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   "source": [
    "#A helpful script for Exercise 3.4.1.\n",
    "\n",
    "#Here is the data for Exercise 3.4.1\n",
    "data = [[0.1, 0.11], [0.6, 0.5], [1.1, 0.6], [1.4, 0.5]];\n",
    "N = len(data);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#A plot:\n",
    "plt1 = scatter_plot(data);\n",
    "show(plt1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#aTo fit a function u(a,t) = a*t to this data by adjusting \"a\", define\n",
    "var('t a');\n",
    "u(t,a) = a*t; #The model function to fit\n",
    "SS = function('SS')(a);\n",
    "SS(a) = add((u(data[i][0],a)-data[i][1])^2 for i in range(N));"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Now minimize SS(a) with respect to a. Repeat for parts (b)-(d)."
   ]
  }
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