{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "code", "collapsed": true, "input": [ "from pylab import *\n", "%matplotlib inline\n", "import statsmodels.api as sm\n", "\n", "# nastavitve za izris grafov (http://matplotlib.org/1.3.1/users/customizing.html)\n", "rc('text', usetex=True)\n", "rc('font', size=12, family='serif', serif=['Computer Modern'])\n", "rc('xtick', labelsize='small')\n", "rc('ytick', labelsize='small')\n", "rc('legend', fontsize='medium')\n", "rc('figure', figsize=(5, 3))\n", "rc('lines', linewidth=2.0)\n", "rc('axes', color_cycle=['k'])" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Linearna regresija" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Linearna zveza $y=kx$ je najpreprostej\u0161a in najpogostej\u0161a zveza med dvema fizikalnima koli\u010dinama, zlasti \u0161e, ker lahko tudi druge funkcijske odvisnosti v ozkem intervalu aproksimiramo z linearno zvezo: $\\Delta y=k\\Delta x$. Vemo, da sorazmernostni koeficient $k$ za majhne $\\Delta x$ limitira k odvodu $\\mathrm{d}y/\\mathrm{d}x$.\n", "\n", "Kadar moramo dolo\u010diti koeficient v linearni zvezi dveh koli\u010din $x$ in $y$, je s stali\u0161\u010da merske tehnike koristno izmeriti ve\u010d kot en par $(x,y)$. \u010ce dolo\u010dimo vrednosti $y_i$, ki ustrezajo celi vrsti izbranih $x_i$, $i = 1, 2, ..., N,$ lahko z njimi dolo\u010dimo $k$ z ve\u010djo natan\u010dnostjo. Obenem preverimo, ali linearna zveza zares velja, pa tudi, ali na\u0161a merska naprava dobro deluje v \u0161ir\u0161em intervalu spremenljivk. Zlasti se lahko zgodi, da ima merilec te ali druge koli\u010dine premaknjeno ni\u010dlo. Tedaj se na\u0161a linearna zveza ne poka\u017ee kot premica skozi izhodi\u0161\u010de koordinatnega sistema, pa\u010d pa je nekoliko premaknjena. Zato velja, da iz vrste meritev $x_i$, $y_i$ nikoli ne ra\u010dunamo koeficienta kot povpre\u010dje kvocientov $y_i/x_i$, pa\u010d pa vedno kot naklon premice, ki jo potegnemo skozi izmerjene to\u010dke.\n", "\n", "Problem najbolj\u0161e premice skozi dane merske to\u010dke je mogo\u010de definirati na mnogo na\u010dinov, ki pa se vsi prevedejo na eno od dveh matemati\u010dnih oblik. \u010ce smo za meritve \u017ee dolo\u010dili korelacijski koeficient $R_{x,y}$, zado\u0161\u010da vedeti, da gre najbolj\u0161a premica vedno skozi te\u017ei\u0161\u010de oblaka to\u010dk $(\\bar x, \\bar y)$ in da ima naklon $R_{x,y}\\sigma_y/\\sigma_x$.\n", "\n", "Sicer pa lahko koeficienta $k$ in $n$ najbolj\u0161e premice $y = kx + n$ dolo\u010dimo tudi z elementarnim ra\u010dunom. Zahtevamo, naj bo vsota kvadratov razdalj to\u010dk od premice najmanj\u0161a (na\u010delo najmanj\u0161ih kvadratov \u2013 least squares principle):\n", "\n", "$$S=\\sum\\left(y_i-kx_i-n\\right)^2=\\mathrm{min}.$$\n", "\n", "V zaresni merilni tehniki se spodobi, da so meritve opremljene s statisti\u010dno napako, torej $y_i= y_i\\pm\\epsilon_i.$ Kadar se $\\epsilon_i$ od izmerka do izmerka znatno spreminja, je te\u017ea posameznih to\u010dk razli\u010dna. Statisti\u010dno neopore\u010den rezultat dobimo, \u010de sumande ute\u017eimo z $\\epsilon_i^{-2}$:\n", "\n", "$$S=\\sum\\left(\\frac{y_i-kx_i-n}{\\epsilon_i}\\right)^2=\\mathrm{min}.$$\n", "\n", "To je druga, popolnej\u0161a oblika za najbolj\u0161o premico. V njej vsoto $S$, ki smo jo minimizirali, obi\u010dajno ozna\u010dimo s $\\chi^2$ in jo lahko uporabljamo tudi za diagnozo kvalitete ujemanja. Za dobro ujemanje je pri\u010dakovana vrednost $\\chi^2/N=1\\pm\\sqrt{2/N}$. Govorimo o testu hi-kvadrat.\n", "\n", "Zgornji postopek lahko uporabimo tudi pri nekaterih nelinearnih zvezah med dvema koli\u010dinama. \u010ce bi npr. skozi to\u010dke radi potegnili najbolj\u0161o eksponentno funkcijo $y = Ae^{-\\lambda x}$, le-to najprej z logaritmiranjem pretvorimo v linearno zvezo: $\\ln{y}=\\ln{A}-\\lambda x.$ Vidimo, da lahko $A$ in $\\lambda$ dolo\u010dimo z obi\u010dajno linearno regresijo za spremenljivki $\\ln{y}$ in $x$.\n", "\n", "Druga posplo\u0161itev je, da poskusimo podatkom prilagoditi linearno kombinacijo poljubnih funkcij $f_i(x)$ s konstantnimi koeficienti $c_i,$\n", "\n", "$$y=c_1 f_1(x)+c_2 f_2(x)+c_3 f_3(x)\\ldots,$$\n", "\n", "tako da minimiziramo vsoto\n", "\n", "$$\\chi^2=\\sum\\left(\\frac{y_i-c_1 f_1(x_i)-c_2 f_2(x_i)-c_3 f_3(x_i)...}{\\epsilon_i}\\right)^2=\\mathrm{min}.$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Kot prvi primer bomo poiskali najbolj\u0161o premico za podatke, prikazane na naslednjih \u0161tirih grafih." ] }, { "cell_type": "code", "collapsed": false, "input": [ "podatki=loadtxt('anscombe.dat')\n", "fig, ((axa, axc), (axb, axd)) = subplots(2, 2, figsize=(10, 6), sharex='col', sharey='row')\n", "axa.set_xlim([3, 20])\n", "axc.set_xlim([3, 20])\n", "axa.set_ylim([2, 13])\n", "axb.set_ylim([2, 13])\n", "axa.set_ylabel(r'$y$')\n", "axb.set_ylabel(r'$y$')\n", "axb.set_xlabel(r'$x$')\n", "axd.set_xlabel(r'$x$')\n", "\n", "x1=podatki[:, 0]\n", "y1=podatki[:, 1]\n", "axa.plot(x1, y1, 'ko');\n", "axa.grid(alpha=0.5)\n", "axa.annotate('(a)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "\n", "x2=podatki[:, 2]\n", "y2=podatki[:, 3]\n", "axb.plot(x2, y2, 'ko');\n", "axb.grid(alpha=0.5)\n", "axb.annotate('(b)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "\n", "x3=podatki[:, 4]\n", "y3=podatki[:, 5]\n", "axc.plot(x3, y3, 'ko');\n", "axc.grid(alpha=0.5)\n", "axc.annotate('(c)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "\n", "x4=podatki[:, 6]\n", "y4=podatki[:, 7]\n", "axd.plot(x4, y4, 'ko');\n", "axd.grid(alpha=0.5)\n", "axd.annotate('(d)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "\n", "subplots_adjust(hspace=0.075, wspace=0.05)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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CzRf5nlheXq6b+Ehnk5+VlZUrfX9nZ2fD811dXUbyvRTFf38/5dtiu9/kk09+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\nQR53Qjn5MvXD14jJH773mf7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"text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Podatki so namenoma pripravljeni tako, da je najbolj\u0161a premica za vse \u0161tiri sete enaka. Primerjava premice in podatkov na naslednjih \u0161tirih grafih poka\u017ee, da je opis podatkov s premico primeren le za podatke (a). Podatki (c) in (d) vsebujejo to\u010dko, ki mo\u010dno odstopa od obna\u0161anja ostalih to\u010dk (outlier). Posledi\u010dno je premica, ki jo dolo\u010dimo z linearno regresijo, zavajajo\u010da. Podatkov (b) pa s premico ne moremo opisati. Linearna regresija s polinomom druge stopnje pa te podatke opi\u0161e pravilno. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ((axa, axc), (axb, axd)) = subplots(2, 2, figsize=(10, 6), sharex='col', sharey='row')\n", "axa.set_xlim([3, 20])\n", "axc.set_xlim([3, 20])\n", "axa.set_ylim([2, 13])\n", "axb.set_ylim([2, 13])\n", "axa.set_ylabel(r'$y$')\n", "axb.set_ylabel(r'$y$')\n", "axb.set_xlabel(r'$x$')\n", "axd.set_xlabel(r'$x$')\n", "\n", "x=linspace(3, 20, 18)\n", "\n", "fit1=sm.OLS(y1, sm.add_constant(x1, prepend=True)).fit()\n", "f1=lambda x: fit1.params[0] + fit1.params[1] * x\n", "axa.plot(x, f1(x), 'r');\n", "axa.plot(x1, y1, 'ko');\n", "axa.grid(alpha=0.5)\n", "axa.annotate('(a)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "\n", "fit2=sm.OLS(y2, sm.add_constant(x2, prepend=True)).fit()\n", "f2=lambda x: fit2.params[0] + fit2.params[1] * x\n", "axb.plot(x, f2(x), 'r');\n", "fit2x=sm.OLS(y2, sm.add_constant(column_stack((x2, x2 ** 2)), prepend=True)).fit()\n", "f2x=lambda x: fit2x.params[0] + fit2x.params[1] * x + + fit2x.params[2] * x ** 2\n", "axb.plot(x, f2x(x), 'b');\n", "axb.plot(x2, y2, 'ko');\n", "axb.grid(alpha=0.5)\n", "axb.annotate('(b)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "axb.legend([r'$y=kx+n$', r'$y=ax^2+kx+n$'], loc=8)\n", "\n", "fit3=sm.OLS(y3, sm.add_constant(x3, prepend=True)).fit()\n", "f3=lambda x: fit3.params[0] + fit3.params[1] * x\n", "axc.plot(x, f3(x), 'r');\n", "axc.plot(x3, y3, 'ko');\n", "axc.grid(alpha=0.5)\n", "axc.annotate('(c)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "\n", "fit4=sm.OLS(y4, sm.add_constant(x4, prepend=True)).fit()\n", "f4=lambda x: fit4.params[0] + fit4.params[1] * x\n", "axd.plot(x, f4(x), 'r');\n", "axd.plot(x4, y4, 'ko');\n", "axd.grid(alpha=0.5)\n", "axd.annotate('(d)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "\n", "subplots_adjust(hspace=0.075, wspace=0.05)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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Qoi2OThBFRckqF08QEUI8wf/+B2RkSMmIP/+UsUsukbqAd90FtGunrX0BjMdzviZMmIDo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\nUFeHDUvfQcfB+wHsB9Cd82W1WrFo2bL4GS+fJ/zz5cuB997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"text": [ "" ] } ], "prompt_number": 3 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Na naslednjih treh grafih smo prilagodili najbolj\u0161o premico podatkom z napakami in izra\u010dunali $\\chi^2/N$. Na grafu (a) so napake tako majhne, da podatkov s premico ne moremo pravilno opisati. To nam potrdi vrednost $\\chi^2/N$, ki mo\u010dno presega $1+\\sqrt{2/N}$. Na grafu (c) je vrednost $\\chi^2/N$ premajhna, kar nakazuje, da smo mogo\u010de precenili napake meritev. Na grafu (b) je $\\chi^2/N$ v mejah med $1\\pm\\sqrt{2/N}$. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "def chi2(x, y, e, f):\n", " return sum(((y - f) / e) ** 2); \n", "\n", "fig, ((axa, axb, axc)) = subplots(3, 1, figsize=(5, 9), sharex='col', sharey='row')\n", "axa.set_xlim([3, 20])\n", "axa.set_ylim([2, 13])\n", "axb.set_ylim([2, 13])\n", "axc.set_ylim([2, 13])\n", "axa.set_ylabel(r'$y$')\n", "axb.set_ylabel(r'$y$')\n", "axc.set_ylabel(r'$y$')\n", "axc.set_xlabel(r'$x$')\n", "\n", "x=linspace(3, 20, 18)\n", "\n", "e1=[0.5 for i in x1]\n", "fit1=sm.WLS(y1, sm.add_constant(x1, prepend=True), [i ** -2 for i in e1]).fit()\n", "f1=lambda x: fit1.params[0] + fit1.params[1] * x\n", "axa.plot(x, f1(x), 'r');\n", "axa.errorbar(x1, y1, yerr=e1, fmt='ko');\n", "axa.grid(alpha=0.5)\n", "axa.annotate('(a)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "h1=chi2(x1, y1, e1, f1(x1)) / len(x1)\n", "axa.annotate(r'$\\chi^2/N=' + '%.2f' % h1 + r'$', xy=(0.4, 0.1), xycoords='axes fraction')\n", "\n", "e2=[1.0 for i in x1]\n", "fit2=sm.WLS(y1, sm.add_constant(x1, prepend=True), [i ** -2 for i in e2]).fit()\n", "f2=lambda x: fit2.params[0] + fit2.params[1] * x\n", "axb.plot(x, f2(x), 'r');\n", "axb.errorbar(x1, y1, yerr=e2, fmt='ko');\n", "axb.grid(alpha=0.5)\n", "axb.annotate('(b)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "h2=chi2(x1, y1, e2, f2(x1)) / len(x1)\n", "axb.annotate(r'$\\chi^2/N=' + '%.2f' % h2 + r'$ ($\\sqrt{2/N}=0.43$)', xy=(0.4, 0.1), xycoords='axes fraction')\n", "\n", "e3=[2.0 for i in x1]\n", "fit3=sm.WLS(y1, sm.add_constant(x1, prepend=True), [i ** -2 for i in e3]).fit()\n", "f3=lambda x: fit3.params[0] + fit3.params[1] * x\n", "axc.plot(x, f3(x), 'r');\n", "axc.errorbar(x1, y1, yerr=e3, fmt='ko');\n", "axc.grid(alpha=0.5)\n", "axc.annotate('(c)', xy=(0.03, 0.92), xycoords='axes fraction')\n", "h3=chi2(x1, y1, e3, f2(x1)) / len(x1)\n", "axc.annotate(r'$\\chi^2/N=' + '%.2f' % h3 + r'$', xy=(0.4, 0.1), xycoords='axes fraction')\n", "\n", "subplots_adjust(hspace=0.075, wspace=0.05)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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GbReSg6Q0kMFxV6LBeHp7e3G73cyYMSNEg38a2tDQwPTp07Hb7X2u7ejoIDso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\nHwuCYByJPcX2+cDhUFPpLVsA6AGWAbO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zzWBluVyuftu9Xq/m8/nCfm4EXq/XtL5FwyE4\nmNDFDNatW6c1NjYGNDQ2NmqNjY3aunXrDNdi6PfQ1qZpV1+taccco2kqcEfTLrxQ8y5erGl79xqn\nox8ifRcSdquhIAwGK2w1tIKGuLN/v9oXvXAhbNig2o46CsrK1MLLRReZq+8gkdqWpExWIQiCQezc\nqTLpLFoE/g0ZI0dCeTlUV8OYMebqi5GE3Go4EP3GW4mGIatBiMP30N0NP/qRyrNYV6eMY06OMpRb\nt8JvftPHOCbiuyAjSEEQBoemwUsvqWn0s8/CgQOq/etfV9Pob30Ljj7aXI06Iz5IIamxgv/PChpi\nYu9ecDqVYfzHP1TbMcfArFnKMObnm6svAsQHKQiCPuzYAQ4HLFmips0AGRkqw84tt8Dpp5urzwDE\nBykakl6DEOH38O9/qzouo0dDfb0yjrm58OCDan/0XXdFZRwT8V2QEaQgCMq/2NqqptErVx4qY1Bc\nrKbRpaW6lTFIJMQHKSQ1VvD/WUFDWHbvhqefhnvvBX+96GHD4Jpr1Or0eeeZq09nxAcpCMLA/Pe/\nsHQpPPAAvP++ajv1VPjBD+Dmm9W/BfFBiobk1yAEfQ+vvaaCuM84Q9V0ef99NUp85BFV36WxMW7G\nMRHfBRlBCkKyo2mwfr1aff7znw+1X3658i8WFhqeqTtREB+kkLS0tLQwdepUAEpKSqipqWHKlCmG\n6zDNB/n55/DEE8q/+Prrqu344+G666C2Vq1MDzHEBykIKONYW1sbOF69enWgvIcZRtJQtm1TvsWl\nS2H7dtV2+ukqdKeiAjIzzdWXQIgPUjQkpYbFixf3qXfU1dXFkiVLTNFjCK+8okaHY8aomi7bt8O4\ncfDEE3SvWwezZ5tqHK3wPkaKjCCFpGT37t39tu/atctgJXHmwAEVt7hwoYpjBOVP/N//Vf7FSZPU\ncQIaJyuQlAYyOJO0aIic1tZWWltbmTt3LgCNjY0AFBQUUFBQYIiGWBk2bFi/7cMNqqccdz75BH73\nO+Vf3LxZtZ14oqoZXVOjMusEkcjvo5nIIo0QFksHOA+A3wcZPM222WwsWrTIcB+krs9xyxa47z6w\n28FfznjMGGUUb7wRUlNj7yOJidi2RJ+8PH7EKsvsNP/JogEdyhWY+RxWrlwZ+B1KS0u1lStXmqJD\nj+eo/f3vmjZrlqYdffShMgYXX6xpK1YMqoxBMryPehDp95CUU2xBgNDV6lWrVpmoJEr27YPmZuVf\n/NvfVNvRRx9KM3bBBebqGwLIFFsISyJPsf1Y4XeIWENvLzz8MCxerHa3AKSlqRAdf5YdISoitS2G\nhPlUVlaGHDscDtxuNw6Hw4juBSEx8HhUgojRo1U5g3feUTWj77tP+R7nzRPjaDBxN5B2ux232x04\n7ujowOfzUVhYSEZGBk6nU/c+rRBvJRqso8HSaBq8+CJMmwZnnaVquuzcCZddBs89B2+9pZLTnnhi\nTN1Y4XuwgoZIibuBrKioICco5MDtdgeOc3JyWLNmTbwlCAlGa2src+bMISUlhZSUFObMmcOcOXNo\n9cf5JQN798KTT8KECaqmy//9n/IvXnstdHbC2rWqxssQzMFoJQzxQZaUlLB69WoAqqqqmD59OoWF\nhXg8HhoaGli+fHmoKPFBWgKz/Xd69G/279BHQ08PLFumps3vvadOyMxUKcZ+8AM47TTTdA4FZC+2\nIFiIlpYWAIYDpaNHU/Phh0zZs0d9eM45ajX6u99VSSQEy2H4+N1ms+E7GODq8/nIyMjQvQ8r+DpE\ng3U0mEXLypXUlpcDsAtYvXUrtXv20JKXBy+8cCg3owHG0QrfgxU0RIrhI8iioiJcLhcAHo+HkpKS\nfs+rq6sjLS0NgNzcXCZOnBjYquR/0OGOtx6swDbY8+NxvHXrVlP7D8bo659++mlefvllFi1aBBDI\nqnPllVdSUFBgmP7grW3d3d3GPf+33oLnnmPxL35B1yefhPwuXcD8k07i3Nxcsg5OveV9jN9xa2sr\nzc3NAAF7Eglx90E2NTVRUVHBHXfcQXl5OampqSxYsID8/Hw8Hg/lB//ChogSH6QliNV/Z/b1et1j\n0Hz4oar898AD8OGHFADr+znt0ksvTa4FpwQiUtsigeJCWMw2cAljIP/5T5U04sknVREsgLFjKd23\nj9Wvvdbn9NLS0sTc2ZMEWDJQ3Gis4OsQDUnOgQPw/POqLOr556uaLnv2qNCctWuhs5OaefOw2Wwh\nl9lsNqqrqw2Xa4V3wQoaIkVWsQUhEj77DB5/XAV0v/mmajvhBLj+elXG4KyzAqf694L7yz6UlpZS\nXV2d/BnNkwiZYgthMXuKbKkp9n/+A/ffr2IYe3pU26hRUF2tVqLT0+OvQYgZiYMUBB3wJw1eNncu\nFwHnp6SAplEAFFxwgYpfLCuDY481WakQT8QHKRqEw9m/nwKfjznr1rENeBaYk5LCnKuuouCvf4WX\nX1YpxxLIOFrhXbCChkiREaQg+Nm5Ex59VPkXPR4AeoGHgB91dUEClgwQYkN8kEJYzPYhGuaDfOcd\nWLIEHA74+GPVlp0NtbWMrKtjpxEaBEOQOEhBN8w2cHE3kC+9pLJ1P/ss7N+v2v7nf5R/8dvfhqOP\nttZCkRAzEgeJeb4Oq6XpSkSfT9zZtw+eeQYmToSLL4YVK1RZ1KuvhrY2+MtfVMnUo482W6muWOFd\nsIKGSEnKEWTwvlszsMqIIdbnYPYIUNfR244dagq9ZInKzg0qNKeyUpUx+NKX4q/BxPfB7P8nrKJB\nptgWwAr/Q+iB2QZOj+d4ZkoKtUD1iBHw6aeq8eyzVWmDa6+FESPiriFZ3odkQOIgBUHT1FR54ULe\n5qAf6dNPYfJk5V+8/HLJ1C0MiqR8SxLR1xEPYnkO/kSvoLbIBR9blj174Pe/h3HjoKAA/vhH9gLz\nATZtArcbpk4dksbRCv9PWEFDpMgIMsnw7wCZO3cuAI2NjQAUFBRQUFAwqHu0tLQEcjgCrF69mq6u\nLgBr7iPevl1tAbz/fti2TbWdcgrcfDNn/OIXfAj85PzzTZUoJCbig4wDVvA5xaKhtLQ0UEPo8PZI\n0nTF3Qf5xhsqzdjjj8OuXart3HPhtttoHT2a1r/9rc8lkfyhGJQGg+4h6IP4IIWY2e3PaXgYu/xG\nyEw0DVwuuOceCDbW3/ym8i8WFUFKitozHSZbvSAMlqR0xiSir8NKDBs2rN/24cOHG6wkiF274OGH\nVe7FkhJlHI8/XoXpvP76odyMB0drwcj7YI1nYAUNkSIjSKEPNTU1dHV1BfyOYF6i11MBGhtVKYP/\n/lc1nnaail2srFQlUwUhTogPMg5YwecUq4aWlpaYE73GpOHVV3l07FiuBgLj2fx8NY3+/+2df3Bc\nVdnHvwGsgJC93RTEl05ld/0RLWKTbKSOUgqbJoyBVyRNIoLiQH4hJk3HppvqvNrxHadJ1xHaorQb\nB5iXQWo2q9VJFJu7MTKg1SS7Iq+/gL1LteOL0m521QoW6H3/ONxL9leSu3v3nrOb5zOTae/de+7z\n3btnnz0/nvOctjZg1Srj98wDGoMsLyhQXABE+EKI8MU2XF7bxuDeezExNYX9YNulnn/JJej7whfQ\nvHNn1i50MRHhORLmQWuxUZpjHSua06fZToDvex9w002YmJrCtooKHAXwBICjL72EbSMjmPjRj/K6\nPdUHMZ6BCBqMwmUMMhgMAgDi8XjWbV+JFcKJE8D99wN+PzA/z86tW4f955+P6LPPplwajUZx4MAB\nMeMwibLF8hZkJBKBJEloaWmB2+3WnaWZ8F4QTyzBzAzLnuNwAMPDzDlu3Miy7ESj+Pc73pG1WL5h\nRlQfxHgGImgwiuUtSEmS4PV64Xa7oSgK6urqrJZAWED6UsW+e+5B86uvsvyLTz3FXjj3XDbhsn07\nc5BvIGSYEbEyUTng9XrV1atXq3v37s36eqGyYrFYQeULBUDB70EEDfneY3x8XHW5XHp5AKrrvPPU\ncRbmrao2m6ru2KGqx48vv7zLpY6Pj+f1PgqpDzyfo5nw/k6IosHo52B5CzKRSKCqqgqBQACtra1o\naGhATU2N1TKIIrJ///6UGEoAiL72Gg5ccAGah4eBz34WuPjinOVpP2lCFCx3kIFAAN3d3aisrMTc\n3ByGh4dx8ODBjOv6+/shSRIAoLq6Ghs3btTHMLTZsFzH2rnlXm/2cTpW20+fLbSs/DvfCfz850jO\nzCAbr9TXA7297PpTpxa93/r16/Vy6fUjn8+jkPpgRvlC9ItSH0rxeHp6GkeOHAEA3Z8YwfI4SJ/P\nh66uLthsNv14YGAgVZTBWCXRECHuzdL4vVdfBcbG2PjizAyaAGSmurA+2YUZFKJBy6yUjtGEGYR5\nlESguM/ng9PpRDweR3t7OyorK1NFFeggF/7a86DUv9jLvsf8PAvRuf9+FrIDAHY7JjwebPvVrxA9\nfly/1OVyYd++fYa6yWY9x0LqgwgazIC3fVE0lEQ2n/QWI1FiPPss2zv64YeBf/2LnauuZtsYfPrT\naL7wQsCEpYq8yZiJ7+srufdAFAYtNSwCZdmCVFVgepqlGZuYYMcAy6CzfTvQ1JSRqVuEPWnyRUsa\nnJ6ww2grmBCLonaxe3p64Ha70dbWltEtNhNeDtKMbNxAeTnIVQD+/fDDbHzx6afZC299K3D77azF\neOWVRdPA8zmalTSYEIuiOshEIgFZljE6OopEIgGXywWv12v6uALvMchS/mKbpuGll/Bfl16KewBc\npp279FLgnnuAnh72/yJr4Dn+t3nzZvzsZz/LOH/ttdfmtc857/E33vZF0VDUZBWSJGHr1q0YHR3F\n0aNHUVNTg4MHD2JqasqwUEJQfvtboLMTWLcO/403nONVVwEPPQT86U/Al7+8LOdY6tBqHgKAsbBy\nr9ertra2qqFQSFVVVZVlWVVVVR0bGzNymyUxKMt0UMDKh/Hxcb18Y2Nj3qs/CsXQezh7VlV//GNV\nbWzURhtVFVB/CKjXAez1YmsoQvlCMHs1DyEGRuuToVnsLVu2wOl0IhAIYGhoCK2trVAUBU6n0zSH\nXcqU3G6AL7/Mtkm97z62ARYAXHghW+mybRv+873vZecqrM3BKAK0mocAYMydJhIJNRwOp5yTZVlV\nFMWQV14Kg7IyKHTNJ/JsuTQ2Nqa0OLS/pqamgvTkw6Lv4S9/UdUvfUlVq6rebDFefrmq7tmjqqdO\nLe8ehWqwoLwG77XYhWowA972RdFg9LM01IK02WwZ66Y9Hk/+3rnMEHo3QACIRNhs9OHDbPULALjd\nLEyntRV4y1v46iMIwSjLTbt4zZQJObD/+uvA+DhzjNqs7DnnALfcwhzjRz5S9l1o3jOnImjgbV8U\nDUYpSwfJC1F2A5yYmMA5YDPQTRdfjL6XX0YzwDLo3HUX0NfHktUSBLE4RerqF0ShsniNQapq6ix2\nU1OT5bOe4w8+qLokKTMX4113qWoyaehehTwHEcpr0Bgkf/uiaDD6WVIL0mQWznJauuLil78E7r0X\n+7/7XUTTXoq+9hoOnDiB5iKufiKIcqQsHWQpjnXkxWuvAd//Phtf/MUvAADZp4kEmijigAj1gbcG\n3vZF0WCUsnSQpcyy1oMnk8C3vw0cOABoKcUkCejqwluPHQOeeCLjvrQChCCMU5bZfMphLXbWeygK\nSzP24IPAP//Jzr373cC2bcAddwAXXWRKFhqzEr2K8BwBygcpgn1RNJREPkjCAKoKPPkk60YfOfJm\nmrHrrmNhOs3NKWnGzFgBQhmvCYJRli1IM+wDfFs+qyoq0Arg0bo6YG7ujZOrgFtvZWnGNmwouoZC\nEeE5FooIGgjzoBZkqROPA4cOIQbgcoA5xzVrgLvvBj73OeCyy5a4AUEQZmEo3VmpkL6LW0nwxz8y\nJ7h2LfDFL+JyAL8FgJERlmbsq18l55gnItQH3hp42xdFg1HK0kGWDKoKyDIbR6yuBg4eZBl2brgB\njQCuBICODuCCCzgLJYiVCZcxyHA4jLk3xtXa2tr0LWB1UeU+BvnKK8B3vsPSjD3zDDt3/vnAZz7D\nZqTf/34avzOhvBmIoIEwj5LY9rWtrQ2jo6MIBoMAgJaWllRR5eog//pX4IEH2N/f/sbOXXbZm9sY\nrFlTfA0Wkq8GkfaTFuE5EuYhvIMcGxtDLBZbdOvXfBykWRtuafYBE53TM8+wMJ1HHwXOnGHnNmxg\nYTrt7WwTrGJr4IAIGgCKgxTBvigahHeQg4ODAFh28snJSQwNDWWKKqAFWbQg7XzKa2nGQiHtBeCm\nm5hjvPbaRdOMkYM0D3KQ/O2LoqGom3aZRUVFBTweD+rr6+Hz+XhIKB6nT6MbwO8B4MYbmXN829uA\nz3+ezVT/4AfA5s1ln4NRJHh/KUXQwNu+KBqMYnkcpMvl0v9vs9kwMzOT9br+/n5IkgQAqK6uxsaN\nG/UHrIUL5DrWzi33+mzlF7Ks8i++iCt++EPg4EEMagXXrgV6e/FCUxNgsxnWY8h+Ecrne3z48GEc\nO3ZMH+bo7+8HANx8883YvHmz5XoKPdbOiaKHjpd/PD09jSNHjgCA7k8MYSg5mgkoiqJ6vV5VVVU1\nEAioPp8v45pCZMGE/H2G7jE7q6q33aaq552n7+9yDFBvBFT1zBlrNBShvFmIkAOQ8kHyty+KBqOf\npeVdbIfDAZfLhWAwiNnZWezYscNqCYsyMTGh/7+pqSnlWOf111masU2b2J4ujz4KnD0LbN0KPPUU\nNgIYB2iPF4IoccpuLXYhg+pLZsL5xz9YJp39+1lmHQCorGTB3L29wBtNfKEmisT7eEsKeo7lhfCz\n2MuBl4NsamrC0aNHM89v2oTH3W6Wg/Hvf2cnHQ4W1H3nnWyvF5M0mHUP+mKbAz3H8qIkZrFFJee2\nrU88AXzjG8w5XnMN8L3vAc89xxxkmnMkUkmfMCINK9O+KBqMQtl8FpBz21YAuO02Fr9YV2epJoIP\n2sIDbSZ+9+7dAChX5kqDutgaiQQmtm/HtkceQfT11/XTLknCvvvuQ/MddxRfg4n3oK4hQWRC+SCN\n8vzzbBuDhx5C8+nTAIAhAFEAVzU0oLe/31A2boIgyoeVOQapqsD0NPDxjwPveQ9w//3A6dNAQwOa\nJybwFID/A/D45CQ5xwIRYdyJNPC3L4oGo6ysFuSZM8Dhw2x99K9/zc6tWgXcfjvbxuADHwDAIoMJ\ngiBWxhjkyZMsGe03vwm8+CI7d8klbAuDu+8G3v72pe+xDMxM00VjkARhPhQHudAx/O53LCntI4+w\nJLUAcOWVbDb6U59iSWqXugcnyEEShPlQHCSAawDghhuA9evZni6vvAJ87GPA5CTwm9+w4O4cztEs\nSnG8pRiI8BxIA3/7omgwSvk4yJdfBkZG8L8A/gcAfvITtpdLTw/w+98DExNAQ0NJpBlb1npwgiCK\nTul3sV98EfjWt9g2BidPAgD+AuA/vvY1oLsbqKrKyz7Ap3u65HrwZUJdbILIZOWMQT79NJuNfuyx\nN7cxqK3F7eEwRgGc4RikXQg514M3NeHxxx9fsrxI+7kQhGiUd6D42bOsq3zvvcBPf8rOVVQAN9/M\nJl6uuQaPniPGqMHCBKtGyLkeXJtkWoKFjjBfDWZCGsTQwNu+KBqMUhoO8vRp4OGH2YqX555j5y66\niE229PUBC7KUlzo514MXeVKJIIhMxO5i//nPbJWL3w8kEuzFdeuYU+zoANL209bKAnzXQReCWWOQ\nBEFkUj5d7FtvBQIBlr0bAD78YdaN/sQngPPElV0omhO88cYbAbCxx97eXnKOBMEBcVuQAHDuuWwb\ng+3bgauvXnZZgH8LstDxFhE0mAFpEEMDb/uiaCifFuTAANsqdd063koIglihiNuCzHNPGa1r2tjY\niL6+vry6piLEEIqggSDKjZJaajg4OLj0RctEm9zQOHr0KLZt20arUAiCyBtuDlKWZciybNr99u/f\nnzLzCwDRaBQHDhwwzYYRRFh3ShpIgyj2RdFgFC4OMplMoqqqCna73bR7FhpgTRAEkQ4XBynLMmpq\naky9p2gB1rxn60gDaRDJvigajGK5g4xEIqitrTX9vn19fXClrahxuVzo7e013RZBECsDy8N8FEUB\nAITDYSiKgqmpKVx//fUZ1/X390OSJABAdXU1Nm7cqP8CaWMZC4/Xr1+Pffv26bPYmzZtws6dO9Hc\n3Jz1+sWO0zFa/oUXXsCJEyfw0Y9+NO/yhdrXuOKKK/Iub8Zxuhar7QPAk08+ibVr13Kzb1Z9KGX7\nGlbXx+npaRw5cgQAdH9iBK5hPm63G7OzsxnnuWz7avI9XqBAcdIgkAbe9kXRUDLpzvx+P3bt2oVA\nIJDRgiwHB1koImggiHKjZBzkYpCDFENDMUgmk5idnUU4HEZtbS08Hg9vScQKoqQCxcuZ9HFE0sAY\nHR2Fy+XCwMAAhoeHs5ZJJpNIJpNF08AD3hp42xdFg1HEXYvNAS0b91e+8hUAwO7duwFQNm4z6ezs\nBMAm6dKjDjT8fj8GBgYAALFYDDt37kQsFtPHq5PJJDo6OvCud70Le/bsMUXX2NgYVq9ejUQipzhx\noQAACBxJREFUAUmSsrZsF14Tj8f196K9n7m5uZRzRBmgCkghsgAUVF4UyuV95MLr9arJZDLra3v3\n7k059vv9qsvlUsPhsH5OlmXTtESjUbW7u1s/3rJlS8Y18/PzKecrKipStLS2tmboJsTD6HeKutiE\n5YyNjWHXrl04depUxmuhUAhbt25NOWe329Hd3Y1Dhw4VRY8syykhIJIkIRKJpFwjSZK+V1A4HEZ3\nd7f+msfjwZYtW4qijeALOcgiIcJ4Cy8NyWQSoVAIbW1tKRpCoRCCwSAGBwfR2toKv9+fUTYcDsPh\ncOjH2sKCrq4ujI6O6ueNLFNd6jloS18X3luL100nEonA7/djaGho2faXo6HY8LYvigaj0BgkYTo2\nmw0ejwfhcBiPPfYYdu3ahWAwiJaWFgDQ/01HG/9biKIo+vVtbW0YGRmB0+nMOfudTCZTHCkAnDx5\nEmvWrAEANDQ0pDjgXGhRBOnU1NRgeHgYdXV1eP7555e8D1HakIMsErwDYkXQ0NXVBY/Hg6uvvjqn\nU1xIIBBAe3t7yrmFDtPr9WLLli1ZW54aNpvN8ESJJElIaHseAYjH43A6nSnXhMNhzM/Pw+PxwPbG\nXki5VoFlg/dnwdu+KBqMQg6SKBo2mw2JRCLD2eQikUigsrIy5+sOhwOSJEFRlJyOKVsLciHZWpBt\nbW3wer0pOjZs2JByzdzcXEa3fuH7UsssXpVgUKB4kaClhmzMUZZl2O12PWwnF4qiIBKJ6C3NWCyG\n4eFhrF69OiWUJxgMwuVyZTiwxVjOcwiFQvr/KyoqdAfsdrsxNTWFyspKBINBXavL5cItt9yilz10\n6BCSySR27tyZtfvP+7PgbV8UDbSShhykaRoKIRKJwOl04vjx47jzzjuzrrlfiM/nW9KJ5osIX0ze\nGnjbF0UDraQRBN4VgaeGWCwGp9MJm82Gq666Cu3t7QgGg4jFYlz0rOTPQhT7omgwCrUgBaVc3sdy\n0GIOzU6iTBDpUAtSEESI+SoVDTU1NUV1jqXyHMrZvigajEKz2IJB68EJQhyoi00QxIqButgEQRAm\nQQ6ySIgw3kIaSIMo9kXRYBRykARBEDmgMUiCIFYMNAZJEARhElwc5MjICEZGRtDT08PDvCWIMN5C\nGkiDKPZF0WAUyx1kKBRCQ0MDOjs7IUkSRkZGrJZgCceOHeMtgTSQBmHsi6LBKJYHiiuKAkVR0NnZ\nCafTiWg0asp9FwZYT09Pcw+w/sMf/mC5TdJAGkS1L4oGo1juIBcmM5VlGZ/85CdNue9CR7h7927d\nQRIEQeQLt0kaRVFQVVWl59Qzk4XZoXlBGkiDSBp42xdFg2Hy30CxMLxeb87XPvjBD+rbntIf/dEf\n/Zn153K5DPkpLnGQfr8f7e3tsNlsKZs5EQRBiITlXWxZltHT0wOHwwG73Y75+XmrJRBFZuGe0QAL\n6wqFQpZGLGTTYGVoWbp9jcHBQUvsZ9MQDof155BMJrloCAaDCAaDJRO9YrmDbGhowNmzZxGPxxGP\nx9HR0VEUO1ZWxHR4VMR0eFVEv9+fsr9LOBxGIpGAx+OB3W7X93WxUoPVoWXp9jVkWYYsy0W1vZiG\noaEhdHZ2wm63W6IjXUMkEoEkSWhpaYHb7bakLmT7YTTyg12WK2msrIjZsLoipsOjImp0dXWl7PYX\nCoX0Y6fTicnJScs1KIqifw5mhpYt1z7AdlusqqrK2BnRKg1jY2Oor68HwPYlt2JYK12DJEkYHh5G\nMpmEoiioq6srqv1sP4yRSMTQD3bZOUirK2I6PCpiOlZXxMWIRqP63tY2mw3xeNxyDZ2dnXp4mSzL\n+NCHPmS5BlmWuW4pMTs7i1OnTiEUCnHrXTkcDtTW1sLhcEBRlKLvUbPwh9HlciEajUKWZUM/2GXn\nIKkiWl8RS4VihpYtRiQSQW1traU2s1FRUQGPx4P6+nr4fD7L7ScSCVRVVSEQCGDPnj36XkTFYuEP\n4+TkJOrr6w3/YJeVg6SKyLC6Ii6Gy+XS498SiQS3lj3AxsQeeOABy+0qioJwOIxgMAhFUTA1NWW5\nBpfLpbecbDYbZmZmLNcQCATQ3d0Nj8eDubk5HDp0yBK72g9jPr25snKQVBEZvCpiNhoaGqAoCgD2\n+TQ2NnLR4ff7sWvXLgCwdEwWeHOopaWlBZIk4frrr7fUPsA+B23sNZFIcBlmSCQSeqoxh8MBl8tl\nid2FP4xGf7DLykFSRYRul0dFBNgY7OzsLL7+9a8jmUzqwx2hUAjz8/OWdG/TNVgdWpZuX8Pv9yMW\ni1nyw52uQasHwWAQs7Oz2LFjh+UaBgYG4Pf79eiKXKFQZpL+w2j0B1vIhLmFoj2UQCDAxUmOjIzA\nbrdjZmYGQ0NDltsHAJ/PB6fTiXg8jvb2dlRWVnLRQRC8kGUZjY2N+pjj3r170dHRAZ/Ph9raWj1p\nzmKUpYMkCIIwg7LqYhMEQZgJOUiCIIgckIMkCILIATlIgiCIHJCDJAiCyAE5SIIgiByQgyQIgsgB\nOUiCIIgckIMkCILIATlIgiCIHJCDJEqSSCSi59wMhUJoa2vjLYkoQ2gtNlFyaBlybDYb3G43Zmdn\nEYvF4HA4OCsjyo3zeAsgCKPYbDYALF2V2+0GAHKORFGgLjZRciSTSSQSCQSDQX2/HZ5Z04nyhbrY\nRMnh8/kgSRLsdjvi8TicTifcbrfesiQIsyAHSRAEkQPqYhMEQeSAHCRBEEQOyEESBEHkgBwkQRBE\nDshBEgRB5IAcJEEQRA7IQRIEQeSAHCRBEEQO/h9BeheRkya+BgAAAABJRU5ErkJggg==\n", "text": [ "" ] } ], "prompt_number": 4 }, { "cell_type": "markdown", "metadata": {}, "source": [ "Poglejmo si \u0161e, kako poi\u0161\u010demo najbolj\u0161o eksponentno funkcijo $y=Ae^{-\\lambda x}$ za podatke na grafu (a) spodaj. Vrednosti $y_i$ najprej logaritmiramo in poi\u0161\u010demo najbolj\u0161o premico $\\ln{y}=\\ln(A)-\\lambda x,$ graf (b). Iz koeficientov te premice preberemo $A$ in $\\lambda$ in nari\u0161emo ustrezno eksponentno funkcijo (c). " ] }, { "cell_type": "code", "collapsed": false, "input": [ "fig, ((axa, axb, axc)) = subplots(3, 1, figsize=(5, 9), sharex='col', sharey='row')\n", "axa.set_xlim([0, 10])\n", "axa.set_ylim([0, 200])\n", "axb.set_ylim([1, 6])\n", "axc.set_ylim([0, 200])\n", "axa.set_ylabel(r'$y$')\n", "axb.set_ylabel(r'$\\ln{y}$')\n", "axc.set_ylabel(r'$y$')\n", "axc.set_xlabel(r'$x$')\n", "\n", "N=50\n", "x=linspace(0, 10, N)\n", "y=exp(log(200.0 * exp(-0.3 * x)) + np.random.normal(0, 0.05, N))\n", "\n", "axa.plot(x, y, 'ko')\n", "axa.legend(['podatki'])\n", "axa.annotate('(a)', xy=(0.03, 0.05), xycoords='axes fraction')\n", "\n", "axb.plot(x, log(y), 'ko')\n", "fit=sm.OLS(log(y), sm.add_constant(x, prepend=True)).fit()\n", "f=lambda x: fit.params[0] + fit.params[1] * x\n", "axb.plot(x, f(x), 'r')\n", "axb.legend(['podatki', r'$\\ln{y}=\\ln{A}-\\lambda x$'])\n", "axb.annotate('(b)', xy=(0.03, 0.05), xycoords='axes fraction')\n", "\n", "axc.plot(x, y, 'ko')\n", "axc.plot(x, exp(f(x)), 'r')\n", "axc.legend(['podatki', r'$y=Ae^{-\\lambda x}$'])\n", "axc.annotate('(c)', xy=(0.03, 0.05), xycoords='axes fraction')\n", "axc.annotate(r'$A=' + '%.3g' % exp(fit.params[0]) + r'$', xy=(0.75, 0.5), xycoords='axes fraction')\n", "axc.annotate(r'$\\lambda=' + '%.3g' % -fit.params[1] + r'$', xy=(0.75, 0.4), xycoords='axes fraction')\n", "\n", "subplots_adjust(hspace=0.075, wspace=0.05)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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YIAN2u93cdtttQCiYzXwktZBMM5l+eDwedu/eHfl5YGAAwzDiZqTJ/v/d7Xbj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\nthabzRYTIOeTaTY1NbFz587Iz36/n5UrV0ZdMzw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    \n", "
  1. V datoteki Kredarica.zip so zbrani vremenski podatki z merilne postaje Kredarica za obdobje od 1. 1. 1955 do 31. 1. 2014. Poi\u0161\u010di premico, ki najbolje opi\u0161e odvisnost med vla\u017enostjo in obla\u010dnostjo v letu 2013.\n", "\n", "
  2. Teorija kemijske kinetike napove za sigmoidno krivuljo iz podatkov adrenalin.dat naslednjo odvisnost $F/F_\\textrm{max}=c/(a+c)$, kjer pomeni $a$ koncentracijo s polovi\u010dnim maksimalnim u\u010dinkom. Dolo\u010di koeficienta $F_\\textrm{max}$ in $a$. Pretvori v linearno zvezo \u2013 ena pot je uvedba recipro\u010dnih spremenljivk $1/F$ in $1/c$, druga pa je uvedba spremenljivke $c/F$.\n", "\n", "
  3. Iz povpre\u010dnih dnevnih temperatur v obdobju od 1. 1. 2000 do 31. 12. 2009 na merilni postaji Kredarica (Kredarica.zip) oceni povpre\u010dno temperaturo za vsak mesec v letu (povpre\u010dna temperatura v januarjih v tem obdobju, ...). Oceni \u0161e napake teh povpre\u010dij. Nekatere mese\u010dne porazdelitve temperatur odstopajo od Gaussove porazdelitve, a je odstopanje dovolj majhno, da lahko uporabimo oceno napake iz teme Povpre\u010dja.\n", "\n", "\u010casovno odvisnost mese\u010dnih povpre\u010dij modeliraj s funkcijama\n", "\n", "$$T(t)=T_0+T_1\\cos\\left(2\\pi\\frac{t}{t_0}\\right)$$ \n", "\n", "in\n", "\n", "$$T(t)=T_0+T_1\\cos\\left(2\\pi\\frac{t-t_1}{t_0}\\right),$$\n", "\n", "kjer je $t$ \u010das, merjen od za\u010detka zime, in $t_0$ eno leto. Dolo\u010di parametre $T_0$, $T_1$ in $t_1$ ter primerjaj vrednosti $\\chi^2$ za obe funkciji. \n", "
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