX70mycIlfel5Xy8vLk1KlTUlRU\nZPoAYrZ9VvVnbcYocnX70mw5q/qytuMUsa4/a9M1/cDC9evXO67AqryRLygoiM6dOwPObxp86623\naNasGcuXLyc2NpaoqCiKioro3Lkzzz//PHBlNyX+knGe66mnnsLd3Z2IiAhGjhxp+k74y41Rapjy\nMgwDgK+++gq4+n15sTj/85//VFl3uX1ZydfXFw8Pj0u6Su9i7Vu+fDlgXX/WRozV7ftq9KXZclb1\nZW3Hea4r7c/adE0njcob9gzDqPamPmc39EVGRjpuDNy5cyeZmZm4urrSpk0bGjVqVKX8ldyUWNtx\nVtbt5eVFSEgIAQEB7N+/n5kzZ3LLLbdQXFxcazHGxMTQtm1bAJ555hnatm1L8+bNHfvMysqqUv5q\n9OXF4szOznZse6V9eSUu1r6DBw+et9256y73hlmrYzx331ezL826mn15qa6H/rymk0ZNzGTre+65\nh+XLl9O5c2cOHz7Mjh078PX1ZebMmYwZM+aK6/+l45w6dSr5+fls2bKFgwcPOkYh6enpLFiwoNZi\ntNls/Pvf/2bYsGEEBgaSnp7OTTfdRIcOHQBwdXW9ovqvRpy11ZdXwmw/WdWfl6O6fV+LfWnW1ezL\nmlwP/XlNJ43KG/ZEhJycHMf3lUO1mm4aPHLkCNu2bQMqhteNGzemRYsWdO3aFcDxnKpzy1fWf6k3\nJf4ScQK0a9fuvAPfAw884Fg280vpcmOEilMT77//PpmZmZw4cYKVK1dy4sQJAMco6Wr3pdk44cr7\n8kKVp8DMMNs+q/qzNmOEq9uXZstZ3ZcX29+VlLO6P2vDNZ004uPjHadoKp+am52dzdq1awHo2bMn\nAD169CAmJoZx48YB4OHhgc1W0bR169YBUFpaytatWwGoW7fueeVFxFH/kiVLKCkpOW/91Y4zNzeX\n6dOnnzc8/fTTTx3LYWFhtRYjwE8//cTx48cdf0+ePNlxj8z9999/Xvmr1Zdm4zxy5MgV9+WFzv3F\neuGv1wvj7Nixo6n2WdWftRnj1e5Ls+Ws7svairM2+rNW1N4cuzVmzJjhuNogPDzccQWHv7+/HDp0\nSEREmjVrJoZhyMMPP+woN3DgQEe5iIgICQoKEsOouPfj73//u2O7QYMGOS7TjI6OFldXVzEMQxIS\nEq6ZOCvvZXF1dZXo6Ghp2rSpo0xsbGy1d9BbGeOYMWPE3d1dYmNjJTAw0FHHfffdd179V7svzcRp\nVV+KiKSkpEhkZKREREQ46vD19ZXIyEgZPHhwjXGaaZ9V/VmbMV4LfWmmnFV9WdtxWtmftemaTxoi\nIsnJydK+fXvx9PQUHx8f6d+/v+zZs8exPiwsTGw223n/JxUXF8ukSZMkNjZWvL29xdfXV26++WaZ\nPXv2eXWbuSnxasd58uRJmTBhgnTq1En8/Pykbt260qpVKxk3bpwUFBTUeozJycnSpk0b8fb2Fi8v\nL2nXrp1MmzatyvXtV7svzcRpZV9+8MEHjgR/4adbt241xmmmfSLW9Gdtxngt9KWZclb1ZW3HaWV/\n1ibLHiOilFLqxndNz2kopZS6tmjSUEopZZomDaWUUqZp0lBKKWWaJg2llFKmadJQSill2v8HjBDJ\n6syLyosAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x107dca550>"
       ]
      }
     ],
     "prompt_number": 48
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.contour(slope_vals[40:60],intc_vals[40:60],delta_chi2[40:60,40:60],inline=True,levels=(1,2.71,6.63),xlim=(0.9,1.05))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 60,
       "text": [
        "<matplotlib.contour.QuadContourSet instance at 0x107e0d128>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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G+epqpJkLJ0uzsxH/88+IXbUKesbG8J0wAd3Gjm3yc1k4MBhro4gI8WvX4sCs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\nBmOMMbX8P6fKawYUsUfgAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10849d510>"
       ]
      }
     ],
     "prompt_number": 60
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now let's see if we can collapse the plot along one dimension (NB: not 100% sure this is correct, depends on remembering which axis is which)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "chi2_slope=chi2_grid.sum(axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 61
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "chi2_intc=chi2_grid.sum(axis=1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 62
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(slope_vals[45:55],chi2_slope[45:55]/9998)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 112,
       "text": [
        "[<matplotlib.lines.Line2D at 0x109c0a6d0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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JZEJYWBhyc3NRVVWlW7v//Oc/mD9/PsxmM4xGI8aMGYO5c+fizJkz/d8jIiLyOCVOrpNd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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x109a7ff90>"
       ]
      }
     ],
     "prompt_number": 112
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.plot(intc_vals[45:55],chi2_intc[45:55]/9998)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 113,
       "text": [
        "[<matplotlib.lines.Line2D at 0x109c36bd0>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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77z40Njbi448/xsmTJ/F///d/iIyMBABs3boVLpcLBoMBH374IaqqqrBmzRoA\nwIYNG3D27Nkr7jQREenPZwKyWCwICQnxee43ODgYmzdvRnp6Omw2G/Ly8pCSkoJdu3bBZDINWe/T\nTz9FZWUlACAsLAwzZsyA2WzGPffcg2PHjmkjrT179gAAbDYbpk2bBgBYsmQJAKCrqwt79+69gu4S\nEVGgGJGbEOrr61FSUqIljZqaGpw8eRILFiwYss6pU6e0+d27d8NqtSIkJARHjx7F/fffj2PHjuH2\n229HQ0MDACA6Olor33u+5/P+1q9fr807HA44HI6r6RoR0XWruLgYxcXF+gUgfvB4PKKUEqWU5Obm\nDlrG6/VKVVWVOBwOUUqJwWAQl8s1ZJt5eXlam/PnzxcRkebmZgkLCxOllKxatUpERJKSkkQpJXPn\nztXqVldXa3U3btw4oG0/u0VERL2M9rHTr+eAhnsNe0+ZpKQk7foMAJSXlw9ZftKkSdr8HXfcAQCI\niorC1KlTAXSPqgBg8uTJANDnWk/v+bi4OD96QEREgcavBCS9rgH1nq+oqNCu0QCA1+tFQUGBVm7C\nhAkAgMbGRtjtdiQnJ8PpdAIA7rrrLkRERADovtsOAL7++mvU1dUBABITEwEAP/jBDwAALpcLJ06c\nAADk5+cD6L7+NG/evCvpb8BSSvmciIiuO76GR/n5+WK1WiUhIUE75WWxWMRqtUpWVpY4nU5RSkl4\neLhMnz5dYmJitHLp6eni9XpFRMTtdmvrt2/frrW/ZcsWbb3VapWbbrpJlFISGRkpbrdbRETa2tok\nMTFRlFJiMpm0eYPBIM8///ygcQ/TrYCE7nfcDzkREV1ro32s8TkC8ng8qK2tRV1dnfY/8dbWVrjd\nbjQ1NcFmsyEzMxMRERFwuVzweDxISUlBTk4OioqKBvzPvf/yM888g+3bt2PGjBloamqCyWTCsmXL\nUFZWpp2KGz9+PA4cOIBHHnkEYWFhqK+vh91ux6ZNm/Diiy+ORA4OMP1zDxHR9Un9NetdV5RSY+61\nIX9LzoP/2NdY6w8RjT2jfezky0iJiEgXTEBERKQLvg074PCONyL6buAIiIiIdMERUIDgTQZE9F3D\nERAREemCCYiIiHTBBERERLrgNSCiADfcuwB5/ZDGKo6AiIhIFxwBEY0Zg7+miWis4giIiIh0wQRE\nRES6YAIiIiJd8BoQ0ZjBaz50feEIiIiIdMEREFGA43M+dL3yOQI6ePAgFi5ciJiYGBgMBhgMBuTm\n5vYpk52Do0xEAAARv0lEQVSdDbvdDrPZDKPRiNjYWCxevBilpaXDbtzhcGjt9p7mzJnTN8hByhgM\nBqxdu/Yquky+9Pz0+lATEdFI8TkCKisrQ2FhIRITE9Hc3Axg4FPZBQUF8Hq9sNvtOH/+PKqrq+F0\nOrF//360tLQgKCho2CCsVismTJigLU+bNm3QcjNnzoTRaNSW4+Lihm2biIgCk88EtHz5cqxatQqX\nL1+G2WwetExlZSWCg4O15Ycffhh5eXno6OhAR0cHTCbTsEGsXbsWy5cv91lGKYXdu3cz6YwaPvRI\nRNeWz1NwFosFISEhPs9BBwcHY/PmzUhPT4fNZkNeXh5SUlKwa9cuv5IPAPzsZz+D0WhEQkICnnzy\nSZw9e3ZAGRFBWloaTCYTUlNTsWHDBnR2dvrVPhERBZ4RuQmhvr4eJSUl2um5mpoanDx5EgsWLPBZ\nTykFk8mESZMmobW1FXV1dfjd736HoqIinDhxok8Cs1gsiIuLQ319PSorK5GTk4NPPvkEO3bsGLTt\n9evXa/MOhwMOh+Nb95OI6HpSXFyM4uJi/QIQP3g8HlFKiVJKcnNzBy3j9XqlqqpKHA6HKKXEYDCI\ny+Xy2e7HH38snZ2d2nJOTo62nbfffltbf/z4cW2+vb1d5s2bp5VraGgY0K6f3aJBoPvcmwDSbwL3\nK9F1brS/4349B+TP3U9KKSQlJWHNmjXauvLycp91br/9dowbN05b/vGPf6zNNzQ0aPN33nmnNh8a\nGooHH3xQ2+bp06eH7wBdBdVv+m7iXYFE145fCUh6XQPqPV9RUYE9e/Zoy16vFwUFBVq5njvbGhsb\nYbfbkZycDKfTCQBobm7Ga6+9hvb2dq3+73//e21+6tSpAIDDhw+joKBA2+6lS5fw7rvvauWmTJni\nX0+JiCiw+Boe5efni9VqlYSEBO2Ul8ViEavVKllZWeJ0OkUpJeHh4TJ9+nSJiYnRyqWnp4vX6xUR\nEbfbra3fvn17n3Xjxo0Tu90ukydP1sqkpqZKR0eHiIi8/vrropSSsLAwue222yQyMlIr99hjjw0a\n9zDdIvIbeEqSvkNG+2/a5wjI4/GgtrYWdXV12imH1tZWuN1uNDU1wWazITMzExEREXC5XPB4PEhJ\nSUFOTg6KiooGnKLovRwdHY1f/epXSEtLQ0tLC86dO4fk5GQ899xzOHLkiHZr95w5c7Bq1SpMmTIF\n9fX1AIBZs2Zh69at2LZt28hlYgooPPVFdP1Tf8161xWlFF9fMsYFys9Q/y2OwZ+L4t8ZXU9G+9jJ\nd8FRgOMDsUTXKyYgIr8w8RGNNP4cAxER6YIjICIfeI2H6NphAqIAx1NfRNcrnoIjIiJdcAREAYmn\nvoiufxwBERGRLpiAiIhIF0xARESkCyYgIiLSBRMQERHpggmIiIh0wQRERES6YAIiIiJdMAEREZEu\nfCaggwcPYuHChYiJiYHBYIDBYEBubm6fMtnZ2bDb7TCbzTAajYiNjcXixYtRWlo67MYdDofWbu9p\nzpw5fcqdOXMGK1euRHR0NIxGI1JTU7Fly5ar6C4REQUKnwmorKwMhYWFiIqK0tb1/6XKgoICdHR0\nwG63Y+rUqfjqq6/gdDrx/e9/H5cvX/YrCKvVitmzZ2vTtGnTtM8uXLiAjIwMvPHGG2hvb0d8fDwq\nKyuxevVqrFu37kr6GnCKi4v1DsEvjHNkjYU4x0KMAOMc63wmoOXLl8Pj8eD48eNDlqmsrITb7UZJ\nSQlOnTqFrKwsAEBHRwc6Ojr8CmLt2rX44IMPtOm1117TPtu6dStcLhcMBgM+/PBDVFVVYc2aNQCA\nDRs24OzZs35tIxCNlT9KxjmyxkKcYyFGgHGOdT4TkMViQUhIiM8XQwYHB2Pz5s1IT0+HzWZDXl4e\nUlJSsGvXLphMJr+C+NnPfgaj0YiEhAQ8+eSTfZLKnj17AAA2m00bGS1ZsgQA0NXVhb179/q1DSIi\nCiwjchNCfX09SkpKUFtbCwCoqanByZMnh62nlILJZMKkSZMQExODuro6/O53v8Pdd9+N9vZ2AEBD\nQwMAIDo6WqvXe77ncyIiGmPEDx6PR5RSopSS3NzcQct4vV6pqqoSh8MhSikxGAzicrl8tvvxxx9L\nZ2entpyTk6Nt5+233xYRkaSkJFFKydy5c7Vy1dXVWrmNGzcOaBcAJ06cOHG6imk0+fV7QP1vPBiq\nTFJSEtasWYMDBw4AAMrLy2Gz2Yasc/vtt/dZ/vGPf4yXXnoJwN9GNnFxcXC5XH1Oy/Wej4uLG9Cu\n8LdkiIgCnl+n4Hof0HvPV1RUaNdoAMDr9aKgoEArN2HCBABAY2Mj7HY7kpOT4XQ6AQDNzc147bXX\ntFNtAPD73/9em586dSoAYP78+QAAl8uFEydOAADy8/MBdF9/mjdvnp9dJSKigOJreJSfny9Wq1US\nEhK0U14Wi0WsVqtkZWWJ0+kUpZSEh4fL9OnTJSYmRiuXnp4uXq9XRETcbre2fvv27X3WjRs3Tux2\nu0yePFkrk5qaKh0dHSIi0tbWJomJiaKUEpPJpM0bDAZ5/vnnr+HgkIiIriWfIyCPx4Pa2lrU1dVB\nKQWlFFpbW+F2u9HU1ASbzYbMzExERETA5XLB4/EgJSUFOTk5KCoqGnDqrvdydHQ0fvWrXyEtLQ0t\nLS04d+4ckpOT8dxzz6G4uBgvvfQSEhISEBkZifPnzyM5ORnjx49HfX097HY7Nm3ahBdffHFAzF1d\nXcjNzUVCQgKCg4MxadIk/PznP0dbW5tW5rPPPsOjjz6K5ORkREREwGw2Y8aMGdi8efOAZ5dKS0sx\nf/58hIeHw2Qy4Xvf+x6Kior83tZQ/K2bnZ2NtLQ0BAcHaw/q9ldcXDzoA70GgwF79+4NmDgDYX/6\n81Bz//3Z87evlEJ4eDiWLl2KmpqaYWPasWMH0tLSEBoaCovFMmi9kYzbn+1d6ziH+jtcu3btqMS5\nbds2ZGRkwGw2a9vuuSQQSPvT3ziH25/XKsa2tjb8/Oc/x6xZszBhwgSEhobCZrNhzZo1aGlpueJ9\nOSS9M+BgfvKTn4hSSm644QZJTk6W4OBgUUqJw+HQRlXfpu7rr78uSimJiIiQtLQ0iYiI0EZfzzzz\njNZWeXm5mEwmUUpJdHS0Nkq74YYb5M9//vM1j1NE5MYbb5SoqCiJjY3VRn797d+/X5RSYjQa5e67\n7+4zffTRRwETp977s62tTbupZfz48dq8UkpeeOGFQfdnQkKCdnE2JCREzGazKKUkJiZGvvrqqyHj\n+c///E+tbavVKjfeeOOg9UYqbn+3dy3jFBGtrbS0tD5/h9u2bRuVOB988EEZP3683Hrrrdrf4YED\nB/q0FQj70584h9uf1zLGnjNUwcHBMmPGDO17rZSSGTNmXPF3aigBl4BKS0u1Dvz7v/+7iIj88Y9/\n1Na9884737ruvn37ZMeOHfLNN9+IiMi5c+ckPj5eS0o9MjMzRSklCQkJ0tbWJt98843Mnj1blFJi\ns9mueZwiIg0NDSIi8o//+I/DJqD4+Hhd9qe/ceq9P1955RVRSklQUJCcOHFCRER+8YtfaF+0M2fO\n9NmfU6dOlaioKFFKydKlS0VEpKmpScLDw0UpJdnZ2YPG09HR4Ve9kYq7oaEhIOIUEe3fvr6+/qq3\n923qNTU1yeXLl+X9998f8sCu9/70N05f+/Na78uvvvpK/vVf/1VaW1tFROSbb76RxYsXa//mn3zy\niV/7suc7NZSAS0C//vWvtZ3ek40vX74sISEhopSSJ5544prU7dm5MTExIiLS1dUloaGhopSSVatW\naeX+5V/+RftHGM04e/5RfSWg4OBgiYiIkIiICElPT5ddu3aN+v4cKk499+eTTz4pIiLf//73RSkl\ndrtdq/vBBx9o2/6v//qvPvvzhhtu0EY/t956q+zatUtERO6//35RSkliYuKg8Rw+fFhrc8eOHdr6\nnnpJSUkjGve6det8bu9ax9n736anvZtuuklCQ0MlJSVFXnrpJeno6Bh2e1cb52D1ehLkYAd2vfbn\nlcYpMvT+7PkbHY0Ye7z66qtarJWVlSLi/3dqKAH3NuzeD5b2PHBqMBi099H5evD0aut+9tln+J//\n+R8AwE9/+lMAQEtLCy5dutSnrd7z0utuwNGKczgxMTGIj49HZ2cnjh8/jqVLl6KwsDAg4tRzf37x\nxRd9yvn7UHNERIQ2//nnn2Pp0qX4j//4D63OUDH1rFdKDbqt/vF827hdLpfP7V3rOPu3b7FYEBcX\nh9DQUFRWViInJwfLly8fdntXG+eVfl/02p9X+70ebH/m5OSMaowejwfbtm0DAMydOxd2u71P+at9\nUcCoJaDnn39+yAtqvS/CqSGeOZJv8WyPr7qHDh1CRkYGLl68iGXLlqGrqwsGgwGxsbGQ7hEi/t//\n+39ajI8//rjP9q5VnP313p/33nsvAOD06dMoLy/HpUuXtNjLy8sDIs5A3Z+DlZk2bRpqamrw29/+\nFkopGAwGREZGAgBeeeWVq47J33pXG/fVbu9q6w1W7tixY2hpaUFZWRlOnz6t/W3+4Q9/wNdff61L\nnCPVlh5xDrU/jx49OmoxNjY2IiMjA5999hlSU1P7PC7zbWPw60HUkXDHHXdgxYoVPsvcfPPNmDx5\nsrZ85swZ3HzzzfB6vdof72APnvbo/Zk/dd988008/vjj+Oabb/D0009jy5Yt2L17N1asWAERwVtv\nvYXLly8jKSkJf/d3fweg++HasrKyPonyWsc5mOH25759+1BfX48LFy4ERJyBsD8nT57s10PNUVFR\niIqKwpdffgmg+wtls9lQUlKChoYGxMfH+4ypZ72I4MyZMwO21fP5SMXd87/R4bZ3reMEgDvvvFOb\nDw0NxYMPPoh9+/ZBKYVx48Zd0zj9NdzD7dd6f14JX/tzNGIsKytDZmYmvvzyS3zve9/Du+++q/1n\nrKf8lb4ooA+fJ+h00PuC529/+1sREXnvvfe0dbt37xYRkdOnT0tSUpLY7XZtnb91Rf722p9x48bJ\nq6++OmgsPRfN4+PjxePxSFdXl6Snp4tSfS+aX8s4e/i6BvT2229rFwVFum8I6Hkma8qUKQETp977\ns+eCqcFgkE8//VRERNasWSNKdd/xdvbs2T77s7OzU7tgazQaRanuu4Z67oRbvXq1iIjce++9Yrfb\n5bnnnhORvhd6f/SjH4mISGNj44B6IxV3Y2OjX9u71nEeOnRI3n//fe0OqYsXL2rXCHoupF/LOHvr\nfW2luLi4z2d6709/4zx8+PCQ+1Op7mcyr2WM77zzjnbX6sMPP6w9m3kl+7LnOzWUgEtAIiIPPfSQ\nKNV9Z4Xdbpdx48aJUkoyMjK0MoM93Opv3f/+7//W6kZGRkp6ero2zZ49WyvX+7bhqKgoueWWW0Sp\n7ovThYWF1zxOEZGMjIw+t0r2HARvvfVWOXbsmIiIPPLII6KUkgkTJsj06dO1i8MGg0HefPPNgIlT\n7/3p70PNvffnLbfc0uc9WT03UkRHR8uXX34pIqIl+UcffVRrY9u2bVqc8fHx2l1GveuNZNz+bO9a\nx9nzeENYWJjcdtttEhkZqbX92GOPjUqczz77rFitVpk4caJWPjY2VqxWq/YfzUDYn/7EOdz+vJYx\nNjY2amVuuOEGmT17dp9jZFlZ2RV9p4YSkAmoq6tL1q1bJ/Hx8WI0GuWWW26R1atXi8fj0cr0HIgM\nBkOfA5E/dd944w2tbu+pZ11vJSUlcv/990t4eLiYTCa555575M9//vOoxCkiMnXq1AFx9kw9d83s\n3btXli1bJgkJCWIymWTixIly//33y969ewMqzkDYn19++aWsWLFCoqOjxWg0SnJysvzmN7/pU6b/\n/rzxxhvFbDaL0WiUyMhIWbJkiVRXVw/oe+8vuYhIXl6ezJw5U0JDQwetN9JxD7e9ax3n559/Lj/9\n6U8lNTVVwsPDJTIyUu68807Ztm2bXL58eVTiXLFixZB/h71fpKz3/vQnTn/257WKsff3bLBjZO/v\ntD/7cihKhG/uJCKi0Rdwt2ETEdF3AxMQERHpggmIiIh0wQRERES6YAIiIiJdMAEREZEu/j8Csqqy\ncOqubQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x109c14350>"
       ]
      }
     ],
     "prompt_number": 113
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Where is the chi2 a minimum as a function of slope and intercept? Notice that it doesn't seem to be at the \"best fit\" location."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.argmin(chi2_slope)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 72,
       "text": [
        "49"
       ]
      }
     ],
     "prompt_number": 72
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "slope_vals[49]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 99,
       "text": [
        "0.99797979797979797"
       ]
      }
     ],
     "prompt_number": 99
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.argmin(chi2_intc)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 74,
       "text": [
        "48"
       ]
      }
     ],
     "prompt_number": 74
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "intc_vals[48]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 75,
       "text": [
        "-0.0060606060606060719"
       ]
      }
     ],
     "prompt_number": 75
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now where is the minimum over the entire grid? (There is probably a way to get the individual indices)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "chi2_grid.argmin()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 100,
       "text": [
        "4556"
       ]
      }
     ],
     "prompt_number": 100
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can figure out the slope and intercept at the combined minimum by making a grid of slopes and intercepts and then finding the ones that correspond to the minimum value. These don't seem to be the same as the ones above."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "slope_grid, int_grid = np.meshgrid(slope_vals,intc_vals)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 82
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "slope_grid.flatten()[4556]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 89,
       "text": [
        "1.0262626262626262"
       ]
      }
     ],
     "prompt_number": 89
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "int_grid.flatten()[4556]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 91,
       "text": [
        "-0.018181818181818188"
       ]
      }
     ],
     "prompt_number": 91
    }
   ],
   "metadata": {}
  }
 ]
}

Note that there's a problem with my use of np.polyfit here -- uncertainties should not be squared. Will fix.