ProblemSets_PartII/Math227C20Sp_P07_PowerLaws.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Math 227C Problem Set 7"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How does the size of the mitochondria in a cell depend on the size of the cell itself?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 180,
       "width": 240
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot settings\n",
    "options(repr.plot.width=4, repr.plot.height=3)\n",
    "\n",
    "# Simulate power-law data\n",
    "\n",
    "N <- 30\n",
    "alpha <- 2.3\n",
    "Y0 <- 100\n",
    "sigma <- 500\n",
    "\n",
    "CellSize <- runif(N,3,10) # independent variable\n",
    "eps <- rnorm(N,0,sigma) # residuals\n",
    "\n",
    "MitoSize <- Y0*CellSize^alpha + eps\n",
    "\n",
    "plot(CellSize,MitoSize)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 1 \n",
    "\n",
    "__(a)__ Use nonlinear least squares (`nls`) to estimate the parameter $\\alpha$ from the simulated data. Use (`b=1,a=5`) as starting guesses in the `nls` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "# Estimate parameter alpha using nls\n",
    "fit <- nls(MitoSize ~ Y0 * CellSize^alpha, start = list(alpha = 5), data = data.frame(MitoSize, CellSize))\n",
    "\n",
    "# Get the estimated value of alpha\n",
    "estimated_alpha <- coef(fit)[\"alpha\"]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": []
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Define the __error__ as $e=|\\hat{\\alpha}-\\alpha|$ where $\\hat{\\alpha}$ is the estimate and $\\alpha$ is the true value (which is known because this is simulated data). \n",
    "\n",
    "__(b)__ Write a function to execute the simulation and nls fitting, taking in the true model parameters $\\alpha, y_0, \\sigma$ and the sample size $N$. Plot the error in $\\alpha$ estimation, $e$, as a function of the magnitude of the noise, $\\sigma$, for a range of $\\sigma=(100,2000)$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ddHuRGBEDOjc3l4iMjIyqrDE0NCSil5KbpEO8E/YDNCuJiYkcDkda12ebaBaOygwNDU1NTeXmPqGI31Pr1q2Jkp48eUL0yWcbHx9PRHp6Yq+sWmKfsB+g6eTm5qakpHTt2lXahfzn5MmTEydObN++/fLly6dOndqiRQsJFxAbG0tNNoSjApfLPXPmTH5+vqamZpPuSBIEIuGHuZsSkf6gLTH5lRYXPdn2pQ4R6Uz6W7R+GqnY30WfiIydfXj51azmZ4Wt7KVBRKbuYWXi26uLiwsRrV+/XnxdQrPg7OysoKBw4MABaRciEAgEUVFRampqhoaG+vr6RNS2bdsdO3YUFhZKsoa5c+cSUVpaWpPu5bfffiOiK1euiNg+LCyMiLy9vZu0qoYR8UEVtv1Kn+ntFV5fWtTDtNuoOT94/PLzTwun9u/Y1S04l3QG/LLWuSl+eVQh0oT9nxM9//tvaU9dDc0dj8fz8/Pj8/murq779++XbjGvXr0aNWpUeXm5n59fUlKSl5dXUVHR/PnzO3TosHXr1oKCAsmUwePxdHV1m24Ih5BcPa4iepaXpV1eN8pC66O7r4oGNq57Y/Ka7hfIx85PUiaiYUeKam5SeNiJiJQnnRffXnEGDQ0wZcoUIjp58mSHDh1YLNbOnTulVUlJSUn//v2J6I8//qhYWFRU5Ovr26ZNGyJq2bLlmjVrcnJymrqSli1bOjg4NPVeCgoKlJSURo4cKWJ7OTiDvr9nzpx5654NO8vLSIu5+s+xA3/8ceDYP6GP0lLu/TnTSmIXejBhP8iGlJSUEydOODo6jhs3LiQkpEOHDvPnz9+5c6dUilmwYEFoaOiiRYtmzJhRsVBZWXn27NnPnj07ePCgjo6Oh4eHqanp8uXLc3JymqiMly9fZmVlNekdQiFVVVW5mdZOxJuEhY/8fH0z/tdt3ezuxlYDnKX13lyrCRO7eK17tNtlvNmBHd/1b/Px3HVlLyP2zq/nhP18Pj8wMLD2l8YmJSURUXl5eS1tACrz8vIqLS1dvnw5EXE4nBs3bgwcOPD7778XCATz58+XZCUHDhzw8fH54osvvLy8qq5t0aLF1KlTJ0yYcPz48Z9//tnLy2vnzp2urq4rVqyobsxWozTpM4Sf4HK5u3fvlodp7UQ70S575NVLhVT7/f60vElP6Ov07v6vA/SJiIitwbEeMHz8VNeZM10njxs5yLadlnAMtJbt6vC3ovYXHBws4gfl4uLSlAcG8uPFixeqqqq2traVF2ZkZHTu3JnFYv3+++8Sq+TmzZvKysrt2rV79epVnY35fP6pU6csLCyISF1d3c3NTbx387Zv305Ely9fFmOfNRFe9D99+rQojZl8iUO23qgi/gn7BwwY4OfnV/sZ9K5du0JDQ9u3b9/wsqE52bZtW2Fh4bJlyyovNDIyCg4OHjhwoLu7OxG5ubk1dRkpKSmjR49WUlI6f/58y5Yt62zPZrO//vrrMWPGnDlzZuPGjdu2bdu7d++sWbPWrl2rqyuGUatNOk3SJypefzV27FgJ7K4JiZbjp8fU0c2Ypv09Uo3ygozYiNBL/mdPHj9x+p8LoZEJr2q5d9gYuEkIonvz5o2Ojk6nTp34fH7VtRkZGRYWFiwWa+vWrU1aRkFBgY2NDYvFOnv2bAM2Ly8v/+eff3r27ElE06ZNE0tJ//vf//T09MTSVZ34fL62tnbfvn1FaSwHZ9BMeqPKfzBhPzDR7t27c3NzN2/ezGZXcwfeyMgoJCRk4MCBCxcu5PP5ixcvbqIyZs2aFRkZuWbNmlGjRjVgcxaL5ezs7OzsbGNjc/78eT6fr6DQ2FkUhLNwNLITEbHZbFtbWzmY1k5236gCwDjFxcW///57mzZtJk+eXFObVq1ahYaGfvHFF0uWLCkqKlq5cqXYy/j111+PHj06cuTI1atXN7Kr4cOHe3h4hIeHOzg4NKafzMzM169fSyygicjOzu7y5cuPHj2ytraW2E7Frh7D7ObM2YOnPwBqceDAgfT09MWLF9f+FLWBgcGVK1esrKxWrVq1YcMG8dYQHBz8448/WlhYHDx4sNqz+HpxcnIiooCAgEb2I8khHELy8biKiN9f4SM/X1/fo7clNycSgIzh8/mbN2/W09ObOXNmnY0NDAxCQ0N79uz5008/rVu3Tlw1PHnyZNy4cdra2n5+flpaYpgzzMbGxsjIyN/fv5H9SD6ghdPa3blzR2J7bAoiBjT3W/deKnT35IlngqatB0BWnT59OiEhwc3NTUOj1vs17+nq6gYHB9va2q5Zs8bDw6PxBeTn548ePTo/P//IkSNmZmaN75CI2Gz2kCFDHj16JHwaoMEkH9DyMa2diAHNb+u6/+D8zjFLBw5dse/CzfuPPpXStGUCMN6mTZvU1dXnzZsn+iY6OjqXLl2ys7Nbu3at8KmWBisvL580aRKPx/vtt9+GDBnSmK4+IbzKERgY2JhOYmNjW7ZsKZycWGK4XG5cXFxeniy//060wR4MHGYnORhmB3US5teiRYsasG1OTo7wgunSpUsbXMCPP/5IRFOmTGlwDzXJz89XVlYeOnRoYzrR09Pr16+fmCoS1ebNm0mEae0wzA5Aznl6erZo0WLhwoUN2FZHR+fixYuDBw/+9ddf+Xz+3LlzP/vss3r1cPr06V9++YXL5e7Zs6cBBdROQ0Ojb9++ISEhBQUFampqdW9QRUZGRnZ2tmQeUams4j7hwIEDJbxrccEwO4DGunXr1vXr111dXYWTwzWA8FrHV199tXnz5s2bN2tra1tZWVlbW3fr1s3a2trS0lJFRaWmbWNiYqZPn25kZHT27NlamjWGk5PT5cuXr1y5Mnz48AZsLvkL0EI9evRQUlKS6cvQMjyEG4AhPD092Wz20qVLG9OJtrZ2cHDwmTNnoqOjY2JioqOjb9y4IVylqKhobm5ekdfdunWruJiblZU1cuTIsrKys2fPNt08y05OTgsXLgwICJCtgFZVVe3atatMD+SoLaD/8fSMp06jlo80r62Heztddtwl2wMH6nFvBEBuPHr0yN/ff/To0ebmtf5FEYGGhobwhodQUlJSzHvR0dHHjh07evSocJWxsbEwrMPCwpKSkvbt2yccVdZEPv/8844dOwYEBAgEgga8kFsyb7qqFpfL9fHxSUtLa926teT33ni1BfSRFSv+ojFmHwL68g/WS4Lpy9+iNzl+aJUUcvDgX/QWAQ3Nk5eXl0AgaOQYjGq1a9euXbt2zs7/va4oLy+vcl6HhoZevHiRiNzc3KZPny72vX9i2LBhW7ZsefDgQbdu3eq7LY/HMzAwkPAQDqG5c+eqqakZGBhIftdiUa9LHLmJMTExZJbbVMUAyJikpCThxPzCeYWalJaWVt++ffv27Sv8Y1lZ2ePHj58/fz548OCm3jUROTk5bdmyxd/fv2EBLa3nrbt06SJ8RaGMauyToADN2aZNm8rKylasWCH5XSsqKlpaWg4dOrTx0xiJom/fvjo6Og145jstLS03N1fyF6DlAwIaoIFevny5f/9+W1tb2R3FJTolJSVHR8eIiIiXL+s34YO07hDKBwQ0QAN5e3sXFhZK5fRZKpycnMrLy4OCguq1FQK6MRDQAA2Rl5fn4+Njbm5ecRNP7jk5ObHZ7Ppe5ZDiEA45gHHQAA3h4+OTm5u7devWxk/pKSsMDAxsbW0vXrxYWlqqpKRU9wZERMTj8Vq1aiXKO7egquYe0HirNzRAxcT8EydOlHYtEuXk5BQREXHz5s3+/fuLuElcXFyPHj2asih5VmdAh/86cuSR//4//e6nSyoWyqqQkJARI0aI0jIxMbGpiwFZsX///oyMDG9v79on5pc/Tk5Oq1evDggIEDGgU1NTMYSjMeoM6PS7587VtUSG4a3eUF/Cifn19fVnzJgh7VokrXv37q1btw4ICNi0aZMo7SX5Jm+5VFtAe4SEzBe1H1l9UEdBQaHO6QWEM0k2n0uNULtTp049ffrUw8NDxIn55QmLxRo6dOjevXufPn0qyjsBMISjkWoLaEuRLzMByJySkpIVK1ZkZWXZ29vb29tbWFiI8jtYIBB4eXlpaGjMny/y2Yt8cXJy2rt3b2BgoJubW52NMYSjkZr7TUJonnJzc8eMGXP16lUiOnToEBHp6ur26dOnT58+Dg4OPXv2rGni4wsXLsTExCxatEhPT0+iFTOGo6OjsrJyQECAKAHN4/GMjIz09fUlUJhcQkBDs5OWlubk5BQTEzNr1ixPT8+oqKiwsLCbN29euXJFOMhXUVGxY8eODg4O9vb2/fr1MzU1rdjW09NTSUlpwYIF0itfytTV1fv37x8aGpqfn6+pqVlLS4FAEBcXJ4FZSuQYAhqal6ioqGHDhr148WLz5s2LFi0iIkdHR0dHRyIqKiq6d+/erVu3wsLCwsPD9+zZI3xBSYcOHezt7fv06aOhoXHjxo0ZM2a0bdtWyochVU5OTkFBQVeuXBk5cmQtzVJSUt68eYML0I2BG1/QjAQGBvbr1y83N/fUqVPCdK5MRUXFwcFh6dKlfn5+L1++jIuL+/PPP6dPn66oqHjo0KE5c+ZMnjy58RPzy4Fhw4YRUZ2PFOICdOPhDBqaC19f3/nz5+vo6Pj5+fXu3bv2xiwWq1OnTp06dXJ1dSWiV69e3bp1Kzw8nMPhdOzYUSL1Mlf79u07d+4cGBhY+/z9GMLReDiDBvknEAjWrl07Z86ctm3bhoWF1ZnOVRkYGDg7O3t6es6bhxdTEBE5OTmlp6dHRUXV0gaDoBsPAQ1yrri4ePLkyR4eHlwuNzw8vPEvpgIicnJyorqucvB4PBMTk2Y73EUsENAgz3JycgYPHnzs2LFRo0aFhIRI5a1LcsnBwUFPT6+WgBYO4cD1jUZCQIPcSkxM7NOnz7Vr19zc3M6cOaOqqirtiuSHgoLCoEGD7t27l5mZWW2D5OTk/Px8XN9oJAQ0yKe7d+/27t07ISFh27Ztv//+O57UFzvh/P0XLlyodi3uEIoFfmpBDp07d65///75+flnz579/vvvpV2OfBK+DrGmqxwIaLFAQIO82bt379ixY1VVVS9duiTiXLLQAHp6elwuNygoqLi4uOpaYUBbWFhIvC65goAG+SEcTjd79ux27dqFh4fb29tLuyI55+Tk9Pbt27CwsKqreDxe69atdXV1JV+VPEFAg8wrKCgIDw/fsWPH4MGDPTw8/ve//0VERHz++efSrkv+1fRIoUAgiI+Px/WNxsOThCB78vPzo6Ojo6KiIiMjo6Ki4uPj+Xy+cNXkyZP/+OMPZWVl6VbYTFhZWXE4HH9//y1btlRe/vz587dv32IIR+MhoEEG5OXlPXjwIPK9+Pj4ildEGhsbDxkyxMbGxsbGxs7OrlWrVtIttblxcnLavXv3kydPKj8B/+jRIyLq0qWL9OqSEzIa0ILCjJiwsKi4xPTs/GKWup6hoaGJWc9+9uY6CtIuDcSEz+fv3Lnz5s2bkZGR//77r0AgICI2m21mZjZu3DgbG5sePXr06NFDR0dH2pU2a8KADggIqBzQmCZJXGQvoEuT/NbMW7I9MOFtlVVK+p0dp/zg5eHSVUsKhYF4rV+/3sPDQ0FBwdzcfNKkScJEtra21tLCt8sgX3zxhaqqakBAwMKFCysW8ng8FouFgG48GQtoQcrh0bZT/bOIrdGW+8Ughy4cg5Z66qyStzkZSbF3gy9ev+A9/UpQ5IWb2weKdveYz+cHBgbW/tLYpKQkIqr4NzVIQGho6IYNG7p3737t2rXaZ4UH6VJVVR04cGBwcHBeXl7F787Y2NjWrVtra2tLtzZ5IJAlxf4u+kRk7OzDy69mNT8rbGUvDSIydQ8rE63H4OBgET8oFxcXsR4L1Ojly5etW7fW0NCIi4uTdi1Qt127dhHR6dOnhX/k8/nq6uqDBw+WblWiEw4T9Pb2lnYh1ZCtM+h7QUGvibq7b5nTubr3KbP17dfvdj9lvSHh77/vb7UX5U07AwYM8PPzq/0MeteuXchJvVkAABhHSURBVKGhoe3bt29g1VAfAoFgxowZaWlphw4d6tSpk7TLgboNGzZs3rx5AQEBY8eOJaKkpKR3795hjJ1YyFZAZ2dnE1Hr1q1rbMEyN+9IlFDTDC5VKCgoDB8+vPY2gYGBRITJHCTjt99+O3/+vKur65QpU6RdC4iEw+F07do1MDCwvLyczWbjIW8xkq3Q4XA4RBQVHl7No6VCZZGRD4jI2NhYclWB2Ny9e3fVqlUdO3b09vaWdi1QD05OTi9fvrx37x5hFg6xkq2AtpowsQuL0ne7jPcOTa0S0mUvI3wmTt2RQmQ27use0qgPGiM3N3f8+PFsNvvUqVO4MShbKs/fLxzCgctTYiFblzhYVssOe91wXBpybuGA8z9xrGytzTkGmi2oKC/7ZWL07aikPD6Rlu3qw6vtanxRWvMQHx+/f/9+BQWFtWvXtmjRQtrliGTmzJmJiYm+vr7dunWTdi1QP7169dLX1/f39/fw8IiNjeVwOBjCIRayFdBEatY/BD2w27Nx467T12OjQ1KiK61jqbXpNWr2Co+lIzo01wd93759e+rUqX379t28eVO4JCws7K+//jIwMJBuYXXatWvXX3/9NW7cuNmzZ0u7Fqg3BQWFIUOGHD16NDU1NT4+vl+/ftKuSE7I1iUOIiJSMuk3b+cl3oucjNiI0Ev+Z08eP3H6nwuhkQkvs1PCj/zUTNP51q1bM2fONDExmTFjxv3796dOnRoaGrp48eIbN25wudyHDx+Kd3cFBQWzZ8/W1NTct29f43uLiYlZvHjxZ599tmfPnsb3BlIxdOhQgUCwY8eOgoICPKIiNtIe5ycDXFxciGj9+vXSLqQaL1682LRpU8Wsu3Z2drt3787Nza1osG/fPmVlZU1NTT8/P3HtNCYmRrhH4UukXF1dCwoKGtxbfn6+ubl5ixYt7ty5I64KQfKys7MVFRWFVzb27dsn7XLqAeOgxa65z8VRXl5+9erVPXv2nDt3rqSkREdHZ/bs2XPmzOnevfsnLadPn25ubj569GhnZ+fVq1evXbu2kbs+dOjQd999V1JSsmbNmgULFsyYMWPfvn1RUVGnT582MzNrQIfz5s17/Pjxli1bbG1tG1kbSJGurm6fPn2uX79OmCZJjKT9G6LeShLPrRj6eXXPqZCSfuch7vsfvBHzHhl1Bp2cnOzp6WlqakpEbDbb0dHx4MGDdZ7ApqSk9OjRg4i++eabBp/tvnr1SjhmvF27drdu3RIuLC8v9/b2VlRU1NTUPHXqVH373L9/PxENHTq0vLy8YVUBc3h5eRERi8XKy8uTdi31wOQzaBkL6PLkQ8NaEhGxNdpynWcuXunhuXX7du/Nv6xZ8u3X/T7TZBFRC4v5V7LFuVMmBDSfzz9+/Hi/fv1YLBYRtW/f3sPDIzk5WfQe8vPznZ2diah3794ZGRn1LeDKlSsmJiZENGXKlKp//S5fvmxoaMhisRYvXlxaWipin3Fxcerq6m3atMnKyqpvPcBAwllGTU1NpV1I/SCgxUX8c3GIQroBLYxm4TVfFRWVCRMmXL58mc/nN6yrFStWsFgsDocTFRUl4lalpaUrVqxgs9laWlqHDx+uqVlqaqqDgwMROTg4pKWl1dltYWGhlZWVoqLi9evXRT0AYLzu3bvL3Kw1CGhxufm9MRF193pWY4vy6FWfE5Hp4rvi26u0AprP5588eVJ4Q1xTU3PVqlViOdM8cuSIioqKurr6mTNn6mz877//9urVi4hsbW2fPn1ae+OSkpJFixaxWKxWrVpduXKl9sZz5syR+r9LAAQIaPE5P0mZiIYdKaq5SeFhJyJSnnRefHuVfECXl5f7+fkJ7/ipq6u7ubllZmaKsf+oqCgOh8NisZYtW1bLyfiZM2d0dXVZLJabm1txcbGInZ87d05HR0dBQWHNmjU1dX769Gki6t+/f1mZGP+pA9AQCGhxiV5uRkQm80JqTOjSMHcOEbVbck98e5VkQAujWXhDrymiuUJaWppw1MTXX3/97t27T9YWFBS4ubkRkaGhYWBgYH07T0hIED4N6OTk9Pr160/WPn/+XE9Pz9DQUJQrIQBNDQEtLuUxq7uwiBRMnbeGpFQJ6dIXt3d9/ZkiEZktjRDjmACJBXRwcLCNjU1FNDfgVl69FBYWTpo0iYisra2fP39esfzhw4fCYVJffvllenp6gzufNWsWEXE4nPDw8IrlJSUlvXv3ZrPZQUFBjT0AAHFAQIvPu/u/DtAn4TgOjvWA4eOnus6c6Tp53MhBtu20hGOgtWxXh78V5z4lENDBwcE9e/YkIjU1NTc3twbHYn2Vl5d7enqy2WxjY+OIiAjhmDllZWUlJaVaLlCI7uDBg2pqasrKyhU//YsWLSKiFStWNLp2APFAQItVSVrojrlfdjao8kQ3S61Nr0nrzj2t5Qp1gzRdQFe+oKGmprZo0aImuqBRu5MnT6qpqamqqgqHYZibm4s+xqNO9+/f79ChAxFNmjTp5MmTLBarT58+og/FA2hqTA5oGXySUMmk37yd/ebtKMyMf/g49VV2Tn4JW1XbgGNmaWnWUibm4cjKykpOTo6Li/P29r53756qqqq7u/uyZcuMjIykUs+4ceM6dOgwcuTIsLAwV1fXbdu2qauri6tza2vryMhIFxeXo0ePHj16VE9P7/jx44qKMviDByBxMvr3pOqj3sWkZvRZ+5bKjHnUWyAQZGRkJCUlPX/+PDk5+fl7whcCCduoqKi4ubktX75c6i8YsLGxiYqKio+P79u3r9g719bWPnv27ObNm9etW3fgwIG2bduKfRcAckn2Aro0yW/NvCXbAxPeVlmlpN/ZccoPXh4uXbVE7U2Mb/U+e/bsw4cPhSmcnJycnJxcUlJSuYGKioqpqam9vb2pqWnbtm1NTU2//PJLaZ01V2VgYNB0s5KyWKwlS5YsWbKkifoHkEsyFtCClMOjbaf6ZxFboy33i0EOXTgGLfXUWSVvczKSYu8GX7x+wXv6laDICze3D9QVqcOQkJARI0aI0jI1NbWWtRkZGWPHjhUIBESkra3dtm3bwYMHm74njGPmZDEAyATZCuiSwNUL/bPI2Nnn8pFqXuxd/vrm6mFfbby9w3XdN8+22otytUOUt3oHBAQcPHhw4sSJtbQxNja+e/euoqKiqampjo6OCHsGAKiDbAX0vaCg10Td3bdUk85ExNa3X7/b/ZT1hoS//76/1b6nCD2K8lbv9PT0gwcPKikp1d5MOIQZAEBcZOuNKtnZ2UTUunXrGluwzM07ElFmZqbEigIAaBqydQbN4XCInkaFhxdP6l/9gLqyyMgHRNQEoyIeP36soqIi7l4ZpLS09MCBA6ampmy2bP3abqDy8vKnT5+amZk1k+Ol5nrIz58/d3FxqeVfwI8fP5ZkSfUj7YHY9SKdR7137twp7W8JAJrWzp07xZcZYsMSCATS/mTqoyB60zDHpSGvidgaHCtba3OOgWYLKsrLfpkYfTsqKY9PpGW7OijEo5fYnrSgN2/eHDx4sLCwUGw9MtKDBw+OHTvm4OAgfF2L3Hv+/HlYWFjzOV5qxoc8ceJEKyurWpqpqqpOmzZN+EJFZpH2b4j6k/ij3s3EqVOniKgBr62SUc3teAU4ZBkkW9egiUgeHvUGABCFDAb0f1iqRhZ2RhbSLgMAoKk0l5u5AAAyR/4C+tKCTp06dVpwSdp1AAA0kuxe4qhJXtrjx4+pS5606wAAaCT5C+h+HiEh88nAUtp1AAA0kvwFtIFl//7SrgEAQAxkNKCrTthvaGLWs5+9uQ5jJuwHAGgk2Qto8U7YDwDAWDIW0GKfsB8qqKqqVvy3OWhux0s4ZFkk7UcZ66XY30WfiIydfXj51azmZ4Wt7KVBRKbuYWUSL07WlZWVBQUFlZU1l0+uuR2vAIcsg2RrsqRbbib22zO6ez2LWvpZ9S0EMT+ZW29IMF18N+k3USbsBwBgLNl6UAUT9gNAMyJbAc3hcIgoKjy8uKYWTTdhPwCAhMlWQFtNmNiFRem7XcZ7h6ZWCemylxE+E6fuSCEyG/d1D2nUBwAgRrJ1DVo6E/YDAEiFrAU0EZWmX9uzceOu09djX318Es1Sa8MdNXuFx9IRHTAtNADIPhkM6P8IMGE/AMg32Q1oAAA5J1s3CQEAmhEENAAAQyGgAQAYCgENAMBQCGgAAIZCQAMAMBQCGgCAoRDQAAAMhYAGAGAoBDQAAEMhoOXb0w3WrGp89cdHr9wtePLX2gl9Oppoqarpteni6Op1KbWM6tWAAUr9pmqwWs4PrW6dWA6QeR9CDYcsj1/6m/v7fxjXp6OxjmoLFU3Dz7kjF/1xN6dyA7F8g4w6ZCGpvnALmli5/2S16r71wXs/vNOxhOc9UP+T9SwDpwNJ5aI2YITXR0ZqEenPC6myRiwHyMQPoYZDlr8vPffqfHOlKsfTovPCq3miVytbh/weAlquJf3Wk+jzFZG1NEneMUCZiM0ZsfXq09yiwpxnoVucOSwi9aH7XonWQKr4hdnPY64e95xmrUlUbUCL5QCZ9CHUdchy96U/WN2ZiNSsZu4Le5ZdWPgmLeYfj0FGRMTq+FO0qNXK1iFXQEDLtaBZWtRi/OnimlvEru5MRK3nXi34sCz/9Bh1Ipb99nRRGkhV4WGnj854qga0WA6QSR9CnYcsb1963BpLIur28+PKZ7JvT4/XJqIePz8R0zfIqEP+ANeg5Vl6fHweWZjkek/q00FPTVlVr13PkYv2R1W6dpd59WosEWfctAGqHxZqDBnpqEyCiBthpXU3kC6Vyf7vf5SPj6mugVgOkFEfQl2HLHdf+r//JhK17j+gI6vSQvXOndsSUVFRkXi+QWYd8gcIaHn2+PFjogfes5cdC/83p7CkKOd55Lmtrr3tZvm9f+n54/h4Ipa1tdVH26l36dKOqCwxMaXuBgwnlgOUqQ9B7r70oYfeCQSp3r0qLyt5cPKfOCJ9B4dO4vkGmXXIHyCg5Vju48cvSdHEcfmxu89ziwpzk6PPbRjxmVLJ0z+mzj2VTUQkyM7OIdI0MFD5eMuWLVsSUX5+fp0NJHMkDSaWA5SpD0H+v/Ti5xd+GjJ4w/2yVs5bf/pSSSzfIGMPWVFaO4ampzPnsmBOpT9zuo1Y+Zc5q0/XlXf9Dvm9GeeiXV5Swq9uSxaLRUTq6up1NmiCssVJLAcoUx+CPH/pgtyHJ35dsdI7ILFYv7fbycObxrUh4ovjG2TsIeMMuplRNB813IKIn5iYTEQK2trqRHnZ2Z+M9szJySEiQ0PDOhtIqOyGEssByvqHIA9fuuD17Z0zbD6znvjLVVa/JYcjE27+Pq5DCyLRvh2ZPGQiQkA3Q6WlpUSkqalJRGRmZkZE0dExHzUpjo39l8jAzEyr7gYMJ5YDlPUPQda/9NInf4zp7jB/f7LZDJ+wfx9f2DTZWvfDHUOxfINMO+QKUhk7ApJweY4OkeqIQ7mVF5bc/cGcRdTK7bpw0FL4gjZE9NkPESUf2rw+MVKLSH9GcJkoDZji+BiqbpidWA6QoR9CNYcsh196+f3VlgqkYOZyJrX6XYvlG2TUIX+AgJZf7/75RouIWvZfcfxmXFreu5ykaL91X7VRIFLsti72v0Gl5Y/WdWMTKXYY53PzeV5RQWbMmR/66BJRO/cbpSI1YIoaAlosB8jQD6GaQ5a/L73s2ndGRKYLwmvcsVi+QSYdciUIaHmWeGi0cdWLWNp9Nt0v+tCoKMrD9tN7ICoWblffiNyAGWoIaDEdICM/hGoPWd6+9IdrzKscTYVu6+NErVaGDrkSBLR842dFHV4+tk+nNjrKLdR0OV2/nL7BL+Hdp63ePjqydHTPdnpqLdT021oPc/O9m13PBgxQY0ALxHSAzPsQajhkufrSy89P+2ToWzUBLWK1MnLIlbEEAkHNhw8AAFKDURwAAAyFgAYAYCgENAAAQyGgAQAYCgENAMBQCGgAAIZCQAMAMBQCGgCAoRDQAAAMhYAGAGAoBDQAAEMhoAEAGAoBDQDAUAhoAACGQkADADAUAhoAgKEQ0AAADIWABgBgKAQ0AABDIaABABgKAQ0AwFAIaAAAhkJAAwAwFAIaAIChENAAAAyFgAYAYCgENAAAQyGgAQAYCgENAMBQCGgAAIZCQAMAMBQCGgCAoRDQICdyoo+unDSwK0dPvYWSqpZRx17O87cEPiv8qM2JsSwWq8uGeCmVCFBPitIuAKDxBGlnpjlMPJxU+n5B6YuECL+ECL8/facdubxvDAcnIiCT8IMLsu/1ibmuh5P4bYasORnxNONNUUnB66R7f28a21G56MnBaTP/zHjf8JszAoHg0apO0iwWQHQsgUAg7RoAGuXNgWH60wOMv7vydNdA5cor0vZ88fm3V4scdqTfmGckreoAGg5n0CDz0pKT+UQm7dsrf7Ki9cTJAxRI8ORJwn8LPrkGXZp66efJ9h301dT02tmNXx+cUnbmG0UWa+SJssrte3mn5kfvmzugo4GGZiuLQQvOJBQT5d/bPbvf5y3VVDRaWXzx/UFe5Wvd5VmRB5aN5nY00VbTNOrQzXHm5svPi5r0EwC5JQCQca98v2QRsVsP23w16W15bS2PjyEiy/VxAoFAUJ50ZKTJRycoCu1mzBykQOR8vLRy+55zlg7QqtSMbb74kKeD2kd/jdrMDyn6b5u3V+d1qHJrR7uv96PS6msCqBnOoEHmtRzz3dcGVJ7mv3hgOz3DTn2dXZds9Dl56V5yfnnNG2UdnDfnn3RWu1G/XX6cVfDu9bMbe6dqnvzjEr9Ky0jf7enDd4Q8y85/Hf/3txaK5Y83T10e13PFXzEZ+e+yHh6a0oFFqUePXRO2fn3M0+dZmX7flecepuUVFmQnRRz8tpvKmxurPAPKqnQNUAdp/4YAEIOC2GNug811PjlzbdHSauTy03EFFc0+nEGnb7dnEXHmXi+q1Msz797KVOUMmrpviKs4L3/mZUtEyo67X1Rs9WB1RyIavDdfIBAIBCHzWhFZePAqdfv2wFdE5OCd2RRHDnINw+xAHqhaTPj94oQtb9PjHz6Ke5zw7OnjRzH374ZHPPjH8+trUX/ev+hqyvpog8h79wTU0ml038rXrT8bPaqbe/idT/o2HTS4U8XGenp6RGRmb29YsV5TU5OIioqKiDSI+u/IFOwgIiJB6dvXLzIy0v4N9X9IRALcjod6Q0CD/FDQMLHsbWLZe9B/f+ZnnJlq9/WxS+t33HHdxK3c8t3r18VEHY2NP+7A2MSkaq/6+vqfLtLR0amxiJLUyzs2bDkRfDsmMadEQEQsAwO9eh8KABFGcYDs85uozGJpTw+qeoKqYDx28iB1oqSEhNKP1ygrKxNRdnb2x4vT09Kq9s9isaourMmrs9O4Xy72vXD33xy+in7bTtzh7ieCf+HWvSFANRDQIOssLTsT5fntO5NVZZXg2cNHBURa+vpKH69QNDMzJUoPvviw0n1EftzhY/caV0vuuV0n0slw8KarCdkF77Kex9322zq6MC62cb1Cs4WABlnXwWXuIDXKPjXNYfwvp249eZFfXFZWmJMcE/zniqEDV94RkN7o0f0+3ch6+PA2JIjdMmHGH+FJOYWFrx9f/n3iiPUPGllLSUkJEbXQ0lER8MtK8jNjr+xfPnjsthQ20dvcnGJ+LcNKAKoh7buUAI1WnvHPHEu16n/AdbjLgrPeN6w8DvrFP9NNFT5qqthp1vS+RDTqZFnl9jabEj/sKmfvYCKy35ryYVHiJhsi6rf9lUAgECTvGaT9cQGa3LWHlncjIiL1aRea/sMAeYIzaJB9LCNnn7sPLmz9fpR9JxMdVSUFJVWd1p16O8/ZcDwy4aanY5WbfEREhs5/3rm2fbZjZ0O1Fsparbs7r/ILXtGpiEhLV1ehug1Ewpl14orvd44WJtqq6i3N+kzw+Cfy2popC9bM7qKnrGbcSrvuHgA+wFwcAO/lHh1uMtm/w9r4h2vMpV0LAOEaNDRT5YFTNVksrb4/BTzKyC8uLc5Lifpr5aiF/oX0+fDhSGdgCJxBQ/NUGrGye9+feZ8Mv1P8bHZApO+gmkc5A0gSAhqaK0H2vUObN/9xNiw2+WWBom4bC/vhrst/mmWrW49hzwBNCgENAMBQuAYNAMBQCGgAAIZCQAMAMBQCGgCAoRDQAAAMhYAGAGAoBDQAAEMhoAEAGAoBDQDAUAhoAACGQkADADAUAhoAgKEQ0AAADIWABgBgKAQ0AABDIaABABgKAQ0AwFAIaAAAhkJAAwAwFAIaAIChENAAAAyFgAYAYCgENAAAQyGgAQAY6v8rGCn/mThTKgAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {
      "image/png": {
       "height": 180,
       "width": 240
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Function to execute simulation and nls fitting\n",
    "simulate_and_fit <- function(alpha, Y0, sigma, N) {\n",
    "  # Simulate power-law data\n",
    "  CellSize <- runif(N, 3, 10) # independent variable\n",
    "  eps <- rnorm(N, 0, sigma) # residuals\n",
    "  MitoSize <- Y0 * CellSize^alpha + eps\n",
    "  \n",
    "  # Estimate parameter alpha using nls\n",
    "  fit <- nls(MitoSize ~ Y0 * CellSize^alpha, start = list(alpha = 5), data = data.frame(MitoSize, CellSize))\n",
    "  \n",
    "  # Get the estimated value of alpha\n",
    "  estimated_alpha <- coef(fit)[\"alpha\"]\n",
    "  \n",
    "  # Calculate the error\n",
    "  error <- abs(estimated_alpha - alpha)\n",
    "  \n",
    "  return(error)\n",
    "}\n",
    "\n",
    "# Define the true model parameters\n",
    "alpha <- 2.3\n",
    "Y0 <- 100\n",
    "\n",
    "# Define the range of sigma values\n",
    "sigma_range <- seq(100, 2000, by = 100)\n",
    "\n",
    "# Initialize a vector to store the errors\n",
    "errors <- numeric(length(sigma_range))\n",
    "\n",
    "# Execute the simulation and nls fitting for each sigma value\n",
    "for (i in seq_along(sigma_range)) {\n",
    "  sigma <- sigma_range[i]\n",
    "  errors[i] <- simulate_and_fit(alpha, Y0, sigma, N = 30)\n",
    "}\n",
    "\n",
    "# Plot the error as a function of sigma\n",
    "plot(sigma_range, errors, type = \"l\", xlab = \"Sigma\", ylab = \"Error\")\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 2\n",
    "\n",
    "__(a)__ Transform the simulated data to $lY = \\mathrm{log}(y)$ and $lX = \\mathrm{log}(x)$. Use linear regression model fit (lm) to estimate the parameter $\\alpha$ from the simulated data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [],
   "source": [
    "# Transform the simulated data to logarithmic scale\n",
    "lY <- log(MitoSize)\n",
    "lX <- log(CellSize)\n",
    "\n",
    "# Perform linear regression using lm\n",
    "fit_lm <- lm(lY ~ lX)\n",
    "\n",
    "# Get the estimated value of alpha\n",
    "estimated_alpha_lm <- coef(fit_lm)[2]\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__(b)__ Write a function that executes the simulation, log-transforms the data, and performs linear regression fitting. Plot the error in $\\alpha$ estimation, $e$, as a function of the magnitude of the noise, $\\sigma$, for a range of $\\sigma=(100,2000)$. \n",
    "\n",
    "Note you may need additional code to handle negative measurements.\n",
    "\n",
    "__(c)__ Overplot the error in $\\alpha$ from nls and the error from lm (as functions of $\\sigma$). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Error in alpha estimation\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 180,
       "width": 240
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Error in alpha estimation\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 180,
       "width": 240
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Error in alpha estimation\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 180,
       "width": 240
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Error in alpha estimation\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 180,
       "width": 240
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Error in alpha estimation\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 180,
       "width": 240
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Error in alpha estimation\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 180,
       "width": 240
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Error in alpha estimation\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 180,
       "width": 240
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Error in alpha estimation\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 180,
       "width": 240
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Error in alpha estimation\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 180,
       "width": 240
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Error in alpha estimation\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 180,
       "width": 240
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Error in alpha estimation\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 180,
       "width": 240
      }
     },
     "output_type": "display_data"
    },
    {
     "ename": "ERROR",
     "evalue": "Error in lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...): NA/NaN/Inf in 'y'\n",
     "output_type": "error",
     "traceback": [
      "Error in lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...): NA/NaN/Inf in 'y'\nTraceback:\n",
      "1. simulate_log_transform_fit(alpha, Y0, sigma, N = 30)",
      "2. lm(lY ~ lX)   # at line 18 of file <text>",
      "3. lm.fit(x, y, offset = offset, singular.ok = singular.ok, ...)"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Error in alpha estimation\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 180,
       "width": 240
      }
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "Plot with title \"Error in alpha estimation\""
      ]
     },
     "metadata": {
      "image/png": {
       "height": 180,
       "width": 240
      }
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Function to execute simulation, log-transform the data, and perform linear regression fitting\n",
    "simulate_log_transform_fit <- function(alpha, Y0, sigma, N) {\n",
    "  # Simulate power-law data\n",
    "  CellSize <- runif(N, 3, 10) # independent variable\n",
    "  eps <- rnorm(N, 0, sigma) # residuals\n",
    "  MitoSize <- Y0 * CellSize^alpha + eps\n",
    "  \n",
    "  # Handle negative measurements\n",
    "  if (any(MitoSize < 0)) {\n",
    "    MitoSize <- MitoSize + abs(min(MitoSize))\n",
    "  }\n",
    "  \n",
    "  # Log-transform the data\n",
    "  lY <- log(MitoSize)\n",
    "  lX <- log(CellSize)\n",
    "  \n",
    "  # Perform linear regression using lm\n",
    "  fit_lm <- lm(lY ~ lX)\n",
    "  \n",
    "  # Get the estimated value of alpha from lm\n",
    "  estimated_alpha_lm <- coef(fit_lm)[2]\n",
    "  \n",
    "  # Estimate parameter alpha using nls\n",
    "  fit_nls <- nls(MitoSize ~ Y0 * CellSize^alpha, start = list(alpha = 5), data = data.frame(MitoSize, CellSize))\n",
    "  \n",
    "  # Get the estimated value of alpha from nls\n",
    "  estimated_alpha_nls <- coef(fit_nls)[\"alpha\"]\n",
    "  \n",
    "  # Calculate the errors\n",
    "  error_lm <- abs(estimated_alpha_lm - alpha)\n",
    "  error_nls <- abs(estimated_alpha_nls - alpha)\n",
    "  \n",
    "  # Plot the errors as a function of sigma\n",
    "  plot(sigma, error_lm, type = \"l\", xlab = \"Sigma\", ylab = \"Error\", ylim = c(0, max(error_lm, error_nls)), col = \"blue\", main = \"Error in alpha estimation\")\n",
    "  lines(sigma, error_nls, type = \"l\", col = \"red\")\n",
    "  legend(\"topright\", legend = c(\"lm\", \"nls\"), col = c(\"blue\", \"red\"), lty = 1)\n",
    "}\n",
    "\n",
    "# Define the true model parameters\n",
    "alpha <- 2.3\n",
    "Y0 <- 100\n",
    "\n",
    "# Define the range of sigma values\n",
    "sigma_range <- seq(100, 2000, by = 100)\n",
    "\n",
    "# Execute the simulation, log-transform the data, and perform linear regression fitting for each sigma value\n",
    "for (sigma in sigma_range) {\n",
    "  simulate_log_transform_fit(alpha, Y0, sigma, N = 30)\n",
    "}\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Part 3\n",
    "\n",
    "In the above simulations, the independent variable $X$ was chosen from a uniform distribution.\n",
    "\n",
    "__(a)__ Find a distribution of $X$ data that makes a very big difference between error from nls and error from lm.\n",
    "\n",
    "__(b)__ Find a distribution of $X$ data that makes a very small difference between the error from nls and error from lm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "vscode": {
     "languageId": "r"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Warning message in log(MitoSize):\n",
      "\"NaNs produced\"\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1] \"Error from nls: 0.272255580614596\"\n",
      "[1] \"Error from lm: 1.92987881796661\"\n"
     ]
    }
   ],
   "source": [
    "# Generate X data from exponential distribution\n",
    "X <- rexp(N, rate = 1)\n",
    "\n",
    "# Simulate power-law data\n",
    "MitoSize <- Y0 * X^alpha + eps\n",
    "\n",
    "# Perform nls fitting\n",
    "fit_nls <- nls(MitoSize ~ Y0 * X^alpha, start = list(alpha = 5), data = data.frame(MitoSize, X))\n",
    "\n",
    "# Perform lm fitting\n",
    "fit_lm <- lm(log(MitoSize) ~ log(X))\n",
    "\n",
    "# Get the estimated values of alpha\n",
    "estimated_alpha_nls <- coef(fit_nls)[\"alpha\"]\n",
    "estimated_alpha_lm <- coef(fit_lm)[2]\n",
    "\n",
    "# Calculate the errors\n",
    "error_nls <- abs(estimated_alpha_nls - alpha)\n",
    "error_lm <- abs(estimated_alpha_lm - alpha)\n",
    "\n",
    "# Print the errors\n",
    "print(paste(\"Error from nls:\", error_nls))\n",
    "print(paste(\"Error from lm:\", error_lm))\n"
   ]
  }
 ],
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