{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Linearna regresija metodom najmanjih kvadrata\n", "\n", "Linearna regresija predstavlja linearni pristup modeliranju relacije između jedne ili više nezavisnih varijabli sa zavisnom varijablom. Kada govorimo o zavisnosti varijable $\\bf{Y}$ od jedne nezavisne $\\bf{X}$ tada govorimo o prostoj linearnoj regresiji. Takav slučaj će biti razmatran u tekstu koji slijedi. \n", "\n", "Definirajmo linearnu vezu između veličina $\\bf{X}$ i $\\bf{Y}$ kao:\n", "\n", "$$ Y=a_0+a_1X $$\n", "gdje $a_0$ predstavlja presjek prave $Y$ sa x-osom, a $a_1$ nagib prave. Ovu jednačinu ćemo koristiti pri modeliranju relacije između dvije veličine. Potrebno je odrediti vrijednosti $a_0$ i $a_1$, koristeći dostupne podatke (vrijednosti za $\\bf{X}$ i $\\bf{Y}$ kako bi dobili pravac $Y(X)$ koji najbolje opisuje relaciju između dvije varijable.\n", " \n", "Kako bi minimizirali grešku koju ćemo pri tome napraviti (podaci obično odstupaju od linearne zavisnosti) potrebno je izračunati grešku. Nekoliko je načina na koji se greška može izračunati tako što se definiše odgovarajuća funkcija pogreške. Metoda najmanjih kvadrata podrazumijeva da se funkcija:\n", "$$ L=\\sum_{i=1}^n (y_i - p_i)^2 $$ \n", " gdje su $y_i$ date vrijednosti (npr. eksperimentalni podaci), a $p_i$ vrijednosti koje će dati naš model. Minimiziranjem funkcije (L(x,y)), tj. određivanjem parcijalnih izvoda i njihovim izjednačavanjem sa nulom, dobiju se odgovarajuće vrijednosti za koeficijente $a_0$ i $a_1$ koji će dati najmanju grešku. \n", " \n", "Nakon nekoliko linija računa stiže se do relacija za koeficijente:\n", "$$ a_1 = \\frac{\\sum_{i=1}^n (x_i - \\bar x)(y_i - \\bar y)}{\\sum_{i=1}^n (x_i - \\bar x)^2}$$\n", " \n", "$$ a_0 = \\bar y - m\\bar x$$ \n", "gdje $\\bar{x}$ i $\\bar{y}$ predstavljaju odgovarajuće srednje vrijednosti ulaznih podataka. \n", "\n", "Implementacija Metoda najmanjih kvadrata podrazumjeva izračunavanje koeficijenata $a_0$ i $a_1$ iz ulaznih podataka.\n", " \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementacija modela u Pythonu" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "# Ucitavanje podataka\n", "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "plt.rcParams['figure.figsize'] = (12.0, 9.0)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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V7gDMkpAMLaSOdrzaFNpnrW0LKwHaaqSQXEpZTPILSd6SpCb5W0luJvmVJA8m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\nAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Pripremanje i prikaz ulaznih podataka\n", "data = pd.read_csv('data.csv')\n", "X = data.iloc[:, 0]\n", "Y = data.iloc[:, 1]\n", "plt.scatter(X, Y)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Koeficijenti su jednaki:\n", "('$a_0$= ', 9.908606190326509)\n", "('$a_1$= ', 1.287357370010931)\n" ] } ], "source": [ "# Izračunavanje koeficijenata --> MODEL\n", "X_mean = np.mean(X)\n", "Y_mean = np.mean(Y)\n", "\n", "num = 0\n", "den = 0\n", "for i in range(len(X)):\n", " num += (X[i] - X_mean)*(Y[i] - Y_mean)\n", " den += (X[i] - X_mean)**2\n", "m = num / den\n", "c = Y_mean - m*X_mean\n", "\n", "print ('Koeficijenti su jednaki:')\n", "print('$a_0$= ', c)\n", "print('$a_1$= ',m)\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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ppHUsL6OmnkDs7Nx0cZUwQR98AIMHw403wpprwkUXxXOP27enD9Bnh42TrhDw\nDa9yz5VkSSXN2bmFwVXCBHz+eTylonNnGD06DsZvvw1VVdC+fdLVfYOHxSjXXEmWVNKcnVsYcrlK\n6OauRixZEq8aDx4MH34IhxwCw4fD5psnXVmDqnp3XenTBvANr7JjSJZU8pydm365aotJS9tGKoN6\nCDBuHJxxBkyfDr16QXU1/PCHydbVRL7hVa4ZkiVJTZZUuMvVKmEappmkJaivZMqU+PCPiROhSxcY\nOxb69IEoSqaeFvINr3LJnmRJUpMsD3c1C2oJfB3uWmPKRJ+eFQzv24OK8rKsJimkYXNXqvqrZ82C\nww+Hykp49VW48sp4isXPf15wAVnKNVeSJUlNkvQqbC5WCdMwzSQNQZ1PPoELLoArroA2bWDgQDjz\nTFhrrdarQUo5V5IlqcQ1df5wKsJdltIwzSTRKQyLFsGll8YTKy6+GA47DN58E4YNMyBLGQzJklTC\nmtNCUQwjtnLVtpGNRIJ6CPC3v0H37vCnP8EOO8DUqXDzzbBxOuYcS2lju4UklbDmtFAUy4itpDd3\ntfoUhqeeijflPfcc9OgB//gH9O6dn9eSioghWZJKWHNaKByxlTutEtRnzID+/eMxbh07xrOPjzwS\n2rZt/LGSDMmSVMqau5Et6VVYNcFHH8E558C110JZGZx/Ppx6KqyxRtKVSQXFnmRJKmFp2MimHPni\ni3gDXufOcUA+4YT4GOmzzjIgF5CmbqRV/rmSLEklzBaKIrB0KdxyCwwaBDU1cNBBMGIEdOuWdGVq\nplQeNFPCDMmSVOJy1UKRyqOWi90jj0BVFbzyCuy0E4wZAz/+cdJVqYWSnkWuldluIUnKWpKn8ZWk\nl1+OJ1T07g2ffQZ33gmTJhmQC1wxzCIvJq4kS5Ky5gpYfmSuzg/abk32vfOvcXtFeTlccgmcdBKs\nvnrSpSoH0nAipL5mSJYkNdmqWipcAcu9FftTv7PoCw67/xZ2H1TN0gjannZafJT02msnXaZyqFhm\nkRcLQ7IkrcC+2lVraFORK2C5N3L8DBYvXMRvXv4Hf3x6DOt98SnVW+7GrQcez70X/jrp8pQHbqRN\nF0OyJNVxZ3nDGmqpcAUsx0Jg6+cf55YnRrP5/Bqe3aQHR+9+DNM27EKUdG3KK2eRp4chWZLq2Ffb\nsIZaKoptBSzRTxQmTYKqKq596ineWndjjvnFYCZsviNEcTx2dV5qHYZkSapjX23DGmupKJYVsMQ+\nUXj7bRgwAO6+GzbYgJcGjuAItubzFd63uTovtR5HwElSnVWt0LlyFyuV0/ka+kQhL+bNg1NOge7d\nYdw4GDwY3nqL7YadyfkHb0em6KG6AAAgAElEQVRFeRkRUFFexvC+PYrijYhUCFxJlqQ69tU2rNha\nKlal1T5RWLgQ/vKX+Cjpzz6DY46Bc86Bjh2/uqVYVuelQmRIlqQ6pRICs1EKoS3vkzqWLYtPxjvr\nLJg9G/bfHy68ELbeOjfPLyknDMmStIJSCIHZKIUReXn9ROGf/4TTT4cXX4SePeHGG2HPPbN/Xkk5\nZ0iWJDVJqYzIy8snCq+/DmecEfccb7IJ3Hor/PrX0Kb+rUGl8GZESjtDsiSpSUppRF7OPlH44AMY\nMgRuuAG+8x0YMQL+8AcoW3XrRqm8GZHSzukWkqQmcUReM3z+OQwdCl26wE03we9+F494O/PMBgMy\nJDBdQ1K9DMmSpCZxRF4TLFkC110Xh+NzzoH99oPp0+Hyy2G99Zr0FL4ZkdLBkCxJapJSmZPcIiHE\n/cbbbgvHHw/f/z4880x8MEjnzs16Kt+MSOlgSJYkNUmfnhUM79vDwy0yvfgi7LUXHHggfPkl3Hsv\nPPUU/OhHLXo634xI6eDGPUlSkzkibwWzZ8ezjm+/PW6l+Mtf4IQToF27rJ7Wed1SOkQhhJY/OIpO\nBY4DAjANOBrYELgTWAd4EfhNCOHLhp6nsrIyTJ48ucV1SKXE0VBSwhYsgAsugCuugCiKj5Tu3x++\n+92cv5R/36Xci6JoSgihsrH7WtxuEUVRBfAHoDKEsDXQFjgUuBC4NITQBfgEOLalryFpZctHQ9Us\nqCXw9Wio6qk1SZcmFb8vv4TLLoPNN4c//xl+9St4800YPjxvAdm/71Jysu1JXg0oi6JoNWAN4ANg\nT+Ceuh8fDfTJ8jUk1XE0lJSAEOINeN27w6mnwvbbx33Io0fDxhvn7WX9+y4lq8U9ySGEmiiK/gy8\nB9QCjwBTgAUhhCV1t80B/FxIyhFHQ6kUJdpy8PTT8THSkybB1lvDww9D795xm0We+fddSlY27RZr\nAwcBnYCOwLeB/eq5td6m5yiKjo+iaHIURZPnzp3b0jKkkuJoKJWaxFoO3nwT+vaFXXaB996LT8x7\n6SXYd98WBeTqqTX0GjGBTv3H0WvEhCbV7993KVnZtFvsDbwbQpgbQlgMjAV2Bsrr2i8ANgLer+/B\nIYRRIYTKEEJlhw4dsihDKh2OhlKpafWWg7lz49PxttoKHn0UzjsvDszHHANt2zb++Hq0NOj7911K\nVjYh+T3gh1EUrRFFUQTsBbwO/BM4uO6efsB92ZUoablCm1PbktUzaUWt1nLwxRfxxIrNN2fZNdcw\ndof92fGoq+m12s5Uv7kgq6duadAvtL/vUrHJpif5uSiK7iEe87YEmAqMAsYBd0ZRdH7dtRtyUaik\nWKHMqV2+erY8HCxfPQMKov7W4oivhnUsL6OmnkCcs5aDpUvh1lth0CCYM4cPdu/Nsd1+wevf7Rj/\neA7+3GYT9Avl77tUjLKabhFCGBJC6BZC2DqE8JsQwqIQwjshhJ1CCJ1DCIeEEBblqlhJhcOd+Y1z\nxFfj8tpy8OijsMMOcPTRsOGG8MQTHNz7jK8Dcp1s/9zaWywVJo+llpQX7sxvnG8kGpeXloNXXok3\n4O2zD3z6KYwZE0+v2HXXvPy5tbdYKkweSy0pL/L+MXkR8I1E0+Ss5aCmJm6ruPlmKC+Hiy+Gk0+G\n1Vf/6pZ8/Ln1mGmpMBmSJeVFVe+uK/Ukg6tnmXwj0Ur++1+46CK45JK4B/lPf4KzzoK11/7GrS35\nc9uUvnJ7i6XCY7uFpLxwZ37j/Bg+zxYvhquugs6dYdgw6NMH3ngjPlK6noAMzf9za1+5VLyiEOo9\n66NVVVZWhsmTJyddhiS1Oqdb5EEIcN990L8/zJgBu+0GI0fCjjvm/KV6jZhQ76cBFeVlPN1/z5y/\nnqTsRVE0JYRQ2dh9tltIUoL8GD7HnnsOqqrgX/+Cbt3isPzTn+btGGn7yluXbyrVmgzJkqTC9847\nMHAg3HUXrL8+XH01HHccrJbff+aKsa88rUHU2etqbfYkS5IK17x58Ua8bt3ggQfi6RUzZ8KJJ+Y9\nIEPx9ZWnucfakYlqbYZkSVLhWbgw3oDXuTNcfjkceSS89Racey6suWarlVFsG1TTHERtbVFrs91C\nklQ4li2DO++MWytmz4b99oMLL4QePRIrqZj6ytMcRIuxtUXp5kqyJKkwTJwIO+0Ehx8ej3B77DF4\n6KFEA3KxSfMR2sXW2qL0MyRLktLt9dfjCRV77AEffQSjR8OUKbDXXklXVnTSHESLrbVF6We7haRU\nSusOe7Wi//wHhgyB66+H73wHhg+HP/4RypJf1SxWaT9Cu5haW5R+hmRJqeOopxL3v//BxRfHR0kv\nWgQnnxxPrejQIenKSoJBVIrZbiEpddK8w155tHRpvGrcpUu8grzvvnGrxRVXGJAltTpXkiWlTpp3\n2CsPQoCHH4YzzoDXXoMf/QjuuQd23jnpyiSVMFeSJaVOmnfYK8defBH23hsOOCBurbjnHnj6aQOy\npMQZkiWlTpp32CtH3nsPfvMb2GEHePnl+ECQ116DX/wCoijp6iTJdgtJ6ZP2HfbKwoIF8ZSKyy+P\nvz7zTBgwAL773WTrkqQMhmRJqeQO++ZJ/ci8L7+Eq6+G886D+fPhiCPg/PNhk01Wui31P48C5K+p\n1DKGZEkqcKkemRcC3Hsv9O8Pb78dHwAyciT07PmNW1P98yhQ/ppKLWdPsiQVuNSOzHvmGejVCw45\nJD4A5KGH4NFH6w3IkOKfRwHz11RqOVeSJanApW5k3ltvxSvHY8fChhvGs4+POgratm3wYan7eRSB\nXP2a2rKhUuRKsiQVuNSMzJs7F37/e9hySxg/Hs49Nw7Mxx7baECGFP08ikgufk2Xt2zULKgl8HXL\nRvXUmhxVKaWTIVmSClziI/Nqa+OJFZ07x5vzjjsu7j8eNAi+/e0mP03iP48ilItfU1s2VKpst5Ck\nApfYyLxly+DWW+Hss2HOHPjpT+HCC6F79xY9naP/ci8Xv6a2wahURSGEpGugsrIyTJ48OekyJElN\n9dhjUFUFL70ElZXw5z/DbrslXVXJaY1e4V4jJlBTTyCuKC/j6f575vS1pNYQRdGUEEJlY/fZbiFJ\narpp02C//eAnP4kPBrnjDnjuOQNyAlqrV9g2GJUqQ7IkqXE1NfEGvO22g0mT4pXjN96Aww6DNv5T\nkoTW6hXu07OC4X17UFFeRkS8gjy8bw/bYFT07EmWVJIcadVEn30GF10EF18MS5fCKafAWWfBOusk\nXVnJa81eYU/AVCkyJEsqOZ5C1gRLlsB118HQofDRR3DooXDBBdCpU4uezjcludexvKzeXmFH5km5\n4WdkkkqOI60aEALcdx9svTWcdBJ07Rr3HI8Zk1VAds5u7tkrLOWXIVlSyXGk1Sq88ALsvjv06RN/\nXV0NTzwBO+2U1dP6piQ/7BWW8st2C0klx4+pM7z7LgwcCHfeCeuvD1ddFR8I0q5dTp7eNyX5Y6+w\nlD+uJEsqOX5MXWf+fDjtNOjWLW6xOPtsmDkT/u//chaQweOmJRUmQ7KkklPyH1MvWhRPq+jcGS69\nFI44At56C847D9ZcM+cv55sSSYXIdgtJJakkP6ZetgzuuiturZg1C/bdNx7v1qNHXl/W46YlFSJD\nsiQlpFXHoj3xRHyM9AsvwLbbwiOPxKfmtZKSfFMiqaAZkiUpAa02q3n6dDjzTHjgAdhoI7j55ri9\nou3X7Q/OMJakb7InWZISkPexaB9+GG/A69EDJk6MDwJ5803o1+8bAdkZxpL0TYZkSUpA3sai/e9/\n8Qa8zp3h+uvjoPz22zBgAJR9c5qEM4wlqX62W0hSApozq7lJ7RBLl8atFIMGwQcfQN++MHw4bLFF\ng3U4w1iS6udKsiQloKlj0RpthwgBHn4YttsuPgBk003hqafg3nsbDchQuDOMq6fW0GvEBDr1H0ev\nERNsD5GUc4ZkSUpAU2c1N9gOMXVqPKFi//2hthbuvhueeQZ69WpyHYU4wzhNfdSGdal42W4hSQlp\nyli0+toeOv73I0578FYYOBHWWQcuvxxOPBG+9a0W1QCFNcO4oTcOrVl3q00okZQIQ7IkpdiKvctr\nLvof/zfpbo594T6IiOceDxgA5eVZvUahzTBOSx91WsK6pPyw3UKSUqyqd1fWarOMflMeYOK1v+Wk\nSfcwvvuPmVj9L7jwwqwDciFKSx91WsK6pPwwJEtSWoVAn3cm8cxtf+Ccx67ljfU34+jfXc2yW26h\n9wE/SLq6xKSljzotYV1SfthuIUlp9MwzcTvFM8/wna22gnHj6LXffvSKoqQrS1xa+qirenddqScZ\n0r/psbV4iqOKQYtDchRFXYG7Vrj0fWAwcEvd9c2AWcAvQwiftLxESSohM2dC//7xCLcNN4TrroOj\njoLVXNNYURr6qNMS1tPGDY0qFlEIIfsniaK2QA3wA+BkYH4IYUQURf2BtUMIZzb0+MrKyjB58uSs\n61DpcbVCRePjj+Hcc+Hqq2H11eGMM+C00+Db3066MqlZeo2YUO9BORXlZTzdf88EKpJWFkXRlBBC\nZWP35WppYi/g7RDC7CiKDgJ2r7s+GpgINBiSpZZwtUJFobYWrrgCLrgAPv8cfvtbGDoUvve9pCtr\nkG9QtSpuaFSxyFVIPhQYU/f9DUIIHwCEED6Iomj9HL2GtBLHL6mgLVsGt98OZ50F//43HHhgPK1i\nyy2TrqxRLXmDaqguHc05cl1Ks6ynW0RR9C3gZ8DdzXzc8VEUTY6iaPLcuXOzLUMlyNUKFazHH4fK\nSjjySFh/ffjnP+GBBwoiIMOq36AOvf+1eu9P0wl5yr+0TB+RspWLEXD7AS+GED6s+/rDKIo2BKj7\n9qP6HhRCGBVCqAwhVHbo0CEHZajUOH5JBefVV+MjpPfeG+bPj1eSn38edt896cqaZVVvRBfULq43\n+DZ4tLaKTlOPXJfSLhftFofxdasFwP1AP2BE3bf35eA1pG9w/JIKxvvvw+DBcNNNsNZaMHIk/O53\n0L590pW1yKo+TgfqbXfyU5/Sk4bpI1K2slpJjqJoDeAnwNgVLo8AfhJF0Vt1PzYim9eQVsXVCqXe\nZ5/F4bhLF7jlFvjjH+MRb6efXrABGWjwjWh9wddPfSQVoqxWkkMIXwDrZlybRzztQso7VyuUSkuW\nwA03wJAh8OGH8KtfxdMrvv/9pCvLiT49Kzjngdf45IvF3/ix+oJvGj71ceOgpObyWGpJypUQ4g14\n22wDJ54YryBPmgR33lk0AXm5IT/dqsmbs5L+1MeNg5JawiOcJCkXJk+O2yieeAK22AL+/nc46CAo\n0mOkm3vaXJKf+jguUlJLGJIlKRuzZsHAgTBmDHToAH/9a3wgSLt2SVeWd4XS7uTGQUktYbuFJLXE\nJ5/EK8ddu0J1dXwoyMyZcNJJJRGQC4kbByW1hCFZkppj0SK45BLYfPP428MPhzffhPPPj8e7KXU8\n3EJSS9huIUlNEQL87W8wYAC8+y707g0XXRRv0lOqNbd/WpLAkCxJjXvyybi14oUX4lA8fjzss0/S\nVakZCqV/WlJ62G4hSasyYwb06QO77RafmnfTTfDiiwZkSSoBriQrtRz+r8R8+CGccw6MGgVrrAHD\nhsEpp8TflySVBEOyUmn58P/ls02XD/8HDMrKny++iDfjXXghLFwYHwgyeDCsv37SlUmSWpntFkql\nhob/Szm3dCnceGN8Qt6gQfCTn8Brr8GVVxqQJalEuZKsVHL4v1pFCPEmvDPOgGnT4Ac/gLvugl12\nafShtgNJUnFzJVmp5PB/5d1LL8Ub8PbbD/73v3i827PPNjkgDxg7jZoFtQS+bgeqnlqT/7olSa3C\nkKxUcvi/8ubf/4Z+/WD77eNJFZddBtOnwyGHQBQ16SlsB5Kk4me7hVLJ4f/KuU8/jTfkXXpp3GZx\n+ukwcCCUlzf7qdLaDmQLiCTljiFZqeXwf+XE4sVw7bXxSLePP46PkR42DDbdtMVP2bG8jJp6AnGS\n7UBOhJGk3LLdQlJxCgHGjoWttoLf/x569IDJk+G227IKyJDOdiBbQCQpt1xJltRsqf9Y/9lnoaoK\nnn4attwSHnwQ9t+/yT3HjUljO1BaW0AkqVAZkiU1S6o/1p85EwYMgHvuge99Lz4x7+ijYbXc/68u\nbe1AaWwBkaRCZruFpGbJ9mP96qk19BoxgU79x9FrxITcjE37+GP44x/jVeOHHoKhQ+Gtt+C3v81L\nQE6jNLaASFIhK41/PSTlTDYf6+d8FXrhQrjiCrjgAvjsMzj22HiD3oYbNutpUt8+0gRpbAGRpEJm\nSJbULNl8rN/QKnSzwtyyZXDHHXDWWfDee3DAAfF4t622avpz1El1+0gzpa0FRJIKme0Wkpolm4/1\nc7K5bMIE2HFH+M1vYL314q8ffLBFARmcCiFJqp8hWVKz9OlZwfC+PagoLyMCKsrLGN63R5NWMLM6\nbvy11+IV4732inuQb7sNXngB9tijmT+DlTkVQpJUH9stJDVbSz/Wr+rddaXWBmjCKvQHH8DgwXDj\njbDmmnDRRfHc4/btW1L6NzgVQpJUH1eSJbWaZq1Cf/45DBkCnTvD6NHwhz/A22/H849zFJDBqRCS\npPq5kiypVTW6Cr1kSbxqPHgwfPghHHIIDB8Om2+et3rAqRCSpJUZkiWlQwgwbhyccQZMnw69ekF1\nNfzwh3l/aadCSJIyGZIlJW/KFDj9dJg4Ebp0gbFjoU+fnB0jLa2oGOZiS8o/e5IlJWfWLDj8cKis\nhFdfhSuvjKdY/PznBmTlxfK52DULagl8PRc7Jyc/SioqriRLan2ffBKfknfFFdCmDQwcCGeeCWut\nlXRlSqFcrvzm7EAbSUXPkCyp9SxaBFddBeefHwflfv3gvPNgo42SrkwplesTEZ2LLampbLeQlH8h\nwN/+Bt27w5/+BDvsAFOnwk03GZDVoFyfiJjVgTaSSoohWVJ+PfUU/OhH8KtfxYeBjB8PjzwC226b\ndGUqALle+XUutqSmMiRLyo8ZM+INeD/+Mfz73/Gq8Ysvwj77JF2ZCkiuV36zOVZdUmmxJ1lSbn30\nEZxzDlx7LayxRtx/fOqp8felZmrRUeaNcC52YXBUn5JmSJaUG198AZdeChdeGH//hBPiY6XXXz/p\nylTAPBGxNOV6w6bUEoZkKQ9KagVk6VK45RYYNAhqauJDQEaMgK72eCo3XPktPY7qUxoYkqUcK6kV\nkEcegaoqeOUV2GknGDMm7kFOuZJ6EyMVIEf1KQ3cuCflWK5HVqXSyy9D797xf59/DnfdBZMmFUxA\n9sQ1Kd0c1ac0MCRLOVbUKyBz5sDRR0PPnvDCC3EP8uuvwy9/udIx0tVTa+g1YgKd+o+j14gJqQqg\nJfEmRipwjupTGthuIeVYx/IyauoJxAW9AvLf/8Yb8i69NO5BPu20+Cjptdf+xq1pbDdZsb0irOKe\nongTIxUJN2wqDQzJUo7lY2QVJNRHu3gxjBoVj3SbOxd+/WsYNgw222yVD0nbhpvM0L4qBf0mRipC\nbthU0gzJUo7lYwWk1VdnQ4DqaujfH958E3bfHUaOhMrKRh+atnaT+kJ7Jj/GlSRlMiRLeZDrFZBW\nXZ2dNCmeWPHUU9C9OzzwABxwwEo9xw1JW7tJQ+E8Aj/GlSTVy5AspVSr99G+/TYMGAB33w0bbBCf\nmHfMMbBa8/43ka92k5ZaVWivKC/j6f57JlBR8hyBJ0mNc7qFlEKZY8pWJSers/PmwSmnxKvG48bF\np+TNnAnHH9/sgAzxKvrwvj2oKC8jIg6jw/v2SCyEuUt+ZY7Ak6SmcSVZSqFW6aNduBD+8pd4I95n\nn8WrxuecAx07tvw566Rpw4275FeWto2VkpRWhmQphfLaR7tsWXwy3llnwezZsP/+cNFFsNVWLS84\n5dIU2pOWto2VkpRWWYXkKIrKgeuBrYEAHAPMAO4CNgNmAb8MIXySVZVSiclbH+0//wmnnw4vvhgf\nCHLjjbBnafbllqq0bayUpLTKtif5cuAfIYRuwLbAdKA/8HgIoQvweN3Xkpoh5320r78OBx4YB+KP\nP4Zbb4XJkw3IJcgebUlqmhaH5CiK1gJ2BW4ACCF8GUJYABwEjK67bTTQJ9sipVKTs81vH3wQb8Dr\n0SMe6XbhhTBjBhxxBLRx324pStvGSklKqyiEhvbON/DAKNoOGAW8TryKPAX4I1ATQihf4b5PQgjf\nOLs2iqLjgeMBNtlkkx1mz57dojok1ePzz+HPf47/W7QITj4Zzj4b1lsv6cokSUpUFEVTQgiNno6V\nTU/yasD2wO9DCM9FUXQ5zWitCCGMIg7ZVFZWtiypS1rZkiVw000weDD85z9w8MEwfDh07txqJTiD\nV5JUDLIJyXOAOSGE5+q+voc4JH8YRdG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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Konstrukcija modela --> izracunavnaje Y(x)\n", "Y_model = m*X + c\n", "\n", "plt.scatter(X, Y,label='podaci') # stvarne vrijednosti\n", "plt.plot([min(X), max(X)], [min(Y_model), max(Y_model)], label='model',color='red') # model\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "## Primjer 2: Matematičko klatno" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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V7gDMkpAMLaSOdrzaFNpnrW0LKwHaaqSQXEpZTPILSd6SpCb5W0luJvmVJA8m\n+VKSH6m1vjjSKKFn1NEyKW1bWAnQVqPWJP+jJL9Wa/2BJG9N8rkk55I8V2t9OMlzg9fAAaijZVJc\nWwD7M/RMcinlzyR5Z5K/mSS11m8n+XYp5bEk7xqc9lSSTyX5qVEGCX2jjpZJcW0B7E+pdbe187u8\nsZS3JXkyyR9kcxb5epKfTLJWa12867wXa62v3eb9TyR5IkkeeOCBv/DlL395qHEAAMB+lVKu11qX\n9zpvlHKL+5K8PcnP11pPJPkPOUBpRa31yVrrcq11+ciRIyMMA2iTK6trOXnxWh4690xOXrymtRgA\nc2mUhXvPJ3m+1vrbg9cfz2ZI/nop5c211q+VUt6c5IVRBwmMx6Q3kZin7bMBYDdDzyTXWv9Nkq+W\nUrZWezyazdKLp5M8Pjj2eJJPjjRCYCymsYnEbj146Q5PC4A+GLVP8n+X5J+VUr47yReT/EQ2g/fH\nSikfTPKVJO8f8WcAYzCNTST04O0+TwuAvhgpJNdafy/JdoXPj47yfYHxm0aA1YO3++zYB/TFqH2S\ngTmxU1AdZ4CdZQ9eJQDT4WkB0BdCMvTENALs6RNLuXDmeJYWF1KyuUPghTPHJz7DOI16azZN42YL\noA1GrUkG5sS0NpE4fWJp6o/dlQBMz9lTx+6pSU7s2Ad0k5AMPTKLADsNSgCmx459QF8IycDc2ur7\nvNO+oUoAJqOrN1sAdxOSgbnUbEXWpAQAgFEIycBc2q4OecuSEgAARiQkA3Npp3rjkuTT5x6Z7mCm\nYNJbigNwLy3ggLnUp1ZkWtwBTJ+QDB3Uh401ZrlxybTt1uIOgMlQbgEd01zQtjXrmKRTj+f71IpM\nizuA6ROSoWP6tLFGX1qRHV1cyNo2gbiLpSUAbaHcAjrGrGP39Km0BKAthGTomD4taOuL0yeWcuHM\n8SwtLqRks8XdhTPHezGLDjAryi2gY86eOvYdm2yYdZx/fSktAWgLIRk6pk8L2gBgUoRkeqFvGzGY\ndQSA0QjJdF5fWqIBAONj4R6dZyMGAOCgzCTTeW1rida30o+u8ucI0G1CMp3Xpo0YlH50gz9HgO5T\nbkHntWkjBqUf3eDPEaD7zCTTeW1qida20g+G488RoPuEZHqhLS3R2lT6wfD8OQJ0n3ILmKI2lX4w\nPH+OAN1nJhmmqE2lHwzPnyNA95Va66zHkOXl5bqysjLrYQAN2pwB0DWllOu11uW9zjOTDGxLmzMA\n+kxNMrAtbc4A6LPeziR7jAy70+YMgD7r5Uzy1mPktfWN1Lz6GPnK6tqshwatsVM7M23OAOiDXoZk\nj5Fhb9qcAdBnvSy38BgZ9qb0En9LAAAKU0lEQVTNGQB91suQbLesbppGnXnfatnbslMhAExbL8st\nPEbunmnUmatl77Yrq2s5efFaHjr3TE5evObPFaDnehmST59YyoUzx7O0uJCSZGlxIRfOHDdjNsem\nUWeulr273AAB0NTLcovEY+SumUaduVr27trtBsi/EwD91MuZZLpnGu3KtETrLjdAADQJyXTCNOrM\n1bJ3lxsgAJqEZDphGnXmatm7yw0QAE2l1jrrMWR5ebmurKzMehhAj/WtvR9AX5VSrtdal/c6r7cL\n94DpansItZgXgLsJycDEbbVY2+ogsdViLYlgCkArqUkGJk6PaQDmjZAMTJwWawDMG+UWtF7ba1nZ\n29HFhaxtE4i1WAOgrcwk02q2C+4GLdYAmDdmkhm7cc782i64G7b+rDwRAGBejBSSSylfSvLvk7yc\n5KVa63Ip5XVJfiXJg0m+lORHaq0vjjZM5sW4uxioZe0OLdYAmCfjKLf4i7XWt93VlPlckudqrQ8n\neW7wmp4YdxcD2wUDALMwiZrkx5I8Nfj8qSSnJ/AzaKlxz/yqZQUAZmHUkFyT/Hop5Xop5YnBsTfV\nWr+WJIOPbxzxZzBHxj3ze/rEUi6cOZ6lxYWUJEuLC7lw5rjH9gDARI26cO9krfVWKeWNSZ4tpfzh\nft84CNVPJMkDDzww4jBoi7Onjt1Tk5yMPvOrlhUAmLaRZpJrrbcGH19I8okk70jy9VLKm5Nk8PGF\nHd77ZK11uda6fOTIkVGGQYuY+QUAumDomeRSyvcm+a5a678ffP5XkvzDJE8neTzJxcHHT45joMwP\nM78AwLwbpdziTUk+UUrZ+j7/vNb6a6WU/zvJx0opH0zylSTvH32YAAAwPUOH5FrrF5O8dZvjf5Lk\n0VEGBTAvbJsO0E123AMY0rg3zwGgPSbRJxmgF8a9eQ4A7SEkAwzJtukA3SUkAwzJtukA3SUkAwzJ\ntukA3WXhHsCQthbn6W4B0D1CMsAIbJ4D0E3KLQAAoEFIBgCABiEZAAAahGQAAGgQkgEAoEFIBgCA\nBiEZAAAahGQAAGgQkgEAoEFIBgCABiEZAAAa7pv1AGDLldW1XLp6M7fWN3J0cSFnTx3L6RNLsx4W\nANBDQjKtcGV1Lecv38jGnZeTJGvrGzl/+UaSCMoAwNQpt6AVLl29+UpA3rJx5+VcunpzRiMCAPpM\nSKYVbq1vHOg4AMAkKbegFY4uLmRtm0B8dHFhBqPpjr3qvNWBA8D2zCTTCmdPHcvC4UP3HFs4fChn\nTx2b0Yjm31ad99r6RmperfO+srq2r68DQJ8JybTC6RNLuXDmeJYWF1KSLC0u5MKZ42Y1R7BXnbc6\ncADYmXILWuP0iSWheIz2qvNWBw4AOzOTDB21Uz331vG9vg4AfSYkQ0ftVeetDhwAdqbcAjpqq3Rl\np+4Ve30dAPqs1FpnPYYsLy/XlZWVWQ8DAICOK6Vcr7Uu73WecgsAAGgQkgEAoEFIBgCABiEZAAAa\nhGQAAGgQkgEAoEFIBgCABiEZAAAahGQAAGgQkgEAoEFIBgCABiEZAAAa7pv1AGAeXFldy6WrN3Nr\nfSNHFxdy9tSxnD6xNOthAQATIiTDHq6sruX85RvZuPNykmRtfSPnL99IEkEZADpKuQXs4dLVm68E\n5C0bd17Opas3ZzQiAGDShGTYw631jQMdBwDmn5AMezi6uHCg4wDA/BOSYQ9nTx3LwuFD9xxbOHwo\nZ08dm9GIAIBJs3AP9rC1OE93CwDoj5FDcinlUJKVJGu11veWUh5K8tEkr0vyu0l+vNb67VF/DszS\n6RNLQjEA9Mg4yi1+Msnn7nr9M0l+ttb6cJIXk3xwDD8DAACmZqSQXEq5P8lfS/ILg9clySNJPj44\n5akkp0f5GQAAMG2jziT/XJK/l+RPB69fn2S91vrS4PXzSTyjBgBgrgwdkksp703yQq31+t2Htzm1\n7vD+J0opK6WUldu3bw87DAAAGLtRZpJPJnlfKeVL2Vyo90g2Z5YXSylbCwLvT3JruzfXWp+stS7X\nWpePHDkywjAAAGC8hg7Jtdbztdb7a60PJvlAkmu11h9L8htJfnhw2uNJPjnyKAEAYIomsZnITyX5\nu6WUL2SzRvkXJ/AzAABgYsaymUit9VNJPjX4/ItJ3jGO7wsAALNgW2oAAGgQkgEAoEFIBgCABiEZ\nAAAahGQAAGgQkgEAoEFIBgCABiEZAAAahGQAAGgotdZZjyGllNtJvjzrcfTYG5L821kPglZybbAd\n1wU7cW2wkzZdG/9JrfXIXie1IiQzW6WUlVrr8qzHQfu4NtiO64KduDbYyTxeG8otAACgQUgGAIAG\nIZkkeXLWA6C1XBtsx3XBTlwb7GTurg01yQAA0GAmGQAAGoTkniml/EellN8ppfx+KeWzpZR/MDj+\nUCnlt0spny+l/Eop5btnPVamr5RyqJSyWkr5F4PXrgtSSvlSKeVGKeX3Sikrg2OvK6U8O7g2ni2l\nvHbW42S6SimLpZSPl1L+sJTyuVLKf+66oJRybPBvxdZ//28p5e/M47UhJPfPt5I8Umt9a5K3JXl3\nKeWHkvxMkp+ttT6c5MUkH5zhGJmdn0zyubteuy7Y8hdrrW+7q4XTuSTPDa6N5wav6Zd/lOTXaq0/\nkOSt2fy3w3XRc7XWm4N/K96W5C8k+WaST2QOrw0huWfqpv9v8PLw4L+a5JEkHx8cfyrJ6RkMjxkq\npdyf5K8l+YXB6xLXBTt7LJvXROLa6J1Syp9J8s4kv5gktdZv11rX47rgXo8m+aNa65czh9eGkNxD\ng0fqv5fkhSTPJvmjJOu11pcGpzyfZGlW42Nmfi7J30vyp4PXr4/rgk01ya+XUq6XUp4YHHtTrfVr\nSTL4+MaZjY5Z+P4kt5P8k0GJ1i+UUr43rgvu9YEkHxl8PnfXhpDcQ7XWlwePQe5P8o4kf3a706Y7\nKmaplPLeJC/UWq/ffXibU10X/XSy1vr2JO9J8qFSyjtnPSBm7r4kb0/y87XWE0n+Q+bg8TnTM1jD\n8r4kvzrrsQxLSO6xwaOxTyX5oSSLpZT7Bl+6P8mtWY2LmTiZ5H2llC8l+Wg2yyx+Lq4LktRabw0+\nvpDN2sJ3JPl6KeXNSTL4+MLsRsgMPJ/k+Vrrbw9efzybodl1wZb3JPndWuvXB6/n7toQknumlHKk\nlLI4+HwhyV/K5mKL30jyw4PTHk/yydmMkFmotZ6vtd5fa30wm4/HrtVafyyui94rpXxvKeU/3vo8\nyV9J8pkkT2fzmkhcG71Ta/03Sb5aSjk2OPRokj+I64JX/WheLbVI5vDasJlIz5RS/nw2C+YPZfMm\n6WO11n9YSvn+bM4gvi7JapL/qtb6rdmNlFkppbwryf9Ya32v64LBNfCJwcv7kvzzWutPl1Jen+Rj\nSR5I8pUk76+1fmNGw2QGSilvy+ZC3+9O8sUkP5HB/1fiuui1Usprknw1yffXWv/d4Njc/ZshJAMA\nQINyCwAAaBCSAQCgQUgGAIAGIRkAABqEZAAAaBCSAQCgQUgGAIAGIRkAABr+f7vauJU1NKqHAAAA\nAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Pripremanje i prikaz ulaznih podataka\n", "data = pd.read_csv('data.csv')\n", "X = data.iloc[:, 0]\n", "Y = data.iloc[:, 1]\n", "plt.scatter(X, Y)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Koeficijenti su jednaki:\n", "('$a_0$= ', 9.908606190326509)\n", "('$a_1$= ', 1.287357370010931)\n" ] } ], "source": [ "# Izračunavanje koeficijenata --> MODEL\n", "X_mean = np.mean(X)\n", "Y_mean = np.mean(Y)\n", "\n", "num = 0\n", "den = 0\n", "for i in range(len(X)):\n", " num += (X[i] - X_mean)*(Y[i] - Y_mean)\n", " den += (X[i] - X_mean)**2\n", "m = num / den\n", "c = Y_mean - m*X_mean\n", "\n", "print ('Koeficijenti su jednaki:')\n", "print('$a_0$= ', c)\n", "print('$a_1$= ',m)\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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HRKRI0NIREREfcjgcfPfDBt6YNZcyZUpRK6Z63k/ysl83bWXRkvR1yy1bZO0EIiIi2VPQ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\nAMR7lVEzdiSJQ3raXJyIc01fsGPIBggnau/XdQoiIplNQVt2m/uzxRi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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Konstrukcija modela --> izracunavnaje Y(x)\n", "Y_model = m*X + c\n", "plt.style.use('Solarize_Light2')\n", "plt.scatter(X, Y,label='podaci') # stvarne vrijednosti\n", "plt.plot([min(X), max(X)], [min(Y_model), max(Y_model)], label='model',color='red') # model\n", "plt.xlabel(\"l(cm)\")\n", "plt.ylabel('T^2(s^2)')\n", "plt.title('Metod najmanjih kvadrata')\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Modeliranje sa SciPy paketom" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import scipy as sc" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": true }, "outputs": [], "source": [ "p1=sc.polyfit(X,Y,1)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": true }, "outputs": [], "source": [ "Y_model2=sc.polyval(p1,X)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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iIyMLojQRERERcTOe27dh6fgQH468B//Xx7u6nKs4PUCnpaUxYcIEGjZsmLXt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\n+vcpJw4w/7U+vBKyj9xICM6FYXl/Y3Dv5YRXqE7qWQecPff82+0BvHl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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.style.use('seaborn-darkgrid')\n", "plt.scatter(X, Y,label='podaci') # stvarne vrijednosti\n", "plt.plot([min(X), max(X)], [min(Y_model), max(Y_model)], label='model',color='red') # model\n", "plt.plot([min(X), max(X)], [min(Y_model2), max(Y_model2)],'g-.' ,label='model2') # model2\n", "plt.xlabel(\"l(cm)\")\n", "plt.ylabel('T^2(s^2)')\n", "plt.title('Matematicko klatno')\n", "plt.legend()\n", "plt.show()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.14" } }, "nbformat": 4, "nbformat_minor": 2 }