Praktikum_Machine_Learning/Regression/Syabrina Bening Putri_F5A2_202310715235_ML0101EN-Reg-NoneLinearRegression.ipynb
2025-11-19 13:34:04 +07:00

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<p style=\"text-align:center\">\n",
" <a href=\"https://skills.network\" target=\"_blank\">\n",
" <img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/assets/logos/SN_web_lightmode.png\" width=\"200\" alt=\"Skills Network Logo\">\n",
" </a>\n",
"</p>\n",
"\n",
"\n",
"# Non Linear Regression Analysis\n",
"\n",
"\n",
"Estimated time needed: **20** minutes\n",
" \n",
"\n",
"## Objectives\n",
"\n",
"After completing this lab you will be able to:\n",
"\n",
"* Differentiate between linear and non-linear regression\n",
"* Use non-linear regression model in Python\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"If the data shows a curvy trend, then linear regression will not produce very accurate results when compared to a non-linear regression since linear regression presumes that the data is linear. \n",
"Let's learn about non linear regressions and apply an example in python. In this notebook, we fit a non-linear model to the datapoints corrensponding to China's GDP from 1960 to 2014. \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2 id=\"importing_libraries\">Importing required libraries</h2>\n"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Although linear regression can do a great job at modeling some datasets, it cannot be used for all datasets. First recall how linear regression, models a dataset. It models the linear relationship between a dependent variable y and the independent variables x. It has a simple equation, of degree 1, for example y = $2x$ + 3.\n"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"##You can adjust the slope and intercept to verify the changes in the graph\n",
"y = 2*(x) + 3\n",
"y_noise = 2 * np.random.normal(size=x.size)\n",
"ydata = y + y_noise\n",
"#plt.figure(figsize=(8,6))\n",
"plt.plot(x, ydata, 'bo')\n",
"plt.plot(x,y, 'r') \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Non-linear regression is a method to model the non-linear relationship between the independent variables $x$ and the dependent variable $y$. Essentially any relationship that is not linear can be termed as non-linear, and is usually represented by the polynomial of $k$ degrees (maximum power of $x$). For example:\n",
"\n",
"$$ \\ y = a x^3 + b x^2 + c x + d \\ $$\n",
"\n",
"Non-linear functions can have elements like exponentials, logarithms, fractions, and so on. For example: $$ y = \\log(x)$$\n",
" \n",
"We can have a function that's even more complicated such as :\n",
"$$ y = \\log(a x^3 + b x^2 + c x + d)$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's take a look at a cubic function's graph.\n"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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x66vYc8+IqCKAgiMRERGhd2/YsQMWL4bZs62v27e7B0afv7aT4/c9CsD9Wc/S9pa61KuXTymRMGczxpfMBqVbZmYm8fHxZGRkULly5WB3R0REJOBS5xtib+jG1XzJctrRgaUYyjin4s4cYQpFnl6/NXIkIiIihbLbYfnAWVzNl5wkhrt4A/N3CJFvrbUwp+BIRERECvW/D/fx5KH7ARjJaH7jHLf7XWutRQIFRyIiIlKolGcHk8AhVtOKF3mwwHbeJpQMVcpzJCIiEsLsdmtEJj3dyrfYvr21/b7EvPsuKatSOUVZBjANeyGhg7cJJUOVgiMREZEQlZpqFYV1rX1Wu7aVl6hEFj/v22eVBgFejXucdUdbQD7buJy11tqXQJ9KgKbVREREQlBqKtxwQ96isHv2WMcDvn3eGBg4EA4cgAsvpN7rI4D8E0UCTJpUwiNaARRWwdGyZcu49tprSU5Oxmaz8cEHH7jdb4xh1KhRJCcnU6FCBTp27MiGDRvc2mRlZXHvvfdSvXp1KlasyHXXXcdub8sRi4iIBJDdbo0Y5Zdsx5PdYXY7LFkCc+ZYX33aRTZjBnzyCURHw6xZ9Lop2uNEkeEurIKjY8eO0aJFC1599dV8758wYQIvvfQSr776KqtWrSIpKYmrrrqKI0eOONsMGzaMBQsWMHfuXL799luOHj1K9+7dsUfK/kMREQl7y5fnHTFyVdjusNRUqFcPOnWCvn2tr14naty504rOAJ5+Gpo1AzxLFBkRTJgCzIIFC5w/5+bmmqSkJPPss886j508edLEx8eb1157zRhjzOHDh025cuXM3LlznW327NljypQpY7744osCn+vkyZMmIyPDedu1a5cBTEZGhv9fmIiIlHqzZxtjhUCF32bPdn/c/PnG2Gx529ls1m3+fA+e3G435oorrAe2bWtMTk5AXmMwZGRkeHT9DquRo8Js376dffv20aVLF+exmJgYOnTowPfffw/AmjVrOHXqlFub5ORkmjVr5myTn/HjxxMfH++8paSkBO6FiIhIqefpri/XdsWdinOaMgW++QZiY2HmzMhZSOSFiAmO9u3bB0BiYqLb8cTEROd9+/btIzo6mqpVqxbYJj/Dhw8nIyPDedu1a5efey8iInJa+/bWWp4zFz872GyQkuK+O6w4U3FOmzbBI49Y30+YAGef7XXfwU9rnoIoYoIjB9sZv0nGmDzHzlRUm5iYGCpXrux2ExERCZSoKGu7Pni+O8zTBIwFtsvKshYpnTgBXbrAv/7lTZed/LLmKcgiJjhKSkoCyDMCtH//fudoUlJSEtnZ2Rw6dKjANiIiIqGgd2+82h3my1ScmyeegLVroVo1a6daGe9DhKCnH/CTiAmO6tevT1JSEosWLXIey87OZunSpbRt2xaAVq1aUa5cObc26enprF+/3tlGREQkVHizO8yXqTinr76CF16wvp82zadU135b8xQCwipD9tGjR9m6davz5+3bt7N27VoSEhKoU6cOw4YNY9y4cTRq1IhGjRoxbtw4YmNj6du3LwDx8fEMGDCABx98kGrVqpGQkMBDDz1E8+bN6dy5c7BeloiISIGioqBjR8/avfyyNUJjs7kHKYUmajxwAPr1s76/+27o0cOnfnqz5smT1xNMPgdH2dnZbN++nYYNG1K2bMnEWKtXr6ZTp07Onx944AEA+vXrx4wZM3jkkUc4ceIE99xzD4cOHaJ169YsXLiQuLg452MmTpxI2bJl6dOnDydOnODKK69kxowZRJXC1fgiIhJZHFNx+ZUcmTQpnxEnRxbsvXvhnHPgpZd8fu5ir3kKITZj8hsAK9jx48e59957mTlzJgC//fYbDRo04L777iM5OZnHHnssIB0NJZmZmcTHx5ORkaHF2SIiEnI8Llb7+uvwf/8H5crBypXQsqXPz7lkibX4uiiLFwdv5MjT67fXa46GDx/Ozz//zJIlSyhfvrzzeOfOnZk3b55vvRURERG/cUzF3XKL9TXfwGjdOrjvPuv7sWOLFRhBMdc8hRivg6MPPviAV199lXbt2rltf2/atCnbtm3za+dEREQkAI4ehT594ORJ6NYNHnyw2Kf0Jf1AqPI6OPrzzz8566yz8hw/duxYkfmEREREJAQMGQK//grJyVYWbB+27efH2/QDocrrd+Piiy/m008/df7sCIhef/112rRp47+eiYiIiP/NnHk6IJo9G2rU8OvpI6E4rdfbzMaPH8/VV1/Nxo0bycnJ4eWXX2bDhg2sWLGCpUuXBqKPIiIi4g+bNsE991jfjxoFHToE5Gk8TT8QqrweOWrbti3fffcdx48fp2HDhixcuJDExERWrFhBq1atAtFHERERKa7jx611RsePw5VXwuOPB7tHIcvrrfyirfwiIuIfHm+5Ly5j4Pbb4e23ITHRKhPyd9mt0sTT67dH02qZmZkeP7GCBRERkaKlpuafrPHll71fn1NkkDV1qhUYRUXBvHmlMjDyhkfBUZUqVTyubG8Ph6IpIiIiQeQo0Hrm3I2jQKs3O7uKDLJWrrSKmgE891zA1hlFEo+m1bxZaN2hFLzpmlYTERFf2e1Qr17BdchsNiu42b696Cm2goIsx3jGx9P2c82TLWHPHsz1N7B08Luk77MFdgovhHl6/daaIx8oOBIREV/5q8xGUUFWWXJYEtOVy7K+IbPWuVxifmDz3tO1RmvXtkqp1ahRAmueQoRf1xyd6dChQ0ybNo1NmzZhs9lo0qQJd9xxBwkJCT53WEREpDTwV4HW5csLDowAnmEEl2V9Q3Z0RS7dk8pm4tzu373b2rzmytc1T5HG6638S5cupV69erzyyiscOnSIgwcP8sorr1C/fn3lORIRESlCzZr+aVdY8NSXd3iUCQAMKvcmm2ji0XM61jylpnrWx0jl9bRas2bNaNu2LVOnTiXq77E3u93OPffcw3fffcf69esD0tFQomk1ERHxlWM6bM+evGuFwPM1RwVNz7ViNctpTwVOMo7hjGCcV/3zZs1TuPH0+u31yNG2bdt48MEHnYERQFRUFA888IAKz4qIiBTBXwVa27e3ghjXcySRzgf0pAIn+ZjuvFT1Ga/7Zwzs2mVN25VWXgdHLVu2ZNOmTXmOb9q0iQsuuMAffRIREYlo/ijQemaQFU0W87me2uxhI034J+9w3zDfC8p6ujYqEnm0IPuXX35xfn/fffcxdOhQtm7dyqWXXgrAypUr+fe//82zzz4bmF6KiIiEmaISM/buDT16FC9DtiPIGnqfYfSef9GWFRyiCoOSPmT6vyvTowe8/nrBU3iF8XRtVCTyaM1RmTJlsNlsFNW0tCSB1JojEREpjD+zX3si97nnKfPYI+TayrDuuc9p9kAXZ5DlyIUEngVIWnPk4cjR9u3b/dYxERGRSObP7NeePmGZ4Y8CUGbiS7QY2sXtbufo0tDCt/6Dd2ueIpmSQPpAI0ciIpIff2a/9siqVVY5kBMnYPBgmDw57ypvl765TuH99Rfcf797X1NSrMAoUvMcBTQJJMDGjRtJS0sjOzvb7fh1113n6ylFRETCWlGJGV13ghWW/dojO3fCtddagVG3blZUU0gd1KiovM/Zq1fx1jxFKq+Do99//51evXqxbt06t3VIjsK0pWHNkYiISH78lf26SBkZ0L07/PEHnH8+zJsHZb0f78gvYBIftvIPHTqU+vXr88cffxAbG8uGDRtYtmwZF110EUuWLAlAF0VERMKDv7JfFyo7G268Edavt070yScQF1f048RjXgdHK1asYMyYMdSoUYMyZcpQpkwZ2rVrx/jx47nvvvsC0UcREZGwkF9iRlc2m7Wup317H58gNxfuvBMWLYKKFeHjj60Til95HRzZ7XYqVaoEQPXq1dm7dy8AdevWZfPmzf7tnYiISBjxV/brAj36KLzzjjWF9v770KqVr12VQngdHDVr1syZFLJ169ZMmDCB7777jjFjxtCgQQO/d1BERCSc+CP7db5eegleeMH6/s034eqri9VPKZjXW/m//PJLjh07Ru/evfn999/p3r07v/76K9WqVWPevHlcccUVgepryNBWfhERKUpRGbK9MmcO9O1rff/cc/DII37rZ2ni6fXbL3mODh48SNWqVZ071iKdgiMRESkxX35pbdk/dcrK5DhxYqFb9qVgAc9z5CohIcEfpxERERFXy5dbyYhOnYKbbrKm1hQYBZxHwVHv3r2ZMWMGlStXpncRk6Wpqal+6ZiIiEiptno1XHONleTxH/+AWbOgTBn/TtdJvjwKjuLj451TZvHx8QHtkIiISKm3YYO14PrIEas8yPvvQ3R0iRe0La28WnNkjCEtLY0aNWoQGxsbyH6FNK05EhGRgNm2zRoOSk+HSy6Br76CuLgCC9o6Ztn8XtA2Anl6/fZqK78xhkaNGrFnz55id1BERMQTdjssWWJt2FqyxPo5HHn0OnbsgCuusAKjZs3g888hLg673Roxym84w3Fs2LDwfW9CjVfBUZkyZWjUqBEHDhwIVH9EREScUlOtKvedOlk72Tt1sn4Ot+WtHr2OHTusQmdpadC4sZUF++8NT94UtJXi8zoJ5IQJE3j44YdZv359IPojIiIC4JxGOjMo2LPHOh5KAVJho0IevY6dO62IaedOKzBavBiSkpxtS6ygrQA+5DmqWrUqx48fJycnh+joaCpUqOB2/8GDB/3awVCkNUciIoFlt1sjKwWNlths1kLk7duDv1OrsEXSPXoU/TouSUpjRUwHbDt2QKNGVnSVnOzWbskSK3YqyuLF1uCT5C9geY4mTZpUnH6JiIgUyZtppGAGAwUtknaMCo0aVfjrSDE7mZ3eCRs74OyzrejmjMAIThe03bMn/3VHjmDR54K24sbr4Khfv36B6IeIiIhTKE0jFZRXqKhF0jbb6SK0+TmbLXzNldRhF0cSGxK3eHHegmx/cxS0veEG67yuz+mXgrbiplgZsk+cOMGpU6fcjmmaSUREiqtmTf+281VhU2YJCUWPbhW00uQ81vMVnUniD37lHA5N/oo2tWsX2hdHQdv8+jNpkrbx+5PXa46OHTvGo48+yrvvvpvvrjV7KdhHqDVHIiKB5VhzVNQ0UiDXHBWVV2joUCsoKUpCAhw6dPo8LVnDQrpQjYP8zPn0T17E6rSzPH4dypDtu4DkOQJ45JFH+Oabb5gyZQoxMTG88cYbjB49muTkZGbNmlWsTouIiMDpaSTIW0qsJKaRPMkr9M47np1r6FDrq80GbfmOb7iCahzkf1zCFSzmycmeB0ZgveaOHeGWW6yvCoz8z+vg6OOPP2bKlCnccMMNlC1blvbt2/PEE08wbtw43vH0NyVARo0ahc1mc7sluWyFNMYwatQokpOTqVChAh07dmTDhg1B7LGIiBTEMY105jKc2rUDnw3akwXhf/4JNWoUXAfWZoOUFBgxwurv7QmfsIiriCeTpVxO/1pf8fr8BLfXESkJL8Od18HRwYMHqV+/PmCtL3Js3W/Xrh3Lli3zb+98cN5555Genu68rVu3znnfhAkTeOmll3j11VdZtWoVSUlJXHXVVRw5ciSIPRYRkYL07m3lRly8GGbPtr5u3x749TWeLvS+9Vbra1GjW70zpjP9cE9iOcHeFt2wff4563fGub2OSEl4GQm8Do4aNGjAjh07AGjatCnvvvsuYI0oValSxZ9980nZsmVJSkpy3mrUqAFYo0aTJk1ixIgR9O7dm2bNmjFz5kyOHz/O7Nmzg9xrEREpSDCmkTxd6N2jRxGjW70MjB8Pd96JzW6Hfv1IXvUhl18d6/Y6winhZWngdXB0xx138PPPPwMwfPhw59qj+++/n4cfftjvHfTWli1bSE5Opn79+tx88838/vvvAGzfvp19+/bRpUsXZ9uYmBg6dOjA999/X+g5s7KyyMzMdLuJiEjkcuQVKmrKrH37Qka3euZaBc8ef9x60KOPwvTpUK6c27lUNy30eLyVf9iwYdx1113cf//9zmOdOnXi119/ZfXq1TRs2JAWLVoEpJOeat26NbNmzaJx48b88ccfPPPMM7Rt25YNGzawb98+ABITE90ek5iYyM6dOws97/jx4xk9enTA+i0i4i3tWAosb/MKOUa3nI4fh9tuOz3kM3GiFeHkI1wSXpYmHo8cffHFF7Ro0YJLLrmE//73v87Rkzp16tC7d++gB0YA3bp14/rrr6d58+Z07tyZTz/9FICZM2c629jO+DPAGJPn2JmGDx9ORkaG87Zr1y7/d15ExENam1IyfF4Qvm+fFcWkpkJ0tDWcVEBgBKGV8FIsHgdHv/76K8uWLaN58+Y89NBDJCcnc/vtt4fEIuyCVKxYkebNm7NlyxbnrjXHCJLD/v3784wmnSkmJobKlSu73UREgkFrU0qW1wvC162D1q1h1SqoVg2++spaLFWIUEl4Kad5tebosssuY9q0aezbt4/JkyezY8cOOnbsSKNGjXj22WfZu3dvoPrpk6ysLDZt2kTNmjWpX78+SUlJLFq0yHl/dnY2S5cupW3btkHspYiIZ7Q2JTg8XhD+xRdw2WWQlgaNG8PKlR4VO/NmfZOUDK8XZAPExsZyxx13sGzZMrZs2UKfPn2YMGEC9erV83P3vPPQQw+xdOlStm/fzv/+9z9uuOEGMjMz6devHzabjWHDhjFu3DgWLFjA+vXr6d+/P7GxsfTt2zeo/RYR8YQ3a1OkBBkDL7wA11wDR45YEdSKFVYhWQ8EO+Gl5FWs2mrHjh1j6dKlLF26lMOHD3POOef4q18+2b17N7fccgt//fUXNWrU4NJLL2XlypXUrVsXsLJ7nzhxgnvuuYdDhw7RunVrFi5cSFxcXFD7LSLiCa1NCUEnTsDAgafTZd95J0ydaq018oLqpoUWr2urASxbtozp06fz/vvvA3DjjTcyYMAALrvsMr93MBSptpqIBMOSJdbi66IsXqxdTSUiLQ169YIff7SGdSZNgsGDC54f84B2IQaWp9dvj0eOdu/ezcyZM5kxYwbbtm2jdevWTJw4kZtvvplKlSr5pdMiIlIwx9qUooqxam1KCViyBPr0sWqIVK8O773nl4g0T0oACQqPg6N69epRrVo1brvtNgYMGECTJk0C2S8RETmDt7l3wlHIj5zk5sKzz8KTT1rfX3ghLFgAfy/fkMjgcXD07rvvct1111G2bLGWKYmISDFE8tqU1NT8X9fLL4fI6zpwAG6/HT77zPq5Xz+YMgViY4PbL/E7n9YclXZacyQiwRbsERZ/P78jf9OZVyTHiFihSRdLwv/+Z02jpaVB+fLw73/DHXcUa32RlDxPr98Kjnyg4EhESjN/j/DY7VaG74LSFDjWUm3fHoQpttxceP55eOIJyMmxtue//z6EQFUI8Z6n12+f8hyJiJR2dru1JnfOHOtraUm8GIgM3SGbv2nPHrjqKnjsMSswuvFGWLMGe7MWpfKzL00UHImIeKm01jYLVIbuQOVvKlYAu2ABnH8+fPONtabojTdg3jxSv6pcKj/70sbr4OjOO+/kyJEjeY4fO3aMO++80y+dEhEJVaW5tlmgRngCUVvM5wA2MxPuusuaHzx4EFq1gp9+ggEDSF1gK7WffWnjdXA0c+ZMTpw4kef4iRMnmDVrll86JSISShwjEO+8A4MGld7aZoEa4fF3bTGfA9ivvsI0awbTpmFsNtJufgT78u+hcWPVtStlPA6OMjMzycjIwBjDkSNHyMzMdN4OHTrEZ599xllnnRXIvoqIlDjXEYh//tPK+VeQSK9t5unIzR9/eBck+LO2mE9BzNGj8K9/wVVXYdu1i200oINZQt25z1GvcTSpqSG8LkoCwuPgqEqVKiQkJGCz2WjcuDFVq1Z13qpXr86dd97J4MGDA9lXEZESVdAIRFEitbZZUSM8Dvff7/06HEf+plq13I/Xru3dNn6vg5iFC6F5c3jtNQBeZTDn8wvLuRw4Pdr04YeePX+kfvaljccZHRcvXowxhiuuuIL58+eTkJDgvC86Opq6deuSnJwckE6KiJS0wkYgiuLN2phwUliG7jM5ggpvApvevaFHj+LlT/I0ODn46354/X6YPRuAXVF16Wd/k8Vc4dbOGOu1OurKFiVSP/vSxus8Rzt37iQlJYUyZUrvRjflORKJfJ4WeXUV1Hw8JSi/PEf5Ccb7UfTnZriD6fwn7iHKHTkEZcqwu9e9NJn/NEeJK/TcNWrAX38VXtcu0j/7cOf3wrMOdevW5fDhw/zwww/s37+f3Nxct/tvv/1273srIuIH/sza7O30SKTUNvOEY4Rn8mRrCq0grlNYBRVT9Xem7cKK8zbnF15lCJezHI5gJXJ8/XWWb72Yo/OLPvett1ojZ5Fa105O8zo4+vjjj7n11ls5duwYcXFx2Fwmn202m4IjEQkKf2dt9nZ6JBJqm3kjKgoSEz1rW1CgGYhaavlN/VXlIGN4in8xlShyyYmuQNlnRlsrs8uVo+Yxz87do4cVfEViXTtx5/W0WuPGjfnHP/7BuHHjiC2lxfY0rSYSfK4jDlu2wKhR/q3L5Shpkd8IhEONGjBxorWIOOSqx5cAT6ceFy/OO3IU6Fpqqalw/312uux5k3E8Tg3+AmB3mxupPfcFqFPH2baoz/rMKbNg17UT3wWstlrFihVZt24dDRo0KHYnw5WCI5Hg8nTNCxRvLYjjAg75T6MEvRhqgHh68fc2qDjzcQGtpfbll5iHH8a2bh0Ax+qdR/n/vkLUVVfk27y0ftalTcBqq3Xt2pXVq1cXq3MiIr7ydnt9cfLP+Gt7eTjJL7N03bowZkzeMhy+5icKaM6gn3+GLl3g6qutwKhKFZg4kYq//VRgYASl87OWgnm95uiaa67h4YcfZuPGjTRv3pxy5cq53X/dddf5rXMiIq6Ks73e1/wznm4vj4SploKmuvbsgZEjT//sui7IEVR4sw4nIJm2t22D0aPh7betFxAdDUOGwIgR4JJ6pjD+SCUgkcHrabXCtvDbbDbspSB3uqbVRILDl+31Dvmte/GXQCwsLmlFTXW5ym+qyZvgsDhrlfJIS4Onn4bp008Pad18M4wbB/XrF/0kUqoEbM2RKDgSKWmOC+/8+fDqq949NtD5ZwK9sLikeBt4Fud99XWtkptdu+C55+D11yE72zrWrZs1/3fRRd51SEqNgK05cnXy5MniPFwkZDkKjZ65xkJKnusaGF8CIyg8/0xxPutIKkbq7bRjcdYFFauW2pYtcNdd0LAh/PvfVmB0xRXw3Xfw2WcKjMQvvA6O7HY7Tz/9NLVq1aJSpUr8/vvvADz55JNMmzbN7x0UKWn5LUj1tk6U+Ievtc0cilpMW9zPOpKKkfpa9qI4a7m8WgC9dq01XXbuuTBtGpw6Zc25ff21dWvb1reOiOTD6+Bo7NixzJgxgwkTJhAdHe083rx5c9544w2/dk6kpBV0MXbUiSrNAVJJj6Z5u/jaMeIwerRVLmvxYmtaprDAqLifdUAWFgeJp0Vlz1ScWmK9e8OOHdZnle9nlpsLn3wCV14JF14I8+ZZx7p3t0aKFi+2Ro1E/M14qWHDhuarr74yxhhTqVIls23bNmOMMZs2bTJVqlTx9nRhKSMjwwAmIyMj2F0RP8rJMaZ2bWOsy3Hem81mTEqK1a60mT8/73tTu7Z1PFAWLy74s8jvlpLieX/89Vl72sfFi4v5ZpSQ+fOt126zFf2aAvrv4cgRY6ZMMaZx49NPGBVlzM03G7N2bb4Pycmx3ufZs62vpfHfqRTN0+u31yNHe/bs4eyzz85zPDc3l1OnTvkhXBMJjkiaIvGnYI2meTraMmRI0aNEZ/LXZ13UaIvNBikpVrtwUNBU15kCVkts/XrrA61VC+65B377DeLj4eGH4fffrWHLFi3yPExT4eJvXgdH5513Hsvz+R/jvffe48ILL/RLp0SCIZKmSPwlmAuOPZ2uuf56a+mJNxdpf33WxVpYHKLOnOoaPdoKAF35NTHi8eNWbqJ27aB5c2uRdWYmNGpkVbbdvRsmTHAr9+FKU+ESCF4ngRw5ciS33XYbe/bsITc3l9TUVDZv3sysWbP45JNPAtFHkRLh6cW4OGsswo03Iyz+ziFUWHV1OL3d25dRGX9+1r4kQQx1UVHun+eIEX5OjGgMrFgBM2ZY64gyM63jZctCz54waJC1lqiQBVCONXADBxYcvNtsVvDeo0d4BagSfD7lOfryyy8ZN24ca9asITc3l5YtW/LUU0/RpUuXQPQx5CjPUWTyS+6VCDNnjjVNUZTZs+GWW/z//IGqdxWIz9rXDNmRkFnbY7/9BnPnWiNFW7acPl6/Ptxxh7VF34OI1JvaehDYBKASXjy9fns9cgRWfbWuXbv63DmRUOSYIrnhBuvimN/FONymSIor2KNpgRqVCcRnfeZoiyciIbN2kdLSrNGhuXPhxx9PH69YEW680QqK2rWDQqovuCoo6WZhStNUuPiHMmT7QCNHkS2/C1ZKimcX40gbBQiV0bRAva/F+az98dz+zKwdMr97xsCmTbBggXVbs+b0fVFRVlHYm2+2XlylSl6d2psSJ64KGzkKmfdNSoRfy4dUrVoVm4fJLw4ePOh5L8OUgqPI58t/mJE6ChCoqa1QEYyLY1EXeW+DzqD/7mVnw7ffWhmqP/rIfcrMZoPLL7fmXa+/HqpX9/lp/F3iJOjvm5Q4vwZHM2fOdH5/4MABnnnmGbp27UqbNm0AWLFiBV9++SVPPvkk999/vx+6H9oUHMmZwqm+lr8Cv/xGWM48d9u28P33WodzJk8v8k88YeU/LOz1e/O759f39fff4auv4PPPra9Hj56+LzoaOneGXr3guuvgrLP88vyeroGDov/thdO/WfEfj6/f3iZQ6t27t5k8eXKe45MnTzY9evTw9nRhSUkgxVU4JY8sTjLHopLs5XfuqCjvnysYCSdL2uzZ3iW4LOj1e/O7V+z3de9eY955x5gBA4ypVy/vkyUmGtOvnzHz5hmTz/+N/vhcvUkMWlhS0HD6Nyv+5en12+vgqGLFimbLli15jv/222+mYsWK3p4uLCk4ElfhkiXZkf04vwuBzVa84KOgc3v7XIHsozcCmW05J8eYiRO9C44Kev2e/u6NHu3l+2q3G7NxozGvv27M7bcb06BB3geXLWtMu3bGPP20MatXW48p4H0cNsy334f8zle7duG/awkJxnz1VeGfWbj8mxX/C1hwVKdOHTNhwoQ8xydMmGDq1Knj7enCkoKj8ObvC5+nowCzZ/uj974J5F/KRZ27qOdyfB5vv21MjRrB/2s+kCNX+Z3b1/fNGM9/9xISCjkvueaimrtNTuoHxjz+uDGdOxsTH59/By680JgHHzTms8+sEh9+eK3efq4FlTjxJtAKh3+zEhgBC46mT59uypQpY/7xj3+Yp59+2jz99NPmmmuuMVFRUWb69Om+9jesKDgKX4G48IXDX6GB7KO3NdBcn8uXYCGQ72MojK558/q9fe+jOWma8Yu5mdnmWR4xX3KV+YMCItLy5Y3p0MGYESOM+fxzYw4fDuhr9eZzze/3xpPaeo5A/Ikngv+7JsHh6fXb6zxH/fv3p0mTJrzyyiukpqZijKFp06Z89913tG7d2pf1USIloqAFmI4yA74uwAxkJmd/CWRpFF9zyHz4obUrKL/3LBDPV5SiSqUUJ9tyYef2luvrL+h3rwqHaMxvNGYLLcpvpt7JTZzHBhqxhbLkrfWSQxRHU5pQpUtruOQS63beeVCunNf98/W1evO59u5tfQ7eLO72JnFkKPybleDyKQlk69ateeedd/zdF5GACeSFLxySRwYymaOvCSDfece3YMGb5/Nmd1QgS6UUdW5v1KyJtTNs926idu3iw+47+PK17dTnd+qznQb8Tg3+Ov2Ak+6Pz6AyGziPtVzAWi7gJy5kPc34fFYFv2SR9vW1evt75E3STW8SR4bKv1kJLp+Co9zcXLZu3cr+/fvJzc11u+/yyy/3S8dE/CnQNcJCvb5WIEe3ijp3fs9VvTr8+ad3z+NtH73NYRPs0bUocji7ygHKHf6T6vxJDf4kiX3UJJ2apJPEPuqW28u5vXbB4cPOx7X8+3amfVHJRJ3bmGptG/PMu+fwfcZ5rOc89lALOJ23zt+jJN6+P4EepfF2JCtU/s1KcHkdHK1cuZK+ffuyc+dOzBm/bTabDXsgynOLFFMgL3wOvgz1l5RAjm4Vdu4zOZ7r1lut5/OUt330ZQrV59G1U6esyvLHj8OJE3DsmDWyc/QoHDkCR49y0ZpMhpNJPBnOW1UOkcBB560KhylzuIgr+Cng8N/fV65sJZuqWxfq1ye3bn02nqjPrnINqHTB2bTtUsn5XjW7Gkb9nciTAI9sejMCVBKjNJ6OZHmSU0pKD6+Do0GDBnHRRRfx6aefUrNmTY8zZ4sEU0nVCPOlvlZJCeToVkHnjoqy/nI/87kSEtyDIxu5xJCV5xZNNtFkU7vGKR66L5sOVbLhy1NWQHLqFOTknP769y03O4e1T+QwzORQljNuJody5HCgXw6535yijP304y/PPsXHFbLJOXGKclg3Rx8cXyuWzaLebSfh5N+3EyfcX2ABGgHjPHwvsyolsOtkDdJzarCPJNKpyYn4JDr/syatute0AqKUFCs4clEGaPb3zdPPJxCjJN6MJJbEKI2nf/A0bRq6/3al5HldW61ixYr8/PPPnH322YHqU4mYMmUKzz//POnp6Zx33nlMmjSJ9h6O6ypDdvgJlRph/hTUKvDGWKMiBw7AoUPWNM/hw+QePMzvP2Vw4o9MqkQdITnuCH9tP8Kpw0epaI5RJfo4tuPHMMeOsX/HCaJzT1CBE5Qny5e3ILSUKQOxsdatUqXTt7g4qFSJHYfiWfCNNW50mHgOksAhl/Gj56clcM3t1aBs2YBlCC+pzOMFlZxxcKzvK4lRGk+zkRdWf00ih6fXb69Hjlq3bs3WrVvDOjiaN28ew4YNY8qUKVx22WX85z//oVu3bmzcuJE6deoEu3sSAOGwaNobxakJVeDoVm4u/PUX7N17+rZvH+zfD3/8YX3dv99qc/CgNVJzhjLAmf8zJObzVLYCjjucJIao2BjKVYyxdkxFR1u3cuWsW9myeb8vWxbKliUtvSzf/VDObczIThSnKOf2c/ee5Wh2wRnniY7mx3XleOfdcvxxqBxZxJBNNJWrx/B/Q6Jp3zkGypeHChWsrzExpwOi6OjTv0z5qAfULaQMyzUun1ugRiBLamSzoJGqkirq6yocdpNK6PF65GjBggU88cQTPPzwwzRv3pxyZ2z1PP/88/3awUBo3bo1LVu2ZOrUqc5jTZo0oWfPnowfPz5P+6ysLLKyTv9lm5mZSUpKikaOwlAwq7D7i881oex2a9X5tm1WXaydOyEt7fRt925riskb5ctbc2RVqpy+xcdbUz5xce63ihVZ8XMsr0yryM6/YjlOLCeowKky5TmaW4GTlOck5UmqXY5JL9t8/jz8MVIQyBGWSK8b5ypUXmukF08Wz/m18KyrMmXK5D2JzYYxJiwWZGdnZxMbG8t7771Hr169nMeHDh3K2rVrWbp0aZ7HjBo1itGjR+c5ruAoPIXKf9i+8KSae/Oaf/HjO5uI2vIrbN4Mv/4Kv/0GO3YUHfzYbFaR0ORk65aUBImJ1jHHrXp1qFbNCopiYz3ue1Hbqf011RKJU6hSfJHwh5EUX8CCo507dxZ6f926db05XYnbu3cvtWrV4rvvvqNt27bO4+PGjWPmzJls3rw5z2M0ciShwnVUJJosmrGeC1hLM9bTnHU0Yz1J/FHwCcqVg/r1oWFDK4KoWxfq1LFuKSlWtFiunN8DSE+COn8GLBopsITzHwKBoPdDArbmKNSDH0+ducvOMfKVn5iYGGJiYkqiWyL5y8mBdeuoOGslr7OGlvxIM9YTTd6RoFxsHK9Rl0qtzoVzzoFzz4XGjeHss6FWrSKvBsVZz1SQQOeZOlOo550qCYH4HMNdKO8mldDiUxLIt956i9dee43t27ezYsUK6taty6RJk6hfvz49evTwdx/9qnr16kRFRbFv3z634/v37ycxsbAlolKSSv1feAcPwrffwnffwcqVsHo1HD/OxcDFLs0OkMBPXMgvnM96mrGO5mykKZ++W9Gni4A3+YG8+YxKIs/UmUIh71Swfo8DVSpHpNTwtmjblClTTPXq1c0zzzxjKlSoYLZt22aMsQrSduzY0dvTBcUll1xi/vWvf7kda9KkiXnsscc8erwKzwZWIKuih6w//zTm3XeNGTzYmObN862CedgWb76gi3maEaYnqaYOOwzkujUrTuX6nJzCi8C6ntvbzygcivP6W7B+j735HEVKG0+v314HR02aNDELFiwwxhhTqVIlZ3C0bt06U61aNe97GgRz58415cqVM9OmTTMbN240w4YNMxUrVjQ7duzw6PEKjgInkFXRQ8qJE8Z89ZUxjz5qTMuW+b/oc881ZuBAs3rwm+ZcNhkb9kIDi+K+R54GMKNHe/8ZOS7YBVVqj7QLdjB/j0tjICriKU+v315Pq23fvp0LL7wwz/GYmBiOHTtW7JGsknDTTTdx4MABxowZQ3p6Os2aNeOzzz6LmPVU4SqQxWFDQno6fPopfPIJfPWVVWbCVbNm1mrrDh2s+ZezzsJuh571wJM6nsVdT+PplNbLL3v/GUVanqnCBPv3OBhTmCKRxuvgqH79+qxduzZPIPH555/TtGlTv3Us0O655x7uueeeYHdD/ma3w+TJJbtot0T8+ivMnw8LFsCaNe731awJV10FnTtbt3xql3haF2riRLj33uJdbD0tnXLwYMH3FfYZlZZF0iW9+PxMJVUqRySSeR0cPfzwwwwePJiTJ09ijOGHH35gzpw5jB8/njfeeCMQfZQIl9+umsKE/F+8GzbAe+9ZkcCGDe73XXIJdO9u3S64oNCMyuD5a01MLP4ohCeZhKtWLTw4ciio36GwSDrQgj1yo4zQIsXndXB0xx13kJOTwyOPPMLx48fp27cvtWrV4uWXX+bmm28ORB8lghWVGDA/wfqLt9CdR2lpMGcOvPMOrFvnfIwpV46DF17J1hbXk3P1tVzaI9GrQKAkRwE8mfoaOhRGjixefyJ9O3WwR25K0xSmSMAUZ2HTn3/+af7444/inCIsaUG2fxS1qyaUFu3mt/OocfIRs/qeacZcfrn7HdHRxlx7rfnh3lmmafKhYu1WCsZC5vxea0qKdby0Laz2Rai8R4V9jiKllafXb68zZDvs37+fzZs3Y7PZOOecc6hRo4Z/o7YQ5mmGTSmcpzWwILiZjd1HtwyXspIBTOMm5hHH0dMd7NAB+vaFG24gdXFV3+qfFfL8kP8oQCDek8JGyZR9umih8h6V+nxhImfw+PrtS9T1z3/+00RFRRmbzWZsNpspW7asufXWW83hw4d9jOXCi0aO/GP2bM9HjYL1F69jFCCODHMPr5p1nOfWsc00MuPjx5uc7Wl5HuPPETBfRwFycqwt27NnW1/9NVqhUYmi6T0SCT0BGznq06cPa9euZfLkybRp0wabzcb333/P0KFDOf/883n33XeLF9aFAY0c+YenI0f+2Inlqx9mbGTVHf/mdmY5R4mOEct73Mg0BvAt7QCbW4V3X6rCe/IXvrejAIEuH6FRiaL56z3Sey3iHwEbOYqNjTXLly/Pc3zZsmUmNjbW29OFJY0c+UeorM3IIzfXmC++MKZzZ7cObeRcM5jJpjKH8/R19uzTD/d0RMzxmEBkUi41yTRLgVKZMV4kQDy9fpfxNuqqVq0a8fHxeY7Hx8dTtWpVb08npZhjVw3k3dEelF012dkwcya0aAFXXw1ffYUpU4ZUenEFX9OUjfybIWSS9/ffdeeRN7uVHGtTzkxj4KiBlZrq/csoKgkhWEkI7Xbvzy0lKxC/HyLiAW+jrv/85z+mc+fOZu/evc5j6enppkuXLua1117zPowLQxo58q+gr804dsyYiRONSU4+3YGKFY0ZNszkbN3u9eiWpyNiWVn+X5uUk2O9FE9GrlQ+IrSpRpqI/wVszdGFF17I1q1bycrKok6dOgCkpaURExNDo0aN3Nr++OOP/orhQorWHPlfUNZUHD0KU6fCCy/A/v3WsZo1rWGX//s/K+MhBe88cnCUgvB2R1dCgvdrkwrjbTLN2bPhlls8ayslz5e1ayJSOE+v314ngezZs2dx+iWSrxJNDHjsmFWr5IUX4MAB61i9ejB8OPTrBzExbs0LKnsRFWUFdZMmWTfXxc6elMqYM8ez7nqSSTmckmmKZ4KdaVukNPM5z1FpppGjMJWdDa+/Dk8/DX/8YR07+2wYMQL7zbeyfGU5j3aLffihFeCcKb8cNoWNiPlrZMBut2I7T0eMHOUjtm/XjqdQppEjEf/z9PrtU3B0+PBh3n//fbZt28bDDz9MQkICP/74I4mJidSqVatYHQ8HCo7CjN1ulfUYORJ27LCO1a8Po0fDLbeQ+lFZj7e8FxWIeBN4OM5VVA2sos4VLsk0xTv++v0QkdM8vX57vVvtl19+oXHjxjz33HO88MILHD58GIAFCxYwfPhwnzssEhDffAMXXWRNl+3YYQ3fTJkCv/4Kt91G6kdlvdoN5E3F9aIUtlvPca7rr7fOVdjOMm+mVWrXVmAULkJuN6dIKeJ1cPTAAw/Qv39/tmzZQvny5Z3Hu3XrxrJly/zaORGf/fabtUr6yith7VqIj4dnn4WtW+Ff/4LoaJ+2vPt7HYhjbdKZA66OC96kSdaoUL16BW/b9nTt0MSJ1iiDAqPwUdDvh4JckcDyOjhatWoVd999d57jtWrVYt++fX7plIjPMjLg/vvhvPPgo4+sKGPIECsoevRRiI11NvVlFCgQFdd797YGtRYvtoIxyDtSVFhem/btrYtlfqNPYB1PSQlelnEpHtffj9mzra8KckUCy+vdauXLlyczMzPP8c2bN5eq4rMSYoyxrhwPPQSOIP2aa6wdaeeem+9DfBkFcgQiRa0Dad/eu+5HRVmPue22/O83xjq3I22Aa5DjmH654QarTX6pAzT9Et4CuZtTpUlE8vJ65KhHjx6MGTOGU6dOAWCz2UhLS+Oxxx7j+uuv93sHRRzsdmvx8Zw51lfn6MqGDdbc0z//aQVGjRrBF1/AJ58UGBiBb6NAgVwHUpz1TJp+EV+kplpTtp06Qd++RU/hipQavmSXvOyyy0yVKlVMVFSUSUlJMeXKlTOXX365OXr0qA/5KsOPMmSXvPyyaJ9d67j5tddjxpQtax2oUMGYsWONOXnSo3MWp7ZbILJ6e1uTraDXtHix1WbxYs+yJ/vyGAl/qr8npVHAMmQ7fPPNN/z444/k5ubSsmVLOnfu7N+oLYRpK3/Jyi/BYXuW8QZ30Zgt1oEePawhm3r1fDo3FJzJuqBRF39PRwQjr01+WbULSmMgkcOfKSlEwklA8xyVdgqOSs6Z/4lXJoPneJRB/AeAvdTkqWpT+M8fPX3+Tzy/ACEl5XQm65JS0nltCsqqrVxIkU8JJqW0Ckieo9zcXN588026d+9Os2bNaN68Oddddx2zZs1CMZYEgus6nM4sYj3NnIHRfxlIUzYy7UBPj/IKFSRUdgOVZF4bX9IYSORQaRKRwnkcHBljuO6667jrrrvYs2cPzZs357zzzmPnzp3079+fXr16BbKfUkqlp0Msx5jMEBbRhRR2s4Wz6chi7ua/ZFDF2a44HLuBbrnF+hqsqYSSWljtz2SWEn4CkZJCJJJ4vJV/xowZLFu2jK+//ppOZ4zHfvPNN/Ts2ZNZs2Zx++23+72TUnqdc2glP3G7c23RqwzmUZ7jOBXd2oXTf+JFrVXq3dtaQhXI7dUaOSjdApWSQiRSeDxyNGfOHB5//PE8gRHAFVdcwWOPPcY777zj185JKZaTAyNHcuG9l9GYLeymFlexkHt51S0wciQ4DJf/xD3dOh3okSyNHJRuKk0iUjiPg6NffvmFq6++usD7u3Xrxs8//+yXTkkpt2sXXHEFjBmDLTeXtMtv5XzW8bXtKrdm4fafuGMBtKd13ALJ06za4RJ0iveUG0ukYB4HRwcPHiQxMbHA+xMTEzl06JBfOiWl2AcfQIsW1pxSXBzMnk2dpW/zxvyqYf2feKgtgNbIgUDobEYQCTUerzmy2+2ULVtw86ioKHJycvzSKSmFsrLgwQfh3/+2fr7oIpg7Fxo2BDxfhxOqpRC8WQBdUlunHSMH+eU5Kuk0BhI8gSxNIhKuPA6OjDH079+fmJiYfO/PysryW6eklElLs+aVVq2yfn7oIRg7FqKj3ZoV9Z94KCc0DNUF0CWx+FtEJNx4HBz169evyDbaqSZeW7jQWpl84AAkJMDbb0O3bl6fpqCEho71PMGefgvlBdAaORARcacM2T5Qhuzisdth+dJcEqaOpfn8kdiMgVatrAjGy/IfjmK0ffrAwYP5twmFUgglnf1aRETyCkiGbJHiSk2FZnUyybiyF+e//xQ2Y3i74v/xwUPf+lQXrV496Ny54MAITq/nGTXKCqSCkfVZC6BFRMKHRo58EMojR4FckFzcc6emwsPX/86HXEczNnCSGAbxGrNs/QHvpr4KmkbzRDDXIYVKHTcRkdJIhWcDKFSDo0AuSC7uue12uCVpMVP/uoFqHGQPyfTkA1ZzMeDdtFJRFcWLEuzCqqG6o05EJNIpOAqgUAyOAllh3R/n/m3YFBq8fB9lsfMDF9OTD0gnOU87T6qAe1pRvDBa4yMiUvpozVEpEsgEg8U+998naPzyYMpi5x360oGl+QZG4NlWdn9sd1dhVRERKYiCowgQyArrxTr38ePWkNMrrwAwnHH8k7c5SYUCz+fJVnZ/bndXYVURETmTgqMIEMgEgz6fe/9+a+7rgw8gJobcOfN4u/ZwbAUU8/KmlldRdcHAqjziCRVWLX0c6R/mzAne7kURCW0KjiJAIBMM+nTuzZvh0kvhhx+sxI5ffUWZm/v4bSt7UdvibTaYNk2FVSUvR/qHTp2s3KOdOlk/l2TRXxEJfQqOIkAgK6x7fe4ffoDLLrNWOjdsCCtWQLt2gH+rgBd1rhtvVF4hcefYWHDmNLEji7oCJBFx0G41H4TybjVwXzztz91qRZ570SLo1QuOHYNLLoFPPoEaNfKcz59b2Ys6l/IKCRSd/kG7F0VKB4+v3yaC1K1b1wBut0cffdStzc6dO0337t1NbGysqVatmrn33ntNVlaWV8+TkZFhAJORkeHP7hfb/PnG1K5tjBXCWLeUFOt4wM89b54x5cpZd1x1lTFHjhT/Sf0kJ8eYxYuNmT3b+pqTE+weSUlbvNj9d7eg2+LFwe6piASSp9dvjwvPhosxY8YwcOBA58+VKlVyfm+327nmmmuoUaMG3377LQcOHKBfv34YY5g8eXIwuutXgaywXui5p06FwYOt60ufPjBrFsTEFP9J/USFVSWQmxZEJPJEXHAUFxdHUlJSvvctXLiQjRs3smvXLpKTrTw7L774Iv3792fs2LEhM0VWHPkFAv6axso3yHjuOXjsMev7QYPg1Vc1LyEhJ5CbFkQk8kTcguznnnuOatWqccEFFzB27Fiys7Od961YsYJmzZo5AyOArl27kpWVxZo1awo8Z1ZWFpmZmW63cBGw3TnGwOjRpwOjESNgyhQFRhKSArlpQUQiT0QFR0OHDmXu3LksXryYIUOGMGnSJO655x7n/fv27SMxMdHtMVWrViU6Opp9+/YVeN7x48cTHx/vvKWkpATsNfhTcXfnFJgPxhgrGBo1yvp57Fh45pnCEw+JBFFR6R9AuxdFxEXJLIHy3ciRI/Mssj7ztmrVqnwf+/777xvA/PXXX8YYYwYOHGi6dOmSp125cuXMnDlzCuzDyZMnTUZGhvO2a9eukFyQ7SonJ+8CatebzWYtqC5ocXJ+C7Br1zZm/vu5xjzwwOmDL75Ysi9MpBgCuWlBREJfxCzIHjJkCDfffHOhberVq5fv8UsvvRSArVu3Uq1aNZKSkvjf//7n1ubQoUOcOnUqz4iSq5iYGGJCaIGxJ7wp+3HmOqKCCs3u2W3Ye8N9wKvWgVdftRZii4SJQG5aEJHIEfLBUfXq1alevbpPj/3pp58AqPn3Kss2bdowduxY0tPTnccWLlxITEwMrVq18k+HQ4Svu3MKLjRreIn7GcKr5GKD1/5DmbsHntlIJORp96KIFCXkgyNPrVixgpUrV9KpUyfi4+NZtWoV999/P9dddx116tQBoEuXLjRt2pTbbruN559/noMHD/LQQw8xcODAiNip5srX3Tn5jzgZJvAIw7AWbdzFG9x+zp10LG4nRUREQlDELMiOiYlh3rx5dOzYkaZNm/LUU08xcOBA5syZ42wTFRXFp59+Svny5bnsssvo06cPPXv25IUXXghizwPD1905eUecDM/wBA9jvUd38xrTuVP5YEREJGJFzMhRy5YtWblyZZHt6tSpwyeffFICPQoux+6cG26wAqH8yn7ktzvnzJGkJ3maEYwD4F5e4b/cnW87ERGRSBExI0eSly+FXl1HnB7iecYwEoAHeJFXuVf5YEREJOJFzMiR5M/b3TmOEacvrn+d53kEgMcYz0QeUD4YEREpFRQclQLe7s7pbX+PXra7wcB4HuM5rCzYtWurmr2IiEQ+BUchwl/1z4pt4UK49VZsxpA78P9oc8s4Zu8rXp9C5rWJiIh4QMFRCEhNtXILuW6hr13bmt4q0VGaFSugVy84dQr69KHM1Cl0jCpeSZCQeW0iIiIe0oLsICtu/TO/2bgRrrkGjh+Hq6+Gt94q9vBOyLw2ERERL9iMyZsLWQqXmZlJfHw8GRkZxUoeabdDvXoFl/mw2axRlu3bAzwNtXcvtGkDaWnW10WLoGLFYp0yZF6biIjI3zy9fmvkKIi8qX8WMJmZ8I9/WIFR48bw0UfFDowgRF6biIiIDxQcBZGv9c/8Jjvbmt/6+Wc46yz4/HPwsY7dmYL+2kRERHyk4CiIfK1/5hfGwMCBp6fQPv0UGjTw2+mD+tpERESKQcFREPla/8wvRo2CWbOsBT/vvgsXXeTX0wf1tYmIiBSDgqMgcmSjhrxBRECzUb/zDowZY33/2mvWmiM/C9prExERKSYFR0HmS/2zYvn+e7jzTuv7Rx6Bu+7y8xOcVuKvTURExA+0ld8H/trK76pEskjv2AGXXAJ//mkVXEtNhTKBj4+VIVtEREKBp9dvZcgOEd7WP/NaZiZce60VGF1wAbz9dokERlACr01ERMSPNK1WGtjt0LcvrF9vDd18/DFUqhTsXomIiIQkjRyVBiNGWFv1y5eHDz/EXrM2y5cEZppLU2giIhLuFBxFunnz4LnnrO+nTyd118UM7R2YQrAqMisiIpFA02qR7Oef3XampUbfHLBCsCoyKyIikUK71XwQiN1qfnfggJXYcccO6NIF+8efUa9hlN8LwdrtsGQJ9OkDBw/699wiIiL+pMKzpVlODtx0kxUYNWgAc+aw/PuCAyPwrRBsairUqwedOxccGPl6bhERkWDRmqNINHw4fP21VTPtgw8gIcHvhWAd02jejDuqyKyIiIQDjRxFmtRUeOEF6/sZM6B5c8C/hWDtdmvhtbcTsioyKyIi4UDBUSTZsgXuuMP6/sEHraGdv/mzEOzy5XkXXhdGRWZFRCScKDiKFCdOWMFQZia0awfjx7vd7c9CsN5Mj6nIrIiIhBsFR5FiyBD45Rc46ywrt1G5cnmaFFYIdt48SEiAOXOs3Wd2e8FP5c30mIrMiohIuNFWfh+E3Fb+N9+EAQOsWmkLF8KVVxba/Mws1n/9Bfff73nyRrvd2qW2Z0/B644SEuDdd62aahoxEhGRUKCt/KXFL7/A4MHW92PGFBkYwelCsLfcYm3B79PHu+SNRU3R2Wzw+utWVxQYiYhIuFFwFM6OHbPyGZ08Cd26WVv4vVDYrjPHsWHD8p9iK2yKTtNoIiISzpTnKJzddx/8+iskJ8PMmda0mheK2nXmmryxY8e89/fuDT16qNCsiIhEFgVH4WrOHGutkc0G77wDNWp4fQp/JIZ0TNGJiIhECk2rhaNt2+Duu63vn3jC5+jEn4khRUREIoWCozBit8PSRdkc6HIzHDmCuawdPPWUz+fzZ2JIERGRSKHgKEw4irz+0GUE1X5fzUGq0nrbbN5bUJYlSzzLT3QmfyaGFBERiRTKc+SDks5z5Cjy2tF8wzdYW/V7soAP6ZmnbWH5iQo7/9Ch7ouzU1KswEi7zkREJFJ4ev1WcOSDkgyOHAkXj+4+xC+cTwq7eY27+Rev5dveMeLj7Xb6MxNDateZiIhEGk+v39qtFuIc2+1ncw8p7OY3GvEgLxbY3hgrQBo2zNpm72mAo11nIiIiFq05CnHp6XALs7mFueQQxT95m+NULPQxrvmJRERExDsKjkJcvTJpTOEeAMbwFKu4xOPHeprHSERERE7TtFoos9u5dMrt2MhgBZcyjse9erjyE4mIiHhPI0eh7OWXsS1bSk75itzG2+TaPItllZ9IRETEdwqOQtWvv8KIEQCUfWUiE+Y3zFPkNT/KTyQiIlI8YRMcjR07lrZt2xIbG0uVKlXybZOWlsa1115LxYoVqV69Ovfddx/Z2dlubdatW0eHDh2oUKECtWrVYsyYMYRcNgO7Hfr3h5MnoWtXuOsueveGHTtg8WKYPdv6+t57Vl4jV7Vre7+NX0RERE4LmzVH2dnZ3HjjjbRp04Zp06blud9ut3PNNddQo0YNvv32Ww4cOEC/fv0wxjB58mTAym9w1VVX0alTJ1atWsVvv/1G//79qVixIg8++GBJv6SCvfgi/O9/EB8Pb7zhHA7Kb7t9r17KTyQiIuJPYZcEcsaMGQwbNozDhw+7Hf/888/p3r07u3btIjk5GYC5c+fSv39/9u/fT+XKlZk6dSrDhw/njz/+ICYmBoBnn32WyZMns3v3bmwFFBnLysoiKyvL+XNmZiYpKSmBSQK5cSO0bAlZWTB9ujWCJCIiIsXmaRLIsJlWK8qKFSto1qyZMzAC6Nq1K1lZWaxZs8bZpkOHDs7AyNFm79697Nixo8Bzjx8/nvj4eOctJSUlMC8iJ8cKhrKy4JproF+/wDyPiIiIFChigqN9+/aRmJjodqxq1apER0ezb9++Ats4fna0yc/w4cPJyMhw3nbt2uXn3v/t+edh1SqoUgX++9+81WBFREQk4IIaHI0aNQqbzVbobfXq1R6fL79pMWOM2/Ez2zhmFQuaUgOIiYmhcuXKbje/27IFRo60vp88GVxGwERERKTkBHVB9pAhQ7j55psLbVOvXj2PzpWUlMT//vc/t2OHDh3i1KlTztGhpKSkPCNE+/fvB8gzolTiGjaEl16C77+HW28Nbl9ERERKsaAGR9WrV6d69ep+OVebNm0YO3Ys6enp1Pw7NfTChQuJiYmhVatWzjaPP/442dnZREdHO9skJyd7HIQFTJkyMGSIdRMREZGgCZs1R2lpaaxdu5a0tDTsdjtr165l7dq1HD16FIAuXbrQtGlTbrvtNn766Se+/vprHnroIQYOHOicBuvbty8xMTH079+f9evXs2DBAsaNG8cDDzxQ6LSaiIiIlB5hs5W/f//+zJw5M8/xxYsX0/Hv5D9paWncc889fPPNN1SoUIG+ffvywgsvuO1OW7duHYMHD+aHH36gatWqDBo0iKeeesqr4MjTrYAiIiISOjy9fodNcBRKFByJiIiEn1KX50hERETEHxQciYiIiLhQcCQiIiLiQsGRiIiIiAsFRyIiIiIuFByJiIiIuFBwJCIiIuJCwZGIiIiICwVHIiIiIi4UHImIiIi4UHAkIiIi4kLBkYiIiIgLBUciIiIiLhQciYiIiLhQcCQiIiLiQsGRiIiIiAsFRyIiIiIuFByJiIiIuCgb7A5Iwex2WL4c0tOhZk1o3x6iooLdKxERkcim4ChEpabC0KGwe/fpY7Vrw8svQ+/eweuXiIhIpNO0WghKTYUbbnAPjAD27LGOp6YGp18iIiKlgYKjEGO3WyNGxuS9z3Fs2DCrnYiIiPifgqMQs3x53hEjV8bArl1WOxEREfE/BUchJj3dv+1ERETEOwqOQkzNmv5tJyIiIt5RcBRi2re3dqXZbPnfb7NBSorVTkRERPxPwVGIiYqytutD3gDJ8fOkScp3JCIiEigKjkJQ797w/vtQq5b78dq1rePKcyQiIhI4SgIZonr3hh49lCFbRESkpCk4CmFRUdCxY7B7ISIiUrpoWk1ERETEhYIjERERERcKjkRERERcKDgSERERcaHgSERERMSFgiMRERERFwqORERERFwoOBIRERFxoeBIRERExIUyZPvAGANAZmZmkHsiIiIinnJctx3X8YIoOPLBkSNHAEhJSQlyT0RERMRbR44cIT4+vsD7baao8EnyyM3NZe/evcTFxWGz2YLdnaDLzMwkJSWFXbt2Ubly5WB3J6LpvS45eq9Ljt7rklPa32tjDEeOHCE5OZkyZQpeWaSRIx+UKVOG2rVrB7sbIady5cql8h9bMOi9Ljl6r0uO3uuSU5rf68JGjBy0IFtERETEhYIjERERERcKjqTYYmJiGDlyJDExMcHuSsTTe11y9F6XHL3XJUfvtWe0IFtERETEhUaORERERFwoOBIRERFxoeBIRERExIWCIxEREREXCo4kILKysrjggguw2WysXbs22N2JODt27GDAgAHUr1+fChUq0LBhQ0aOHEl2dnawuxYRpkyZQv369SlfvjytWrVi+fLlwe5SxBk/fjwXX3wxcXFxnHXWWfTs2ZPNmzcHu1ulwvjx47HZbAwbNizYXQlZCo4kIB555BGSk5OD3Y2I9euvv5Kbm8t//vMfNmzYwMSJE3nttdd4/PHHg921sDdv3jyGDRvGiBEj+Omnn2jfvj3dunUjLS0t2F2LKEuXLmXw4MGsXLmSRYsWkZOTQ5cuXTh27FiwuxbRVq1axX//+1/OP//8YHclpGkrv/jd559/zgMPPMD8+fM577zz+Omnn7jggguC3a2I9/zzzzN16lR+//33YHclrLVu3ZqWLVsydepU57EmTZrQs2dPxo8fH8SeRbY///yTs846i6VLl3L55ZcHuzsR6ejRo7Rs2ZIpU6bwzDPPcMEFFzBp0qRgdyskaeRI/OqPP/5g4MCBvPXWW8TGxga7O6VKRkYGCQkJwe5GWMvOzmbNmjV06dLF7XiXLl34/vvvg9Sr0iEjIwNAv8MBNHjwYK655ho6d+4c7K6EPBWeFb8xxtC/f38GDRrERRddxI4dO4LdpVJj27ZtTJ48mRdffDHYXQlrf/31F3a7ncTERLfjiYmJ7Nu3L0i9inzGGB544AHatWtHs2bNgt2diDR37lx+/PFHVq1aFeyuhAWNHEmRRo0ahc1mK/S2evVqJk+eTGZmJsOHDw92l8OWp++1q71793L11Vdz4403ctdddwWp55HFZrO5/WyMyXNM/GfIkCH88ssvzJkzJ9hdiUi7du1i6NChvP3225QvXz7Y3QkLWnMkRfrrr7/466+/Cm1Tr149br75Zj7++GO3i4jdbicqKopbb72VmTNnBrqrYc/T99rxH9zevXvp1KkTrVu3ZsaMGZQpo793iiM7O5vY2Fjee+89evXq5Tw+dOhQ1q5dy9KlS4PYu8h077338sEHH7Bs2TLq168f7O5EpA8++IBevXoRFRXlPGa327HZbJQpU4asrCy3+0TBkfhRWloamZmZzp/37t1L165def/992ndujW1a9cOYu8iz549e+jUqROtWrXi7bff1n9uftK6dWtatWrFlClTnMeaNm1Kjx49tCDbj4wx3HvvvSxYsIAlS5bQqFGjYHcpYh05coSdO3e6Hbvjjjs499xzefTRRzWVmQ+tORK/qVOnjtvPlSpVAqBhw4YKjPxs7969dOzYkTp16vDCCy/w559/Ou9LSkoKYs/C3wMPPMBtt93GRRddRJs2bfjvf/9LWloagwYNCnbXIsrgwYOZPXs2H374IXFxcc41XfHx8VSoUCHIvYsscXFxeQKgihUrUq1aNQVGBVBwJBKGFi5cyNatW9m6dWuewFODwcVz0003ceDAAcaMGUN6ejrNmjXjs88+o27dusHuWkRxpEro2LGj2/Hp06fTv3//ku+QiAtNq4mIiIi40OpNERERERcKjkRERERcKDgSERERcaHgSERERMSFgiMRERERFwqORERERFwoOBIRERFxoeBIRERExIWCIxHxms1m44MPPgh2NzwyatQoLrjggmB3w+86duzIsGHDPG6/ZMkSbDYbhw8fLrDNjBkzqFKlSrH7JhLuFByJlCL9+/enZ8+ewe5G2PMkiHjxxReJj4/n+PHjee47efIkVapU4aWXXvK5D6mpqTz99NM+P15ECqbgSEQkAG6//XZOnDjB/Pnz89w3f/58jh8/zm233eb1eU+dOgVAQkICcXFxxe6niOSl4EikFOvYsSP33XcfjzzyCAkJCSQlJTFq1Ci3Nlu2bOHyyy+nfPnyNG3alEWLFuU5z549e7jpppuoWrUq1apVo0ePHuzYscN5v2PEavTo0Zx11llUrlyZu+++m+zsbGcbYwwTJkygQYMGVKhQgRYtWvD+++8773dMC3399ddcdNFFxMbG0rZtWzZv3uzWl2effZbExETi4uIYMGAAJ0+ezNPf6dOn06RJE8qXL8+5557LlClTnPft2LEDm81GamoqnTp1IjY2lhYtWrBixQpnP+644w4yMjKw2WzYbLY87xlAjRo1uPbaa3nzzTfz3Pfmm29y3XXXUaNGDR599FEaN25MbGwsDRo04Mknn3QGQHB6WvDNN9+kQYMGxMTEYIzJM6329ttvc9FFFxEXF0dSUhJ9+/Zl//79eZ77u+++o0WLFpQvX57WrVuzbt26PG1cffzxx7Rq1Yry5cvToEEDRo8eTU5OTqGPEQl7RkRKjX79+pkePXo4f+7QoYOpXLmyGTVqlPntt9/MzJkzjc1mMwsXLjTGGGO3202zZs1Mx44dzU8//WSWLl1qLrzwQgOYBQsWGGOMOXbsmGnUqJG58847zS+//GI2btxo+vbta8455xyTlZXlfN5KlSqZm266yaxfv9588sknpkaNGubxxx939uXxxx835557rvniiy/Mtm3bzPTp001MTIxZsmSJMcaYxYsXG8C0bt3aLFmyxGzYsMG0b9/etG3b1nmOefPmmejoaPP666+bX3/91YwYMcLExcWZFi1aONv897//NTVr1jTz5883v//+u5k/f75JSEgwM2bMMMYYs337dgOYc88913zyySdm8+bN5oYbbjB169Y1p06dMllZWWbSpEmmcuXKJj093aSnp5sjR47k+35/+umnxmazmd9//915bPv27cZms5nPPvvMGGPM008/bb777juzfft289FHH5nExETz3HPPOduPHDnSVKxY0XTt2tX8+OOP5ueffza5ubmmQ4cOZujQoc5206ZNM5999pnZtm2bWbFihbn00ktNt27dnPc73r8mTZqYhQsXml9++cV0797d1KtXz2RnZxtjjJk+fbqJj493PuaLL74wlStXNjNmzDDbtm0zCxcuNPXq1TOjRo3K/xdMJEIoOBIpRfILjtq1a+fW5uKLLzaPPvqoMcaYL7/80kRFRZldu3Y57//888/dgqNp06aZc845x+Tm5jrbZGVlmQoVKpgvv/zS+bwJCQnm2LFjzjZTp041lSpVMna73Rw9etSUL1/efP/99259GTBggLnllluMMacv7l999ZXz/k8//dQA5sSJE8YYY9q0aWMGDRrkdo7WrVu7BUcpKSlm9uzZbm2efvpp06ZNG2PM6eDojTfecN6/YcMGA5hNmzYZY/IGEQXJyckxtWrVMk899ZTz2FNPPWVq1aplcnJy8n3MhAkTTKtWrZw/jxw50pQrV87s37/frd2ZwdGZfvjhBwM4AzfH+zd37lxnmwMHDpgKFSqYefPm5fu62rdvb8aNG+d23rfeesvUrFmz8BcuEubKBmnASkRCxPnnn+/2c82aNZ3TMZs2baJOnTrUrl3beX+bNm3c2q9Zs4atW7fmWf9y8uRJtm3b5vy5RYsWxMbGup3n6NGj7Nq1i/3793Py5Emuuuoqt3NkZ2dz4YUXFtjfmjVrArB//37q1KnDpk2bGDRokFv7Nm3asHjxYgD+/PNPdu3axYABAxg4cKCzTU5ODvHx8R49z7nnnounoqKi6NevHzNmzGDkyJHYbDZmzpxJ//79iYqKAuD9999n0qRJbN26laNHj5KTk0PlypXdzlO3bl1q1KhR6HP99NNPjBo1irVr13Lw4EFyc3MBSEtLo2nTpm7vh0NCQgLnnHMOmzZtyveca9asYdWqVYwdO9Z5zG63c/LkSY4fP+72eYpEEgVHIqVcuXLl3H622WzOC6sxJk97m83m9nNubi6tWrXinXfeydO2qAv6mc/36aefUqtWLbf7Y2JiCuyvoy+OxxfF0e7111+ndevWbvc5ghV/PI+rO++8k/Hjx/PNN98AVrByxx13ALBy5UpuvvlmRo8eTdeuXYmPj2fu3Lm8+OKLbueoWLFioc9x7NgxunTpQpcuXXj77bepUaMGaWlpdO3a1W1dV0HO/EwdcnNzGT16NL17985zX/ny5Ys8r0i4UnAkIgVq2rQpaWlp7N27l+TkZADnwmSHli1bMm/ePOdC64L8/PPPnDhxggoVKgBWYFCpUiVq165N1apViYmJIS0tjQ4dOvjc3yZNmrBy5Upuv/1257GVK1c6v09MTKRWrVr8/vvv3HrrrT4/T3R0NHa73aO2DRs2pEOHDkyfPt25kLphw4aAtTi6bt26jBgxwtl+586dXvfn119/5a+//uLZZ58lJSUFgNWrV+fbduXKldSpUweAQ4cO8dtvvxU4GtayZUs2b97M2Wef7XWfRMKZgiMRKVDnzp0555xzuP3223nxxRfJzMx0u5AD3HrrrTz//PP06NGDMWPGULt2bdLS0khNTeXhhx92TsllZ2czYMAAnnjiCXbu3MnIkSMZMmQIZcqUIS4ujoceeoj777+f3Nxc2rVrR2ZmJt9//z2VKlWiX79+HvV36NCh9OvXj4suuoh27drxzjvvsGHDBho0aOBsM2rUKO677z4qV65Mt27dyMrKYvXq1Rw6dIgHHnjAo+epV68eR48e5euvv3ZOFxY2xeQ6jffGG284j5999tmkpaUxd+5cLr74Yj799FMWLFjgUR9c1alTh+joaCZPnsygQYNYv359gTmQxowZQ7Vq1UhMTGTEiBFUr169wNxXTz31FN27dyclJYUbb7yRMmXK8Msvv7Bu3TqeeeYZr/spEi60lV9EClSmTBkWLFhAVlYWl1xyCXfddZfb+hOA2NhYli1bRp06dejduzdNmjThzjvv5MSJE24jSVdeeSWNGjXi8ssvp0+fPlx77bVuW+CffvppnnrqKcaPH0+TJk3o2rUrH3/8MfXr1/e4vzfddBNPPfUUjz76KK1atWLnzp3861//cmtz11138cYbbzBjxgyaN29Ohw4dmDFjhlfP07ZtWwYNGsRNN91EjRo1mDBhQqHtr7/+emJiYoiJiXGbourRowf3338/Q4YM4YILLuD777/nySef9LgfDjVq1GDGjBm89957NG3alGeffZYXXngh37bPPvssQ4cOpVWrVqSnp/PRRx8RHR2db9uuXbvyySefsGjRIi6++GIuvfRSXnrpJerWret1H0XCic3kt6hARMSP+vfvz+HDh8Om5IiIlG4aORIRERFxoeBIRERExIWm1URERERcaORIRERExIWCIxEREREXCo5EREREXCg4EhEREXGh4EhERETEhYIjERERERcKjkRERERcKDgSERERcfH/wl/ivIdDR7sAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"##You can adjust the slope and intercept to verify the changes in the graph\n",
"y = 1*(x**3) + 1*(x**2) + 1*x + 3\n",
"y_noise = 20 * np.random.normal(size=x.size)\n",
"ydata = y + y_noise\n",
"plt.plot(x, ydata, 'bo')\n",
"plt.plot(x,y, 'r') \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see, this function has $x^3$ and $x^2$ as independent variables. Also, the graphic of this function is not a straight line over the 2D plane. So this is a non-linear function.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Some other types of non-linear functions are:\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Quadratic\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ Y = X^2 $$\n"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"##You can adjust the slope and intercept to verify the changes in the graph\n",
"\n",
"y = np.power(x,2)\n",
"y_noise = 2 * np.random.normal(size=x.size)\n",
"ydata = y + y_noise\n",
"plt.plot(x, ydata, 'bo')\n",
"plt.plot(x,y, 'r') \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exponential\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"An exponential function with base c is defined by $$ Y = a + b c^X$$ where b ≠0, c > 0 , c ≠1, and x is any real number. The base, c, is constant and the exponent, x, is a variable. \n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"##You can adjust the slope and intercept to verify the changes in the graph\n",
"\n",
"Y= np.exp(X)\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Logarithmic\n",
"\n",
"The response $y$ is a results of applying the logarithmic map from the input $x$ to the output $y$. It is one of the simplest form of __log()__: i.e. $$ y = \\log(x)$$\n",
"\n",
"Please consider that instead of $x$, we can use $X$, which can be a polynomial representation of the $x$ values. In general form it would be written as \n",
"\\begin{equation}\n",
"y = \\log(X)\n",
"\\end{equation}\n"
]
},
{
"cell_type": "code",
"execution_count": 69,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jupyterlab/conda/envs/python/lib/python3.7/site-packages/ipykernel_launcher.py:3: RuntimeWarning: invalid value encountered in log\n",
" This is separate from the ipykernel package so we can avoid doing imports until\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"Y = np.log(X)\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Sigmoidal/Logistic\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ Y = a + \\frac{b}{1+ c^{(X-d)}}$$\n"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"\n",
"\n",
"Y = 1-4/(1+np.power(3, X-2))\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a id=\"ref2\"></a>\n",
"# Non-Linear Regression example\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For an example, we're going to try and fit a non-linear model to the datapoints corresponding to China's GDP from 1960 to 2014. We download a dataset with two columns, the first, a year between 1960 and 2014, the second, China's corresponding annual gross domestic income in US dollars for that year. \n"
]
},
{
"cell_type": "code",
"execution_count": 59,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2025-10-20 07:48:40 URL:https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/china_gdp.csv [1218/1218] -> \"china_gdp.csv\" [1]\n"
]
},
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Year</th>\n",
" <th>Value</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1960</td>\n",
" <td>5.918412e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1961</td>\n",
" <td>4.955705e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1962</td>\n",
" <td>4.668518e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>1963</td>\n",
" <td>5.009730e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>1964</td>\n",
" <td>5.906225e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td>1965</td>\n",
" <td>6.970915e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td>1966</td>\n",
" <td>7.587943e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td>1967</td>\n",
" <td>7.205703e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>8</th>\n",
" <td>1968</td>\n",
" <td>6.999350e+10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>1969</td>\n",
" <td>7.871882e+10</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"text/plain": [
" Year Value\n",
"0 1960 5.918412e+10\n",
"1 1961 4.955705e+10\n",
"2 1962 4.668518e+10\n",
"3 1963 5.009730e+10\n",
"4 1964 5.906225e+10\n",
"5 1965 6.970915e+10\n",
"6 1966 7.587943e+10\n",
"7 1967 7.205703e+10\n",
"8 1968 6.999350e+10\n",
"9 1969 7.871882e+10"
]
},
"execution_count": 59,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import numpy as np\n",
"import pandas as pd\n",
"\n",
"#downloading dataset\n",
"!wget -nv -O china_gdp.csv https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork/labs/Module%202/data/china_gdp.csv\n",
" \n",
"df = pd.read_csv(\"china_gdp.csv\")\n",
"df.head(10)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__Did you know?__ When it comes to Machine Learning, you will likely be working with large datasets. As a business, where can you host your data? IBM is offering a unique opportunity for businesses, with 10 Tb of IBM Cloud Object Storage: [Sign up now for free](http://cocl.us/ML0101EN-IBM-Offer-CC)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plotting the Dataset ###\n",
"This is what the datapoints look like. It kind of looks like an either logistic or exponential function. The growth starts off slow, then from 2005 on forward, the growth is very significant. And finally, it decelerates slightly in the 2010s.\n"
]
},
{
"cell_type": "code",
"execution_count": 60,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 800x500 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8,5))\n",
"x_data, y_data = (df[\"Year\"].values, df[\"Value\"].values)\n",
"plt.plot(x_data, y_data, 'ro')\n",
"plt.ylabel('GDP')\n",
"plt.xlabel('Year')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Choosing a model ###\n",
"\n",
"From an initial look at the plot, we determine that the logistic function could be a good approximation,\n",
"since it has the property of starting with a slow growth, increasing growth in the middle, and then decreasing again at the end; as illustrated below:\n"
]
},
{
"cell_type": "code",
"execution_count": 61,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"X = np.arange(-5.0, 5.0, 0.1)\n",
"Y = 1.0 / (1.0 + np.exp(-X))\n",
"\n",
"plt.plot(X,Y) \n",
"plt.ylabel('Dependent Variable')\n",
"plt.xlabel('Independent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"\n",
"The formula for the logistic function is the following:\n",
"\n",
"$$ \\hat{Y} = \\frac1{1+e^{-\\beta_1(X-\\beta_2)}}$$\n",
"\n",
"$\\beta_1$: Controls the curve's steepness,\n",
"\n",
"$\\beta_2$: Slides the curve on the x-axis.\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Building The Model ###\n",
"Now, let's build our regression model and initialize its parameters. \n"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {},
"outputs": [],
"source": [
"def sigmoid(x, Beta_1, Beta_2):\n",
" y = 1 / (1 + np.exp(-Beta_1*(x-Beta_2)))\n",
" return y"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets look at a sample sigmoid line that might fit with the data:\n"
]
},
{
"cell_type": "code",
"execution_count": 63,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7b6b9fee9d50>]"
]
},
"execution_count": 63,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"beta_1 = 0.10\n",
"beta_2 = 1990.0\n",
"\n",
"#logistic function\n",
"Y_pred = sigmoid(x_data, beta_1 , beta_2)\n",
"\n",
"#plot initial prediction against datapoints\n",
"plt.plot(x_data, Y_pred*15000000000000.)\n",
"plt.plot(x_data, y_data, 'ro')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Our task here is to find the best parameters for our model. Lets first normalize our x and y:\n"
]
},
{
"cell_type": "code",
"execution_count": 64,
"metadata": {},
"outputs": [],
"source": [
"# Lets normalize our data\n",
"xdata =x_data/max(x_data)\n",
"ydata =y_data/max(y_data)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"#### How we find the best parameters for our fit line?\n",
"we can use __curve_fit__ which uses non-linear least squares to fit our sigmoid function, to data. Optimize values for the parameters so that the sum of the squared residuals of sigmoid(xdata, *popt) - ydata is minimized.\n",
"\n",
"popt are our optimized parameters.\n"
]
},
{
"cell_type": "code",
"execution_count": 65,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" beta_1 = 690.451712, beta_2 = 0.997207\n"
]
}
],
"source": [
"from scipy.optimize import curve_fit\n",
"popt, pcov = curve_fit(sigmoid, xdata, ydata)\n",
"#print the final parameters\n",
"print(\" beta_1 = %f, beta_2 = %f\" % (popt[0], popt[1]))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we plot our resulting regression model.\n"
]
},
{
"cell_type": "code",
"execution_count": 66,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 800x500 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"x = np.linspace(1960, 2015, 55)\n",
"x = x/max(x)\n",
"plt.figure(figsize=(8,5))\n",
"y = sigmoid(x, *popt)\n",
"plt.plot(xdata, ydata, 'ro', label='data')\n",
"plt.plot(x,y, linewidth=3.0, label='fit')\n",
"plt.legend(loc='best')\n",
"plt.ylabel('GDP')\n",
"plt.xlabel('Year')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Practice\n",
"Can you calculate what is the accuracy of our model?\n"
]
},
{
"cell_type": "code",
"execution_count": 68,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mean Absolute Error (MAE): 0.04\n",
"Mean Squared Error (MSE): 0.00\n",
"Root Mean Squared Error (RMSE): 0.04\n",
"R2-score: 0.92\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from sklearn.metrics import r2_score, mean_squared_error, mean_absolute_error\n",
"from scipy.optimize import curve_fit\n",
"\n",
"# Misal fungsi sigmoid\n",
"def sigmoid(x, beta1, beta2):\n",
" return 1 / (1 + np.exp(-beta1*(x-beta2)))\n",
"\n",
"# split data into train/test\n",
"msk = np.random.rand(len(df)) < 0.8\n",
"train_x = xdata[msk]\n",
"test_x = xdata[~msk]\n",
"train_y = ydata[msk]\n",
"test_y = ydata[~msk]\n",
"\n",
"# build the model using train set\n",
"popt, pcov = curve_fit(sigmoid, train_x, train_y)\n",
"\n",
"# predict using test set\n",
"y_hat = sigmoid(test_x, *popt)\n",
"\n",
"# evaluation metrics\n",
"mae = mean_absolute_error(test_y, y_hat)\n",
"mse = mean_squared_error(test_y, y_hat)\n",
"rmse = np.sqrt(mse)\n",
"r2 = r2_score(test_y, y_hat)\n",
"\n",
"print(\"Mean Absolute Error (MAE): %.2f\" % mae)\n",
"print(\"Mean Squared Error (MSE): %.2f\" % mse)\n",
"print(\"Root Mean Squared Error (RMSE): %.2f\" % rmse)\n",
"print(\"R2-score: %.2f\" % r2)\n",
"\n",
"# Optional: plot actual vs predicted\n",
"plt.scatter(test_x, test_y, label='Actual', color='blue')\n",
"plt.scatter(test_x, y_hat, label='Predicted', color='red')\n",
"plt.xlabel('X')\n",
"plt.ylabel('Y')\n",
"plt.title('Sigmoid Regression: Actual vs Predicted')\n",
"plt.legend()\n",
"plt.show()\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<details><summary>Click here for the solution</summary>\n",
"\n",
"```python \n",
"# split data into train/test\n",
"msk = np.random.rand(len(df)) < 0.8\n",
"train_x = xdata[msk]\n",
"test_x = xdata[~msk]\n",
"train_y = ydata[msk]\n",
"test_y = ydata[~msk]\n",
"\n",
"# build the model using train set\n",
"popt, pcov = curve_fit(sigmoid, train_x, train_y)\n",
"\n",
"# predict using test set\n",
"y_hat = sigmoid(test_x, *popt)\n",
"\n",
"# evaluation\n",
"print(\"Mean absolute error: %.2f\" % np.mean(np.absolute(y_hat - test_y)))\n",
"print(\"Residual sum of squares (MSE): %.2f\" % np.mean((y_hat - test_y) ** 2))\n",
"from sklearn.metrics import r2_score\n",
"print(\"R2-score: %.2f\" % r2_score(test_y,y_hat) )\n",
"\n",
"```\n",
"\n",
"</details>\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2>Want to learn more?</h2>\n",
"\n",
"IBM SPSS Modeler is a comprehensive analytics platform that has many machine learning algorithms. It has been designed to bring predictive intelligence to decisions made by individuals, by groups, by systems by your enterprise as a whole. A free trial is available through this course, available here: <a href=\"https://www.ibm.com/analytics/spss-statistics-software?utm_source=skills_network&utm_content=in_lab_content_link&utm_id=Lab-IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork\">SPSS Modeler</a>\n",
"\n",
"Also, you can use Watson Studio to run these notebooks faster with bigger datasets. Watson Studio is IBM's leading cloud solution for data scientists, built by data scientists. With Jupyter notebooks, RStudio, Apache Spark and popular libraries pre-packaged in the cloud, Watson Studio enables data scientists to collaborate on their projects without having to install anything. Join the fast-growing community of Watson Studio users today with a free account at <a href=\"https://www.ibm.com/cloud/watson-studio?utm_source=skills_network&utm_content=in_lab_content_link&utm_id=Lab-IBMDeveloperSkillsNetwork-ML0101EN-SkillsNetwork\">Watson Studio</a>\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Thank you for completing this lab!\n",
"\n",
"\n",
"## Author\n",
"\n",
"Saeed Aghabozorgi\n",
"\n",
"\n",
"### Other Contributors\n",
"\n",
"<a href=\"https://www.linkedin.com/in/joseph-s-50398b136/\" target=\"_blank\">Joseph Santarcangelo</a>\n",
"\n",
"\n",
"## <h3 align=\"center\"> © IBM Corporation 2020. All rights reserved. <h3/>\n",
"\n",
"<!--## Change Log\n",
"\n",
"\n",
"| Date (YYYY-MM-DD) | Version | Changed By | Change Description |\n",
"|---|---|---|---|\n",
"| 2020-11-03 | 2.1 | Lakshmi | Made changes in URL |\n",
"| 2020-08-27 | 2.0 | Lavanya | Moved lab to course repo in GitLab |\n",
"| | | | |\n",
"| | | | | --!>\n",
"\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python",
"language": "python",
"name": "conda-env-python-py"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.12"
},
"prev_pub_hash": "f873d3177bf529d2d648c46bab1627042a257e5ec6ce42ca68028520459f817e"
},
"nbformat": 4,
"nbformat_minor": 4
}