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Created on Skills Network Labs
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a href=\"https://www.bigdatauniversity.com\"><img src = \"https://ibm.box.com/shared/static/cw2c7r3o20w9zn8gkecaeyjhgw3xdgbj.png\" width=\"400\" align=\"center\"></a>\n",
"\n",
"<h1><center>Non Linear Regression Analysis</center></h1>"
]
},
{
"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 because, as the name implies, linear regression presumes that the data is linear. \n",
"Let's learn about non linear regressions and apply an example on python. In this notebook, we fit a non-linear model to the datapoints corrensponding to China's GDP from 1960 to 2014."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h2 id=\"importing_libraries\">Importing required libraries</h2>"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Though Linear regression is very good to solve many problems, it cannot be used for all datasets. First recall how linear regression, could model a dataset. It models a linear relation between a dependent variable y and independent variable x. It had a simple equation, of degree 1, for example y = $2x$ + 3."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"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('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Non-linear regressions are a relationship between independent variables $x$ and a dependent variable $y$ which result in a non-linear function modeled data. 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 $x$). \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 others. For example: $$ y = \\log(x)$$\n",
" \n",
"Or even, more complicated such as :\n",
"$$ y = \\log(a x^3 + b x^2 + c x + d)$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's take a look at a cubic function's graph."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"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('Indepdendent 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."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Some other types of non-linear functions are:"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Quadratic"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ Y = X^2 $$"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"image/png": 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21adqW3yqgIJMB91eRO4QkddE5O3IlkSAeQ9YkUpwqg/85gU66qia7UPrKeZcHmEXvmQ4Q7csERe5g1i4sO54sXydQ9yY+iqltXirquCcc6BlSzfZmyfoAvF5LVZUiN6ACcC5wFxcF9AxwO2Jzqt1ja7ULQEsAGZ419s+zrkDgQqgoqSkJPRImax4dxSxSgL3cZFWIbo/72+5Y4h+XaTm+caYzIpVYo/rjjtUQS9pN67GOZHvau1NJPzPkCx8SgBBMu8p3s8ZUfsmJTqv1jVqB4COQCNcG8RwYEyQ6+RjFZDfP4FfEGjJav0fXXUe3XWborVW7WNMHqkdHF4eMVcrmzTTlxr9QaG6RlVP27aJv/v5wi8ABBkHsNn7uVhEfi8ivXGrgqVMVZeoapVunWiubzrXC1OiRp5463zGqg5ayzacyyPsyhfcWB17UlVr+DUm+2pX5369sIr2QwawqrKYgVV/J3qJx0jVj98wgMh3P+8bhWNFhegNNyfQtsBewDvAFODYROfVukZXapYAOkU9vgx4Ksh1sl0CCNLIE+uYeCWByJ3FvN9eqFWIHsAkKwEYkwdqV9cO4nZV0DMY61vVE6uaNx+/yyQ7DiBTRORJ4GCgHbAEuN573gvXtXQBcL6qJuxamu1xAEH7DJeXu4afWMeCa9ytrq61c80aVnfbh+XLlJ76KWtoBbg7inxdP9SYhqyoyGXbAHsxkwr68CpHcxLPEX33HxGdD0SfGy3mdz8H/MYBxBsINlhVR4jIfcSYFlpV/5z5ZMaX7QCQ7B816UEmH3yAHnggT7Y8j/5rH6KkxPVGsMzfmOyLfH+bsIn/8ks68w09mI22bc/69XVn/42+Ucv3gZypDASb6/2swFX71N4aPL/6fb/9SXcx+/WvkSuv5Iw1o6l+7XUWLLDM35hciXx/hzKcnzONgYxmXXF77rkn8ey/KXUvzQex6oUiG66nzh3xjsnmlo9tALHOSaqL2fr1qj16qHbqpLp8eQZTb4xJ1r9v/Fg300gf5Y9J9+RJ+rufRaTaBiAib6vqIVmIRQnlYi6gSP3+okWEV0UzbRr06wfHHQfPPGMriBmTC2vXQu/esGEDzJgB222X6xRlTCorgkVME5GXgWeBtZGdqvp8BtOXt8rKslAt07u3m2L2qqvgiSfgj38M+Q2NMXVccQXMnw9vv92gMv94gowDaAP8ABwCHONttlxkpg0aBAccABdfDAsW1Bh/0K6d2+rthFPG5LtXXnHz+195JRx8MNAAJnoLIPRuoJlUn6aDTsmCBdCzJ0s77UO3r99lzfrY64xaV1FjMmjJEth7b9hhB/j4Y2jWbMugsHg9f+qTlFcEE5HmInKRiDzoTe08RkSyvhxkQ+J7Z9G1KzzwAB0+/4C/rL/F9/x6N+GUMfmquhrOPhtWr4axY6FZM6CBTPQWQJAqoCeAnwFHAJNw00CsDjNRDZnf7KFbgkD//pRzBtdzI/vxke91bLoIYzLg3nvh9de5pngkRT332nJDVijrcwTpBTRNVXuLyAxV7SkiTYA3ctEzqCFUAQUZMLJ3yUpe+ro3gtKL6axi27jHG2NSMH06Vb/ox7/1SI6pepHIaN/iYmjRAn74oe4p9fV7l86i8JHJ4H4Skb1w8wJ1zWDaCkqQO4sht27LgGbj6MLXjOICag/ErhcDTIzJZ+vWwemns1zbcnbVIwSZ6K0hfu+CBIDRIrI9cA3wMjAHuD3UVDVgQUYXl5XBeY/8kru2u5HTeYpLWv6Ttm39RyEaY5L05z/DvHn0r3qcH2hX5+UVKxKP/m0QYo0O86qFOvq9lqstH9cDSFZSo4srK1UPOUS1RQvVWbN8r5evow+NyUtjx7ov3tChBbMUK8kuCAN8D0wEBgDb+h2Xza0hBADVJDPt775T7dBBdc89VdeurXOd+rImqTFhSer7NG+e6jbbqP7616qbNxfMdyiVANAI1/Pnn7hpnF8ETgVa+J0T9tZQAkDSJkxw/93nnltjd6HcvRjjJ6kMfP161V69VNu0Uf366xrXaOilaL8AEGggmIg0BX4HnAb8BnhLVbNeG9YQegGl7Oqr4dZb3VQR/fsD+T8HuTFhS2oa5gsvhFGj4OWX4ZhjspC6/JFOLyBUdROu8XcusArYM7PJMwkNGwYHHgjnnw+zZwPJT1dtTEMTuL/+uHEu8x80qOAy/3jiBgARKRGRQSIyFXgVVy10nKr2zkrqzFaNG8NTT0GrVnDSSbBmTf2dg9yYDAl0EzRnjhttecAB9uWoxTcAiMhHwPtAR2Cgqu6mqter6ly/c0zIOnWCJ5+Ezz+H886j7AwtjK5qxvhIeBO0Zo27YWrZ0t1ANWmS9TTms3jTQV8FvKdBGglM1pR/9xu+bX0Tg58ayvVv/Ipd77ukXo5MNCYTIjc7MdfsUIXzzoN582DiRDfZm6nBNwCo6qRsJsQkFplHaP26IezOf7nmx8v53bm9gV/bXb8pWL5rdtx9t7vrv/VWOCQv1rTKOzYddD0S3eOhNSv5hF/QitUct+MUJn9jdzfGbPHuu3DooXDssTB+fMGvspfOdNA7BdkX5/wxIrJURGZF7WsjIhNF5Avv5/ZBr1fIons2rGJbTuB5WrOKu749GTZtyl3CjMkn33wDp5wC3bvDo48WfOYfT5BuoONj7Hsuifd4FDiy1r4huLEE3YG3vOcmgdo9HmazFwMYw/58BJdemvT1CmHFI1Ng1q+H4493P59/Hlq3znWK8lq8XkC7i8iJwLYickLUdjbQPOgbqOp7wIpau48DHvMePwb8IblkF6ZYPR5eLT6V2Uf/1fVxHjUq8LUSrktgTB5I6iZF1f0TV1S4xV322CNLqazHYg0P9toFjsNNA/GD9zOy3Qv8yu88n2t1BWZFPf+p1us/xjl3IFABVJSUlGR8iHR9E3PYemWl6u9+p1WNGutJHd8LNKTdppEw+S7peXpGjnQHDRuW1XTWByQ7F5BuzYD3S3RMgGukHACit4KdCyiApx/6UefJrrqE9tqFhQouSEQy9dpfmshrtTeRnCTfmDqSukl54w3VoiLVE05Qraqq83IhzPcTj18ACNIGMF9ErhaR0RlcE3iJiHQC8H4uTfN6BW/wLdtxrL5EMzbyCsfQkjVb5gmKVb1j00iYVGSz3chvmoeFC2u992efuUbfHj3gscdc4mql2ao7fcSKCtEb8BFuAZhTgBMjW6Lzal2jKzVLAHcAQ7zHQ4ARQa5jJQB/kTv6w3ldKynSFzlWhSrfO6dCmQbXZE62/2f8SgDR7/3M35erduvmpkxfsCCp6xRSdSdpVAFNT3RMgvOfBBbjlpb8BjgXaIvr/fOF97NNkGtZAPAX/U9+Mfeqgt7G4LjVO4VeLDbJyXZGGivgRG9N2KgfNTtYtWlT1Q8/9L2OVXemFwBuBo5KdFw2NgsA/mp+War1AS5UBT2HRwryjsdkXrYy0ugbk7Zt3Vb3fav1H5zrnvjcuUSu4xdACun7kE4AWA1UAxtwU0GvBlYlOi+MzQJAfNH/8E3YpK9zuG6isR7KhKSK6lYyMLFkowTgV81UOwhcxXBV0Hu2vSbwdQq5ujPlAJBPmwWA4MaOVe3RZaV+yt66Ulrrq7fOCHyetQ2YWLLxv+EXZNq23frep1OuCjquUX8d+0R1Utfx6xXX0KVTAhCgP3Ct97wL0DfReWFsFgBSsGiR6g47qHbpovrttwkPtwYzE0/YpcN41Uxjx6qe3HGSbqCp/rfZgTrunxtSuk4h8gsAQbqBPgjsB5zhPV8DPBCkh5HJA126wKuvwo8/wlFHwcqVcQ8PvMKSKUhlZW6pxepq9zPTs9DG655c1ms2z2w8jma77cSie17gqhua+XZHtW7OwQQJAP1U9SJcGwCq+iPQNNRUmczq3dvNiDh7Nt//6nh2Ld1oXxyTl/wWePnb5d/AkUdC8+a8eMHrnH15m7j9+m21vIBiFQuiN+Bj3FKQU73n7YFpic4LY7MqoPR8eMHjqqBPccqWMQK163CtDcDkWu1qpmceWqHao4dq69aq06fHraaM1YPIOjOk1wZQBryM68M/HJgHnJzovDA2CwDpKS1VvZIRqqD3cIlCdcz6ffsSmbyxdq3qr3/t+vq//baq+tfvR25W7OalrpQDgDuX3YGLgIuBPYKcE8ZmASA97otTrXdyuSroddwQt2HMSgMmpzZuVD3qKPcP+swzW3b7lQAaNfIvGRQ6vwAQbzroNpENN1fPk8A43Dw+bTJfGWXC5urxhSu5kzGcw43cwCXc61u/P3QorFtXc9+6dW6/MUGlNH9QVRWcdRa89ho89BCcfPKWl/zq96uqYl/KOjDEESsquIDBV8D/vJ9VwHLc1NBVwFd+54W5WQkgPdF39I3YrOM5XhX0w/Mfi3m8daUz6UqpFFldrXrBBe7g227zvW7t7qjWhdkfabQBjCJqKgjgd8DIROeFsVkASF/0F2fXkvX63V6Huml0n366zrH2hTLpSvp/qLpa9XJXRamDByf1XlZl6S+dADAlxr6YFwt7swAQgjVrVA84QLVxY9UXX6zxkn2hTLriNdjG7FQwdKh78ZJLXDBIkk1jEls6AeAN4BrclM6lwFDgjUTnhbFZAEhNwi/FypWq/fq5nhb//ndy5xoTR5Apnbf8T918s9v5pz/FXNTFpC6dANAGuAeY5m33EHD65kxvFgCSF/gufsUK1d69VZs1U3399UDXtcBgEkk0KVukJDDtZDe522OcqTuVVNr/U4alHADyabMAkLyk6mCXL1ft1csFgVolgWhWNWSSkWha5qtxd/5PUKZFVNr/UwjSKQHsCowGJgBvR7ZE54WxWQBIXtCePJEvaVuW68ymvbWySTPV116LeU1rHDaJBO2lE8n8H6f/lszf/p8yL50A8ClwIdAX2DeyJTovjM0CQPKCZNa17+i35wedJr21snHTOg3DqtY91MTnV0K88MKaixYN4xrfzN/+nzIro72AcrVZAEhekOqaWEFiO1bo1Kb93PDKceNqXDPTJQBrT2hYEs7VU1Ktf+MyVdAvDv6T7lRSN/O3EkBmpRMAbgD+D+jkNQi3sUbg+iVRBut3R9+KVaoHHugOePjhGtcL0gYQJGO39oSGJ24Jsapq6yCvP/9ZtarK/geyIJ0A8FWM7X+JzgtjswAQjrh39GvXqh5xhNsxYsSWcxJl7kG/1Nae0PD4/U13Kdmoeuqp7slVV9Xo52+lwHBZLyDjK2FmvWGD6imnuBcGDw40QCdoxm7tCQ1PrP+ndi3W6Ld7H17nRsJkh18AaJxoriARKQYuB0pUdaCIdAd2U9VXE50b4NoLcIvMVwGVqton3Wua5EVWdRo61E2cVVLiJtzastpTs2Ywbhy0bQsjRsDy5TBqFDRp4nvNoCuLlZS4BT1qswVo6q/a/0/77Licic2Opt2cChgzBs45J7cJNFvFigrRG/A0MBiY5T1vAUxPdF6QDVgAtAt6vJUAcqy6WvW669xd3JFHqq5e7Xto0BKA1f82cPPnq3bvrtq8ecweZSY7SGNN4G6qOgLY7AWM9biF4k2hEYEbb4TRo2HiRDjoIPj++5iHBl2Sr6zMXa601F2+tNQ9z/RasyZcMad8njwZ9tsPVqyAt96C447LcSpNHbGiQvQGfIS7648sCdkNmJzovCAbrkF5KjAFGOhzzECgAqgoKSkJM0iaBKIb6s7q8C/d1Kyl2zFzZsLjrWGv4YpVijut6Xjd3LSF6s47q86bl+skFjzS6AV0GDAJWAaU46ptDk50XpAN2MH72QE34OzAeMdbFVDuxPqS/6p5ha7drpNqq1aq//pXrpNocqRmdV+1DuEWVdApTX+pumRJrpNnNI0qIFWdCJwAnI1bFayPqr6bXrljy7W/834uBV7AjTY2eSjW6mAfbdiXQ1pOhl12gWOOgbvuonysJr/6k6nXIg37TdnIo5zNrVzNOE5n/03vQIcOuU2ciStIGwDAQcBvgd8AB2TijUWkpYi0ijwGDgdmZeLaJvP8evVM/q4zvP++q9+9/HL07HP4fuEGVF3vnoEDLQjUd4mWdCwpgR34lkkcxFk8zrUMo4xyOpY2z0VyTRISBgAReRC4AJiJy6DPF5EHMvDeHYEPRORTYMCCE2sAABRySURBVDLwL1V9PQPXNSHw65ZZUgK0bAnPPcfd215P/6rHeJ8D6MzXgK0hnO8SZe7l5S6IL1yIb1AffdaHTKEPezGLExjPzVxLcbHUafA3eShWvZDWrKefDUjU8yJgdqLzwtisDSB3gnTXFFE9lhd1Ja10Ce31EN70HdRlDcS5l+o8UVu681ZXq95/v2qTJrqy4y56aKdZ9vfMU6TRCPw8UBr1vBR4MtF5YWwWAHIrUaYdySx2Y67OZg+tpEiHcpN2Lamqcx3r+597QcZqxJ0nKjKtw+9/r/rjj7n6GCYAvwAg7jV/IjIJ+AWumgbv8X+AdV4J4tjMlkn89enTRysqKrL1diZJkeqCdeugJWt4iPMpYxzf9TySHd58HNq3B1xVQ6zRv6WlsGBBVpNc0IqKXHZemwhUV7vHsf5WezODFxqfQrfqL9zAjsGD3cVM3hKRKRpjpoWEU0EA14WQHtMA1ZwCYBuGdhnLLr89kH7jLoWePeHxx+GwwwJPE2HCFWQajuHDtwZ1UC7mfu5gENpye3jpbTcY0NRfsYoFtTdctc+h3uMWQKsg52V6syqgeurTT1X32MNVFwwapLuUbLQZQPNAMtN69+68VF/maFXQb3r9XnXp0twk2qSEVMcBiMh5wHPAQ96uzsCLoUQj0zD17AkVFXD++XDHHXxMX/o2n1HjkFjTRIQhUa+XQhJ0Go6ybV5i6qa9OKbZRLj3Xnac+gq0b2+/y4YgVlSI3oDpQFNgWtS+mYnOC2OzEkAD8NJLqh06aGWjJnrrdrdpIyqz1muk0Bqfoxvt27Z1W1K9dH76SfWcc9wvqlcv1Rkzaly7kH6X9R1p9AL62Ps5zfvZGJiR6LwwNgsA+SnpLp1Ll6qecIL79+vbt0bGEqZCWnwmVgadTGb9zuUv63eNdtRKivSeba/RcY9urPF6If0uG4J0AsAI4GrgM9y8QC8AwxOdF8ZmASD/pHwnWF2t+uSTqu3bqzZurHrttW7hmRCFufhMvo1r8MugE2bWS5boV7903TtnsJf+go99x3zYQj71RzoBoAg4D3gW1xZwHlEDw7K5WQDIP2nfCS5bpnrmme6k7t1V33gjf9PqIx+rQ/wyaN/MurJS9cEHVbfbTjfQVIdykzZho+/vKRO/y3wLmg1ZygHAnUt7oH2QY8PcLADkn4zdCU6Y4AIAqJ50kuqiRRlPa6Yz6kgGltQddpYkVQL4+GPVPn3czkMO0d2Zm/Bvmu7vMh+DZkOWdADALfpyA7Ac+AFYgZsS+jq/c8LeLADkn2TuBBPe8W3YoHrTTW71qBYtXLVQnFXHgvJrDE2pYTTqmvHq2DNdHZLs3XKQNoDx93yt2r+/29Gpk6uSq65OajW3VO/grQ0hu1IJAJcBE4GdovbtDLwBXOZ3XpibBYD8k0xf8sB3fAsWqJ522taM6eGHVTdvzmj6LrwwvTvQlOvYM/gZggSBWIFvry4/6Yw/XOuCbLNmqlddpbpqVdrvlwxrQ8iuVALANGKs1+tVB03zOy/MzQJAfgpyJ5jSHd9HH6n26+cO3G031WeeUa2qinNC8Pdt1Ci9TDtRHXuqGWas32XGSlnr1qneeadqmzbuAqeeqvrVVzHPTad0FISVALIrlQAwK5XXwtwsANRfKd/xVVervvCC6p57uhN69VJ97rnAgSBIY2gqd6CJ6v5Tzfxj3XkHTavf+U8+slb17rtVd9jB7TziCNWKikDnhlUnb20A2ZVKAJiaymthbhYA6q+07/gqK1Uff3xrQ3GPHi632LQppfdNtwQQRgaWblprn9+an3QQt+vSog5ux0EHqb7zTlLvHeYdufUCyp5UAkAVsCrGthrY7HdemJsFgPorYxlmZaXquHFbSwSdO6uOGOFGrdZ6v0imVrsUkIk2gOj3yFQGFq+0UjutTZrUraKJnF/CAh3JZbqSVqqgEzhU9b33Unpvq5NvGNLqBpovmwWA+i2jGWZVleorr6gefLD7N27ZUnXgQNVp02IGm0gGF/2++XYHGu8uvHb9fNOmNY9p2aJKT271b32RY7WSIt1EY32CMu3NlEC9d6xOvmGzAGDqncCNklOmqA4Y4LqPgk5r2lcv4EHdjhX1IjOLV1qJFbiiM+tSvtJruVHns7Mq6BI66HCu0s4silmqCatXlMlvFgBMvZLSXDYrVqjedZfOYC9V0A001Wc5UU/maS1mTV5WZ8QrrcSquho7VrUj3+sFPKjvcJAqaBWib3KInsaTOu7RjYFWbUtUysiHEpHJHAsApl5Jp599aUm19maK3s2fdTEdVUHX0kJfKz5BdcwY1e+/TyotYWaMwRp+q3VXPtPLGKn/aXaQVuEiwxx216u5WbuwMHAJx+r6C5MFAFOvJD2XjcauSimiUg/kXR3V+P907fY7bD15331VBw9W/fe/4442Dru7ot/nbM8SPZmn9UEu0C/otuWFmfTQT4+/Tvs0n6lQnXSarK6/MOVlAACOBOYB84EhiY63AFA4ki0BBGr4ra5WnTrVTTex//5uFtLI7Xbv3qoXXOBKCFOmqK5fHzcdmcowS0tdd839eV8v5l59gjL9nF22vNFKWukr/F7/j/u1lK+2vG+qpRLrf1+Y/AJAwkXhwyIijYDPcVNMfwN8ApyuqnP8zrFF4QtH9ALzsRQX11y9KqWF5teuhQ8/hEmTYPJkt61a5V5r1Ai6d+flz7rzJd34HzvzDZ1ZTCcW04kfacOq6m3cUlrxVFW5ay5fDosXu+3rr+HLL+HLL1k7dR4tf9i6GPJ3dKKiUT+qfvFL7p52MB9u3Jcqb+nu2p85VeXlkXWb3fq/w4enf02T3/wWhc9lANgPuEFVj/CeXwWgqrf6nWMBoLBEZ1Rt2rh9K1bUzLQix8TK/MHlz9XVAd+wuhq++AJmzICZM2HWLOa+Op+SzV/SkhiRqKgIWreG5s2hSRO3qcLmzW5buxbWrIn9Xm3aQLdu0L070yr35t539ubNZfvQqGRHht8iNT6bZdQmXfkYAE4CjlTVP3nPzwT6qerFtY4bCAwEKCkp2Xeh3zfdNAjJZHqJSgmQoAQQMD0Dz1NarV/CDnxHJxZT0vR7zjvxR37ebSX89BNs3Lg10xfZGgyKi2Hbbd3Wti1vzenE7Y93omLxjrQu3d4ydJM1fgEgl/X/JwMPRz0/E7gv3jnWBtCwJTOzaJA2gkzVbWeiF5DVvZtcwqcNoCibUaiWb4AuUc87A9/lKC0mDwwdWvduft06tz8ictefqCBYWpqZ+nJw11iwwNUQLViQ+Jrl5a5NoqjI/YyUahJ9NmOyLZdVQI1xjcC/Bb7FNQKfoaqz/c6xNoCGrajI3RvXFl2P79fYGy3dap90xKqWKi72r6ZKqo3CmBT5VQHlrASgqpXAxbgFZuYCz8TL/E3DV1KSeP+iRbGPiSgudu0GueJ3p9+oUezj/T6zMdmQyyogVPU1Vd1VVbupag6/tiYfDB/uMvBotTP0eBlmJqt9UuUXoKqq6n42EVeaiVQTGZNtOQ0AxkQrK3MZeGmpyxxjZeh+QWLs2GD182HzC1CRz1Ja6p6LbK3uWrjQVRtZEDDZlrM2gFRYG4CB/O4f79cGkPagNWPSkHdtAMakKtleOUHF6r2TStoSlWL8qokStW8Yk2mNc50AY/JB7Tv3SLUMJB9gysrin1NSErsEYA3CJtusBGAM2e2nH6Sx25hssABgDP7VL2H00glSTWRMNlgAMIb41S/RvXQy0U4AmW3HyFSaTOGxNgBjcNUv8SaWW7cOLr0U1q/PTDtBpmSy7cIUHusGaown0dTSfnLZfdO6lJogrBuoMQlEqmUig7WCymX3TetSatJhAcCYWvx66bRtG/v4XHbfDDJ/kjF+LAAYU4tfL5177sm/7pvWpdSkwxqBjYkh3mCufJqGIvLe+ZQmU39YI7AxxjRw1ghsjDGmBgsAxhhToCwAGGNMgbIAYIwxBcoCgDHGFCgLAMYYU6AsABhjTIHKSQAQkRtE5FsRme5tR+UiHcYYU8hyORL4LlW9M4fvb4wxBc2qgIwxpkDlMgBcLCIzRGSMiGzvd5CIDBSRChGpWLZsWTbTZ4wxDVpocwGJyJvAz2K8NBT4L7AcUOAmoJOqDkh0TZsLyBhjkuc3F1BobQCqemiQ40TkH8CrYaXDGGNMbLnqBdQp6unxwKxcpMMYYwpZrnoBjRCRXrgqoAXA+TlKhzHGFKycBABVPTMX72uMMWYr6wZqjDEFygKAMSEqL4euXaGoyP0sL891iozZytYENiYk5eUwcCCsW+eeL1zonoOt2Wvyg5UAjAnJ0KFbM/+IdevcfmPygQUAY0KyaFFy+43JNgsAxoSkpCS5/cZkmwUAY0IyfDgUF9fcV1zs9huTDywAGBOSsjIYPRpKS0HE/Rw92hqATf6wXkDGhKiszDJ8k7+sBGCMMQXKAoAxxhQoCwDGGFOgLAAYY0yBsgBgjDEFKrQlIcMgIsuAhblORwra4ZbALCSF+JmhMD93IX5mqF+fu1RV29feWa8CQH0lIhWx1uNsyArxM0Nhfu5C/MzQMD63VQEZY0yBsgBgjDEFygJAdozOdQJyoBA/MxTm5y7EzwwN4HNbG4AxxhQoKwEYY0yBsgBgjDEFygJAlonIlSKiItIu12kJm4jcISKficgMEXlBRLbLdZrCIiJHisg8EZkvIkNynZ5sEJEuIvKOiMwVkdkicmmu05QtItJIRKaJyKu5Tks6LABkkYh0AQ4DCmVRwInAXqraE/gcuCrH6QmFiDQCHgB+B+wJnC4ie+Y2VVlRCVyhqnsAvwQuKpDPDXApMDfXiUiXBYDsugsYDBREy7uqTlDVSu/pf4HOuUxPiPoC81X1f6q6CXgKOC7HaQqdqi5W1ane49W4DHHH3KYqfCLSGfg98HCu05IuCwBZIiLHAt+q6qe5TkuODAD+netEhGRH4Ouo599QABlhNBHpCvQGPs5tSrLibtyNXHWuE5IuWxEsg0TkTeBnMV4aClwNHJ7dFIUv3mdW1Ze8Y4biqgvKs5m2LJIY+wqilAcgItsA44G/qOqqXKcnTCJyNLBUVaeIyMG5Tk+6LABkkKoeGmu/iOwN7AR8KiLgqkKmikhfVf0+i0nMOL/PHCEiZwFHA7/Vhjvo5BugS9TzzsB3OUpLVolIE1zmX66qz+c6PVmwP3CsiBwFNAdai8hYVe2f43SlxAaC5YCILAD6qGp9mUkwJSJyJPA34CBVXZbr9IRFRBrjGrl/C3wLfAKcoaqzc5qwkIm7m3kMWKGqf8l1erLNKwFcqapH5zotqbI2ABOm+4FWwEQRmS4io3KdoDB4Dd0XA2/gGkKfaeiZv2d/4EzgEO/vO927Mzb1hJUAjDGmQFkJwBhjCpQFAGOMKVAWAIwxpkBZADDGmAJlAcAYYwqUBQCTFSKyJsnjD87UTIsicoOIXJmhaz0qIieleG6vWN0kRaSliPwgItvW2v+iiJySxPV3EJHnEhzj+3sVkQWFMEut2coCgDHZ0wuoEwBUdS0wAfhDZJ8XDH4NBAqCItJYVb9T1ZSCkylMFgBMVnl3oO+KyHPeWgHl3ojSyJz6n4nIB8AJUee0FJExIvKJNwf7cd7+s0XkJRF53ZuL//qoc4Z6+94Edova3807foqIvC8iu3v7HxWRe0XkIxH5X+QuX5z7RWSOiPwL6BB1rX1FZJJ3rTdEpJO3/10RuV1EJovI5yJygIg0BYYBp3oDpk6t9at5Ejgt6vnxwOuquk5E+nrpmub93C3q8z8rIq8AE0Skq4jM8l7r6n2+qd72q6hrtxa3PsMcERklInXyARHp76V/uog8JG7Ka9PQqKpttoW+AWu8nwcDK3Hz5RQB/8Hd6TbHzajZHTe52jPAq945twD9vcfb4aZdaAmcDSwG2gItgFlAH2BfYCZQDLQG5uOG7AO8BXT3HvcD3vYePwo866VpT9z0zuAC0USgEbAD8BNwEtAE+Aho7x13KjDGe/wuMNJ7fBTwpvf4bOB+n99PU2Ap0NZ7/jrwe+9xa6Cx9/hQYHzU9b4B2njPuwKzvMfFQHPvcXegIur3vwHY2ftME4GTvNcWAO2APYBXgCbe/geBP+b6f8i2zG82GZzJhcmq+g2AiEzHZVxrgK9U9Qtv/1hgoHf84bgJuCL1+M2BEu/xRFX9wTvneVwwAXhBVdd5+1/2fm4D/Ap41it0ADSLSteLqloNzBGRjt6+A4EnVbUK+E5E3vb27wbshZvmAlxmujjqWpGJ0aZ4ny8uVd3kpfMkERmPqy6a4L28LfCYiHTHzTLaJOrUiaq6IsYlmwD3i0gvoArYNeq1yar6PwAReRL3O4tuO/gtLoh+4n22FrjgZBoYCwAmFzZGPa5i6/+h37wkApyoqvNq7BTpF+Mc9Y6Pda0i4CdV7RUgXdFTPMe6lgCzVXW/BNeK/nyJPAlc4137JVXd7O2/CXhHVY8XN+/+u1HnrPW51mXAEmAf3OfeEPVarN9ZNAEeU9UGuYKb2craAEy++AzYSUS6ec9Pj3rtDeCSqLaC3lGvHSYibUSkBa4R9UPgPeB4EWkhIq2AYwDUzVX/lYic7F1HRGSfBOl6DzhN3BqwnYDfePvnAe1FZD/vWk1EpEeCa63GTY7n5x1cdc1FuGAQsS1ullFw1T5BbAss9ko0Z+JKKBF9RWQnr+7/VOCDWue+hSuJdADwfr+lAd/X1CMWAExeUNUNuCqff3mNwAujXr4JV6Uxw2vkvCnqtQ+AJ4DpuLrxCnXLFD4d2Qe8H3V8GXCuiHwKzCbx0o0vAF/g2hT+Dkzy0rsJ1xZwu3et6bjqpXjeAfb0aQTGy6zH49o03ot6aQRwq4h8SM2MPJ4HgbNE5L+46p/oksJ/gNtwbSZfeZ8xOh1zcCWRCSIyA9dO0Cng+5p6xGYDNfWWiJyNW1fh4lynxZj6yEoAxhhToKwEYIwxBcpKAMYYU6AsABhjTIGyAGCMMQXKAoAxxhQoCwDGGFOg/h/IBibstE87qQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"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('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Exponential"
]
},
{
"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": 5,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"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('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Logarithmic\n",
"\n",
"The response $y$ is a results of applying logarithmic map from input $x$'s to output variable $y$. 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 polynomial representation of the $x$'s. In general form it would be written as \n",
"\\begin{equation}\n",
"y = \\log(X)\n",
"\\end{equation}"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jupyterlab/conda/envs/python/lib/python3.6/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 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"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('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Sigmoidal/Logistic"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"$$ Y = a + \\frac{b}{1+ c^{(X-d)}}$$"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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cf9oRuh22kdlvoXD376ciiIhkrpoa55evLKRrm3yuPlG3wzY2+y0UZpYPXAUMBv5Z5sOuPERE6u2lecV8UrSD/75gKC3yErnQIamUSF9PjxN0xXEG8DZB9x0lcT8hIpKgsspq7nltMYO6teHcYT2ijiO1SKRQHO7udwCl7v4ocBZwZHJjiUimeOyDVazdvofbzhqo3mEbqUQKxd5OAbeb2RCgLcGAQyIi9bKttIL73ljGKf07c8LhnaKOI3VI5GLgBDNrD9xO0EdTK+COpKYSkYxw3xvLKC2v4pYxA6OOInHE6+vpEHff4O4Tw0XvAIemJpaINHWrt+zm8Rmr+G5hL444pHXUcSSOeJeePjGzaWZ2ZdjNuIhIg7lnavBw3fXfPCLqKLIf8QpFD+C/ga8DS8zsBTP7npk1T000EWmq5q7Zzsvz1nH11/vq4bo0UGehcPdqd58aPnDXC/gTwdjWK83syVQFFJGmxd35rymf0bFlHuNPOizqOJKARO56wt0rgIUEXY/vBAYlM5SINF1vLNrIzJVbue60frRqpofr0kHcQmFmBWZ2o5l9BLwMZANj3X1YStKJSJNSVV3D3a8uom+nlowbobHt00W8u57eJ2ineBYY7+4NPoCRiGSW5z4qYunGXTxw8THkZid0QUMagXj/pW4B+rj7DQ1dJMzsAjP71MxqzKwwznajzWyxmS0zs5sbMoOIpNaeimp+O20JwwraMXqIRq5LJ/Eas99296+Mld1AFgDnETybUatwdL37gTMJ2kQuNDO1jYikqUf+sZINO8u55cyBGrkuzUTSkuTunwH7+2UZASwLx87GzJ4GxhI0qotIGtlaWsGDby3ntIGHMKJvh6jjyAHa70VCM/tK5/C1LUuCHsCamPmicJmIpJn73lhKaUUVN43WyHXpKJHWpOdqWfa3/X3IzKab2YJaXmMTzFbb6Uadl8LMbLyZzTaz2Zs2bUrwECKSbKu37OaJGZ/z3cJe9FNXHWkp3l1PAwgGK2prZufFrGpDzABGdXH30+qZrYjgQb+9egLFcY43AZgAUFhYmKy2FRE5QPe+vpjsLFNXHWksXhtFf+BsoB3wrZjlJcDVyQwVmgX0Cy9zrQXGARel4Lgi0kDmFW3npU+KufaUw9VVRxqrs1C4+2Rgspkd5+4fNORBzexc4D6gM/CKmc119zPMrDsw0d3HuHuVmV0LTCV40O8Rd/+0IXOISPIEXXUsokPLPK45SR1Pp7NE7npaZma3EgxW9M/t6zNmtrtPAibVsrwYGBMzPwWYcrDHEZHovLVkEx+s2MLPvjWI1vm5UceRekikUEwG3gWmA9XJjSMiTUF1jfPrVxfRu2MLLhrZO+o4Uk+JFIoW7n5T0pOISJPx/EdFLFpfwn0XDiMvR111pLtE/gu+bGZj9r+ZiAiUVVbzm9eXMLRXO84+qlvUcaQBJFIofkxQLMrMbKeZlZjZzmQHE5H09Mg/VrJ+Zxm3njlAXXU0Efu99OTuekJGRBKytbSCB94MuuoYeWjHqONIA0mkCw8zs0vM7I5wvpeZjUh+NBFJN3u76rj5THXV0ZQkcunpj8BxfPGw2y6CXl1FRP5p1eZSnpjxOd87theHd9GFiKYkkbueRrr7MWb2MYC7bzOzvCTnEpE0c8/UReRmZ6mrjiYokTOKynBsCAcws85ATVJTiUhamfP5VqbMX881Jx5Gl9bqqqOpSaRQ/J7gKeouZvZL4D3gV0lNJSJpw935xSuf0aV1M64+MRUjEEiqJXLX05NmNgc4laDr72/vHXhIRGTK/PV8vHo795x/FC3yIhkLTZIsXjfjscNQbQSeil3n7luTGUxEGr/yqmp+/doiBnRtzfnDe0YdR5IkXvmfQ9AuYUABsC2cbgesBnSOKZLhHnv/c1Zv3c1jV44gO0sP1zVVdbZRuHtfdz+UoJvvb7l7J3fvSDBGxfOpCigijdOWXeX8/o2lnNK/Myce0TnqOJJEiTRmHxt29w2Au78KnJS8SCKSDv7370vZXVHNrWMGRh1FkiyRlqfNZnY78ATBpahLgC1JTSUijdrSDSU8OXM1F40o0DjYGSCRM4oLCUaimwS8AHQJl4lIhvrVlM9okZvNdaf1izqKpEAit8duJehBtsGY2QXAz4CBwAh3n13HdqsIxuiuBqrcvbAhc4jIgXtr8UbeXLyJW84cQMdWzaKOIymw30JhZkcAN/DVoVC/UY/jLgDOAx5KYNtT3H1zPY4lIg2ksrqGu15eSJ+OLbjihD5Rx5EUSaSN4lngQWAiDTQU6t4H9tRXvUh6efyDz1m+qZSJlxXSLCc76jiSIokUiip3fyDpSWrnwOtm5sBD7j4hohwiGW/LrnL+Z/oSvt6vE6cO7BJ1HEmhRArFS2b2Q4LG7PK9C/f3ZLaZTQe61rLqNnefnGC+E9y92My6ANPMbJG7v1PH8cYD4wEKCgoS3L2IJOq305awu6Kan5w9SFcDMkwiheLy8P3GmGUOHBrvQ+5+2sGGitlHcfi+0cwmASOAWgtFeLYxAaCwsNDre2wR+cLC4p089eFqLjuuj26HzUCJ3PUUSVcdZtYSyHL3knD6dODOKLKIZDJ35yeTF9CuRR7Xn6axJjJRIkOhtjCz281sQjjfz8zOrs9BzexcMysiGDnvFTObGi7vbmZ7nwI/BHjPzD4BPgRecffX6nNcETlwL8xdy+zPt3HT6P60bZEbdRyJQCKXnv5E0EHg8eF8EcGdUC8f7EHdfRJBm8e+y4uBMeH0CmDowR5DROqvpKySX01ZxNBe7bhgeK+o40hEEnky+zB3vweoBHD3PQS9yIpIE/e/05eyeVc5d54zmCz1DpuxEikUFWbWnC+GQj2MmLufRKRpWrKhhD+/v4pxx/ZiaK92UceRCCVy6emnwGtALzN7EjgBuCKZoUQkWjU1zm2T5tMqP4cbzxgQdRyJWCJ3PU0zs4+AUQSXnH6sLjVEmra/fVTErFXb+PX5R9KhZV7UcSRiiQ5wexLwNYLLT7nU0hAtIk3DttIK/mvKZxT2bq8GbAESuz32j8APgPkEnfldY2b3JzuYiETj7lcXUVJWxS/OHaIGbAESO6M4CRji7nsbsx8lKBoi0sTMWrWVZ2av4ZoTD2VA1zZRx5FGIpG7nhYDsZ0n9QLmJSeOiESlrLKam56bR492zfmxBiSSGImcUXQEPjOzD8P5Y4EPzOxFAHc/J1nhRCR17n9zGSs2lfLolSNokZdo86VkgkR+G36S9BQiEqlF63fywFvLOW9YD046onPUcaSRSeT22LfNrDfQz92nhw/f5bh7SfLjiUiyVdc4Nz03n7bNc7nj7EFRx5FGKJG7nq4G/sYXw5b2BF5IZigRSZ0//WMln6zZzk++NYj2emZCapFIY/aPCJ7G3gng7ksBDW8l0gQs37SLe6cu5rSBh3DO0O5Rx5FGKpFCUe7uFXtnzCyHsN8nEUlf1TXODc9+Qn5uNr86d4hGrZM6JVIo3jazW4HmZvZNgi7GX0puLBFJtonvruDj1du5c+xgurTJjzqONGKJFIqbgU0ED9ldA0wBbk9mKBFJrqUbSvjNtCWcMViXnGT/ErnrqcbMXgBecPdNKcgkIklUUVXDdc/MpWVeNr/49pG65CT7VecZhQV+ZmabgUXAYjPbZGb1fq7CzO41s0VmNs/MJplZrZ3dm9loM1tsZsvM7Ob6HldE4LfTlvBp8U5+ff5RdG7dLOo4kgbiXXq6juBup2PdvaO7dwBGAieY2fX1PO40gv6jjgKWALfsu4GZZQP3A2cCg4ALzUw3eYvUw4wVW3joneVcOKIXpw/uGnUcSRPxCsVlwIXuvnLvgnAc60vCdQfN3V9396pwdgbBsxn7GgEsc/cV4V1XTwNj63NckUy2Y08l//7MXHp3aMHtZ+nfXJK4eIUit7YBisJ2itwGzHAl8Goty3sAa2Lmi8JlInKA3J1bn5/PhpJyfjduGC2bqS8nSVy835aKg1wHgJlNB2o7t73N3SeH29wGVAFP1raLWpbV+fyGmY0HxgMUFBTUtZlIRnpi5mpemb+Om0YP4GiNfy0HKF6hGGpmO2tZbsB+b7p299PirTezy4GzgVP3jnWxjyKCLs336gkUxzneBGACQGFhoR4IFAl9WryDu15eyMn9O3PNiYdGHUfSUJ2Fwt2zk3VQMxsN3ASc5O6769hsFtDPzPoCa4FxwEXJyiTSFO0qr+Lav3xM+xa5/OaCoRqxTg5KIg/cJcMfgNbANDOba2YPAphZdzObAhA2dl8LTAU+A/7q7p9GlFck7bg7Nz03j8+3lPL7ccPo2Eq3wsrBiaRFy90Pr2N5MTAmZn4KwZPgInKAJr67klfmBe0SIw/tGHUcSWNRnVGISBK9v2wz//XqZ5w5pCs/OEntElI/KhQiTcza7Xu49qmPOaxzK+69YKi66JB6U6EQaUJ2V1Qx/rHZVFbV8OClw2ml5yWkAei3SKSJqKlxrnt6Lp+t28nDlx/LYZ1bRR1JmgidUYg0EfdMXczrCzdw+1mDOGWABqGUhqNCIdIE/HX2Gh58ezkXjyzg+yf0iTqONDEqFCJp7s3FG7nl+fl87fBO/OycwWq8lganQiGSxuau2c4Pn/iIAV1b88Alx5Cbrf+lpeHpt0okTa3YtIsr/zyLTq3z+NP3j6V1fkN26izyBRUKkTRUtG03lz78IQY8duVIurTebz+dIgdNt8eKpJn1O8q4eOJMdpZV8tTVo+jbqWXUkaSJ0xmFSBrZVFLORRNnsLmknMeuHMGQHm2jjiQZQGcUImliY0kZl0ycybrtZTx65QiGFbSPOpJkCBUKkTRQvH0PF0+cyYadZTx8RSEj+naIOpJkEBUKkUZu9ZbdXPh/M9i5p5LHrxrB8N4qEpJaKhQijdhn63ZyxZ8+pLyqhr9cPYoje6pNQlIvkkJhZvcC3wIqgOXA9919ey3brQJKgGqgyt0LU5lTJErvL9vMNY/PoWWzHJ4Zfxz9u7aOOpJkqKjuepoGDHH3o4AlwC1xtj3F3Y9WkZBMMnnuWi7/04d0a5fP8z88XkVCIhXVUKivx8zOAL4TRQ6Rxqamxvnd9CX8/o1ljOzbgQmXFdK2uZ64lmg1hjaKK4Fn6ljnwOtm5sBD7j4hdbFEUqu0vIrrn5nL6ws3cMHwnvzi3CE0y8mOOpZI8gqFmU0Hutay6jZ3nxxucxtQBTxZx25OcPdiM+sCTDOzRe7+Th3HGw+MBygoKKh3fpFUWrFpFz988iOWbCjhJ2cP4vsn9FEvsNJoJK1QuPtp8dab2eXA2cCp7u517KM4fN9oZpOAEUCthSI825gAUFhYWOv+RBqjlz4p5ubn5pGXk8WjV47g6/06Rx1J5EuiuutpNHATcJK7765jm5ZAlruXhNOnA3emMKZIUpVVVnPXywt5cuZqhvduz30XDqN7u+ZRxxL5iqjaKP4ANCO4nAQww91/YGbdgYnuPgY4BJgUrs8B/uLur0WUV6RBzSvazvXPzGX5plLGn3goN57RX2NJSKMV1V1Ph9exvBgYE06vAIamMpdIslVW1/DHN5dz3xtL6dSqGY9fpUtN0vg1hrueRDLCx6u3ccvz81m0voSxR3fnznOG0LaFbn2Vxk+FQiTJSsoq+c3rS3j0g1V0ad2Mhy4dzhmDa7shUKRxUqEQSZKaGudvc4q4Z+oitpRWcOmo3tx4Rn8NWSppR4VCJAk+WL6FX035jPlrd3BMQTsevvxYhvZqF3UskYOiQiHSgOYX7eCeqYt4d+lmurXN53/HHc05Q7vr4TlJayoUIg3gkzXb+cOby5i2cAPtWuRy25iBXHpcb/Jz1QWHpD8VCpGD5O58sHwLD7y9nHeXbqZNfg4/PrUfV329L23UDiFNiAqFyAEqq6zmxbnFPPKPlSxaX0KnVnncNHoAl4wqUEO1NEkqFCIJWrKhhKc+XM3zH61lx55KBnRtzT3nH8U5R3fXJSZp0lQoROLYsqucV+avY9LHa/l49XZys40zBnflopEFHHdoRzVSS0ZQoRDZx7bSCqYt3MCrC9bx7tLNVNU4A7q25rYxAznvmB50bNUs6ogiKaVCIQKs3FzKG4s28saiDcxYsZXqGqdn++Zc9bW+fHtYD/1G7B0AAAvGSURBVAZ2axN1RJHIqFBIRtqxu5IPVmzhvWWbeG/pZlZtCXq779elFeNPPJQxQ7oxpEcbXVoSQYVCMoC7U7yjjI9Xb2PWyq18uGobi9bvxB1a5GUz6tCOXHF8H04deAi9OrSIOq5Io6NCIU3OxpIyPl27kwVrdzB/7Q7mrtnOxpJyAJrnZjO8d3uuO/UIjj+8I0N7tiMvR+NAiMSjQiFpyd3ZWlrB8k2lLNu4i6UbS1i8PnhtKa3453Z9Orbg+MM6MqygPUf3aseg7m00QJDIAVKhkEarvKqa9TvKWLttD2u27WbN1j2s3rqbz7eUsnJzKTvLqv65bfPcbI44pBWnDuxC/65tGNw9eOkBOJH6i2rM7LuAsUANsBG4Ihzdbt/tRgP/C2QTDJF6d0qDSlLsrqhiy64KNu8qZ3P4vqmknA07y9iwM3hft6OMzbvKv/S57CyjW9t8+nZqyTlHd6dPx5Yc3qUVh3VuRY92zcnKUsOzSDJEdUZxr7vfAWBm/wb8BPhB7AZmlg3cD3wTKAJmmdmL7r4w1WHlCzU1zp7KakrLqyitCN53lVexqyx4LymrZGdZFTv3VLIj5rVtdyXbd1ewbXcFZZU1te67fYtcDmmTzyFt8hnUrQ3d2zWnW7t8erRrTkGHFnRtm6/LRiIRiGrM7J0xsy0Br2WzEcCycOxszOxpgrOQJlUoamqcGneq3XGH6ppguqbGqa5xamKWVVeH7zU1VIXrq6qdqhqnqjpYVlldEy6roXLve5VTUV1DZXUNFVVfvJfvfa+qobyyhvKqasr++R5M76msZk9FMF9aUVXnH/l95eVk0bZ5Lu2a59K2eS492uUzpHsb2rfMo32LPDq2yqNTqzw6tGxGl9bN6Ngqj2Y56gZDpDGKrI3CzH4JXAbsAE6pZZMewJqY+SJgZDIznX3fu+ypqA6qlgfVy93Dd3CCP+bB64vlNbHbhNM14R/72G2CV7DN3gIQpbycLJplZ5GXk0V+bjbNcr6Yzs/NomOrPFrkZZOfm03z3Gxa5GXTIi8neG+WQ6tm2bTMy6FVfg6tm+XSslk2bZrn0jo/R3/0RZqQpBUKM5sO1DYw8G3uPtndbwNuM7NbgGuBn+67i1o+W+dfVjMbD4wHKCgoOKjM/bq0pqKqBiw4uJmF71+exyArZl2WGRauyIqZ3/tuGNlZwTwG2WZkWbhtVjCdnfXFsuwvLYPsrCxysoysLPvne7YZOdnBfHaWkZsdbJOTnUVutpGTFb6HhSA328jNCqbzcoJt9TCZiCQiaYXC3U9LcNO/AK/w1UJRBPSKme8JfKXBO+Z4E4AJAIWFhQf1T/X/+d7RB/MxEZEmLZKWQTPrFzN7DrCols1mAf3MrK+Z5QHjgBdTkU9ERL4QVRvF3WbWn+D22M8J73gys+4Et8GOcfcqM7sWmEpwe+wj7v5pRHlFRDJWVHc9nV/H8mJgTMz8FGBKqnKJiMhX6aZ0ERGJS4VCRETiUqEQEZG4VChERCQuFQoREYnL3KPtRiIZzGwTwW236aYTsDnqECmWid8ZMvN76zs3br3dvXNtK5pkoUhXZjbb3QujzpFKmfidITO/t75z+tKlJxERiUuFQkRE4lKhaFwmRB0gApn4nSEzv7e+c5pSG4WIiMSlMwoREYlLhaIRMrMbzMzNrFPUWVLBzO41s0VmNs/MJplZu6gzJYuZjTazxWa2zMxujjpPKphZLzN708w+M7NPzezHUWdKFTPLNrOPzezlqLPUhwpFI2NmvYBvAqujzpJC04Ah7n4UsAS4JeI8SWFm2cD9wJnAIOBCMxsUbaqUqAL+w90HAqOAH2XI9wb4MfBZ1CHqS4Wi8fkf4D+JM+xrU+Pur7t7VTg7g2A0w6ZoBLDM3Ve4ewXwNDA24kxJ5+7r3P2jcLqE4A9nj2hTJZ+Z9QTOAiZGnaW+VCgaETM7B1jr7p9EnSVCVwKvRh0iSXoAa2Lmi8iAP5ixzKwPMAyYGW2SlPgdwT/6aqIOUl9RjXCXscxsOtC1llW3AbcCp6c2UWrE+97uPjnc5jaCyxRPpjJbClktyzLmzNHMWgHPAde5+86o8ySTmZ0NbHT3OWZ2ctR56kuFIsXc/bTalpvZkUBf4BMzg+Dyy0dmNsLd16cwYlLU9b33MrPLgbOBU73p3rNdBPSKme8JFEeUJaXMLJegSDzp7s9HnScFTgDOMbMxQD7QxsyecPdLIs51UPQcRSNlZquAQndPlw7FDpqZjQZ+C5zk7puizpMsZpZD0Fh/KrAWmAVc1NTHgrfgXz6PAlvd/bqo86RaeEZxg7ufHXWWg6U2CmkM/gC0BqaZ2VwzezDqQMkQNthfC0wlaND9a1MvEqETgEuBb4T/feeG/9KWNKEzChERiUtnFCIiEpcKhYiIxKVCISIicalQiIhIXCoUIiISlwqFNCpmtusAtz+5oXrmNLOfmdkNDbSvP5vZdw7ys0fXdvuombU0sy1m1naf5S+Y2XcPYP/dzexv+9mmzp+rma3KlJ6NJaBCIdL4HA18pVC4eynwOvDtvcvCovE1IKFiaWY57l7s7gdVxCQzqVBIoxT+i/YtM/tbOFbFk+ETvnvHdFhkZu8B58V8pqWZPWJms8IxAMaGy68ws8lm9lo4FsRPYz5zW7hsOtA/Zvlh4fZzzOxdMxsQLv+zmf3ezN43sxV7zxos8AczW2hmrwBdYvY13MzeDvc11cy6hcvfMrNfm9mHZrbEzL5uZnnAncD3wgfTvrfPj+YpYFzM/LnAa+6+28xGhLk+Dt/7x3z/Z83sJeB1M+tjZgvCdX3C7/dR+Do+Zt9tLBgfZKGZPWhmX/l7YWaXhPnnmtlDFnSlLk2Nu+ulV6N5AbvC95OBHQT9IWUBHxD8yzmfoAfWfgSd7P0VeDn8zK+AS8LpdgTdZbQErgDWAR2B5sACoBAYDswHWgBtgGUEXS0A/B3oF06PBN4Ip/8MPBtmGkTQbTgEBWsakA10B7YD3wFygfeBzuF23wMeCaffAn4TTo8BpofTVwB/qOPnkwdsBDqG868BZ4XTbYCccPo04LmY/RUBHcL5PsCCcLoFkB9O9wNmx/z8y4BDw+80DfhOuG4V0AkYCLwE5IbL/whcFvXvkF4N/1KngNKYfejuRQBmNpfgD9wuYKW7Lw2XPwGMD7c/naAjtr3tDPlAQTg9zd23hJ95nqDoAExy993h8hfD91bA8cCz4UkMQLOYXC+4ew2w0MwOCZedCDzl7tVAsZm9ES7vDwwh6J4Egj+662L2tbeDvDnh94vL3SvCnN8xs+cILlO9Hq5uCzxqZv0IeqXNjfnoNHffWssuc4E/mNnRQDVwRMy6D919BYCZPUXwM4tt2ziVoNjOCr9bc4IiJk2MCoU0ZuUx09V88ftaV78zBpzv7ou/tNBsZC2f8XD72vaVBWx396MTyBXbdXht+zLgU3c/bj/7iv1++/MUcHu478nuXhkuvwt4093PtWDch7diPlNax76uBzYAQwm+d1nMutp+ZrEMeNTdm+SIhPIFtVFIulkE9DWzw8L5C2PWTQX+X0xbxrCYdd80sw5m1pygMfgfwDvAuWbW3MxaA98C8GCshJVmdkG4HzOzofvJ9Q4wzoIxkrsBp4TLFwOdzey4cF+5ZjZ4P/sqIegksS5vElwm+hFB0dirLUGvtBBcbkpEW2BdeIZ0KcEZz14jzKxv2DbxPeC9fT77d4Izmy4A4c+3d4LHlTSiQiFpxd3LCC41vRI2Zn8es/ougksp88LG2rti1r0HPA7MJbh2P9uD4Tmf2bsMeDdm+4uBq8zsE+BT9j9k6SRgKUGbxwPA22HeCoK2il+H+5pLcFkrnjeBQXU0ZhP+UX+OoM3lnZhV9wD/ZWb/4Mt/8OP5I3C5mc0guOwUe+bxAXA3QZvOyvA7xuZYSHBm87qZzSNox+iW4HEljaj3WGnyzOwKgrE9ro06i0g60hmFiIjEpTMKERGJS2cUIiISlwqFiIjEpUIhIiJxqVCIiEhcKhQiIhKXCoWIiMT1/wFxmK2tBs4//QAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"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('Indepdendent Variable')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<a id=\"ref2\"></a>\n",
"# Non-Linear Regression example"
]
},
{
"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. "
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2020-06-08 06:51:58 URL:https://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/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": 8,
"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://s3-api.us-geo.objectstorage.softlayer.net/cf-courses-data/CognitiveClass/ML0101ENv3/labs/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)"
]
},
{
"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 decelerate slightly in the 2010s."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"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:"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"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('Indepdendent 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."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Building The Model ###\n",
"Now, let's build our regression model and initialize its parameters. "
]
},
{
"cell_type": "code",
"execution_count": 11,
"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:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false,
"jupyter": {
"outputs_hidden": false
}
},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f82028f7160>]"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"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:"
]
},
{
"cell_type": "code",
"execution_count": 13,
"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. Optimal 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."
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[690.4475266 0.99720712]\n"
]
}
],
"source": [
"from scipy.optimize import curve_fit\n",
"popt, pcov = curve_fit(sigmoid, xdata, ydata)\n",
"#print the final parameters\n",
"print(popt)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we plot our resulting regression model."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"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?"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/scipy/optimize/minpack.py:808: OptimizeWarning: Covariance of the parameters could not be estimated\n",
" category=OptimizeWarning)\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Mean absolute error: 0.20\n",
"Residual sum of squares (MSE): 0.16\n",
"R2-score: -1878368497973913920259227648000.00\n"
]
}
],
"source": [
"# write your code here\n",
"\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",
"popt, pcov = curve_fit(sigmoid, train_x, train_y)\n",
"y_hat = sigmoid(test_x, *popt)\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(y_hat , test_y) )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Double-click __here__ for the solution.\n",
"\n",
"<!-- Your answer is below:\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\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(y_hat , test_y) )\n",
"\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=\"http://cocl.us/ML0101EN-SPSSModeler\">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://cocl.us/ML0101EN_DSX\">Watson Studio</a>\n",
"\n",
"<h3>Thanks for completing this lesson!</h3>\n",
"\n",
"<h4>Author: <a href=\"https://ca.linkedin.com/in/saeedaghabozorgi\">Saeed Aghabozorgi</a></h4>\n",
"<p><a href=\"https://ca.linkedin.com/in/saeedaghabozorgi\">Saeed Aghabozorgi</a>, PhD is a Data Scientist in IBM with a track record of developing enterprise level applications that substantially increases clients’ ability to turn data into actionable knowledge. He is a researcher in data mining field and expert in developing advanced analytic methods like machine learning and statistical modelling on large datasets.</p>\n",
"\n",
"<hr>\n",
"\n",
"<p>Copyright &copy; 2018 <a href=\"https://cocl.us/DX0108EN_CC\">Cognitive Class</a>. This notebook and its source code are released under the terms of the <a href=\"https://bigdatauniversity.com/mit-license/\">MIT License</a>.</p>"
]
}
],
"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": "3.6.10"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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