diff --git a/SUMIH_202310715145_ML0101EN-Reg-NoneLinearRegression.ipynb b/SUMIH_202310715145_ML0101EN-Reg-NoneLinearRegression.ipynb deleted file mode 100644 index 7e315c7..0000000 --- a/SUMIH_202310715145_ML0101EN-Reg-NoneLinearRegression.ipynb +++ /dev/null @@ -1,888 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "

\n", - " \n", - " \"Skills\n", - " \n", - "

\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": [ - "

Importing required libraries

\n" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": { - "tags": [] - }, - "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": 2, - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "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": 3, - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "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": 4, - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "image/png": 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\n", - "text/plain": [ - "
" - ] - }, - "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": 5, - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "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": 6, - "metadata": { - "tags": [] - }, - "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": [ - "
" - ] - }, - "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": 7, - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "image/png": 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" - ] - }, - "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": [ - "\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": 8, - "metadata": { - "tags": [] - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "2025-10-17 02:42:15 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": [ - "
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919697.871882e+10
\n", - "
" - ], - "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://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": 9, - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "image/png": 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sAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHCvV7g4AAAAkJb9fqq6WfD4pJ0cqLpZcLrt75TiEWQAAgN7m9UqzZ0u7dn3Z5vFICxZIZWX29cuBbF9msGjRIhUWFio9PV2jRo1SdXX1UetbWlp05513Kj8/X2lpaTr55JP11FNP9VJvAQAAesjrla68MjTISlJDQ6Dd67WnXw5l68zssmXLVF5erkWLFun888/X448/rgkTJmjz5s066aSTwr7nqquu0u7du/Xkk0/qlFNO0Z49e9TW1tbLPQcAAOgGvz8wI2tM59eMkSxLKi+XJk1iyUGELGPC/TZ7x5gxYzRy5Eg9+uijwbYRI0Zo8uTJqqio6FS/cuVKff/739f27duVlZXVrc9sbm6W2+1WU1OTMjMzu913AACAqK1eLY0ff+y6VaukkpJ49yZhRZPXbFtm0Nraqk2bNqm0tDSkvbS0VOvXrw/7nr/+9a8aPXq0fvWrX2nYsGEaPny4brvtNn322Wddfk5LS4uam5tDHgAAALbw+WJbB/uWGezdu1d+v1/Z2dkh7dnZ2WpsbAz7nu3bt2vt2rVKT0/XCy+8oL179+rf//3f9fHHH3e5braiokL33ntvzPsPAAAQtZyc2NbB/hvALMsKeW6M6dTWob29XZZl6dlnn9W5556ryy67TA899JD+8Ic/dDk7O3fuXDU1NQUf9fX1Mf8OAAAAESkuDuxa0EXWkWVJeXmBOkTEtjB74oknyuVydZqF3bNnT6fZ2g45OTkaNmyY3G53sG3EiBEyxmjXkXcE/n9paWnKzMwMeQAAANjC5QpsvyV1DrQdz+fP5+avKNgWZvv3769Ro0apqqoqpL2qqkrjxo0L+57zzz9fH374oT799NNg2/vvv6+UlBR5PJ649hcAACAmysqkykpp2LDQdo8n0M4+s1GxdTeDZcuWaerUqXrsscc0duxYPfHEE1q8eLHeeecd5efna+7cuWpoaNAzzzwjSfr00081YsQInXfeebr33nu1d+9e3Xjjjbrwwgu1ePHiiD6T3QwAAEBC4ASwLkWT12zdZ3bKlCnat2+f7rvvPvl8PhUVFWnFihXKz8+XJPl8Pu3cuTNYf/zxx6uqqkq33HKLRo8erUGDBumqq67S/fffb9dXAAAA6B6XK6m334oVW2dm7cDMLAAAQGJzxD6zAAAAQE8RZgEAAOBYhFkAAAA4FmEWAAAAjkWYBQAAgGMRZgEAAOBYhFkAAAA4FmEWAAAAjhX1CWAffPCBXnrpJX3xxRe68MILdfrpp8ejXwAAAMAxRRVm16xZo8suu0yHDh0KvDk1VX/84x919dVXx6VzAAAAwNFEtczgP//zPzV+/Hjt2rVL+/bt0/XXX6+f/vSn8eobAAAAcFSWMcZEWpyVlaU1a9aoqKhIknTw4EFlZmZq7969+spXvhK3TsZSNGf9AgAAoPdFk9eimpndv3+/hgwZEnyekZGhAQMGaP/+/d3qKAAAANATUd8AtnnzZjU2NgafG2P07rvv6sCBA8G2M888Mza9AwAAAI4iqmUGKSkpsixL4d7S0W5Zlvx+f0w7GUssMwAAAEhs0eS1qGZm6+rqetQxAAAAIJaiCrP5+fnx6gcAAAAQtajXzErSli1b9Je//EU7duyQZVkqLCzU5MmT9dWvfjXW/QMAAAC6FHWYraio0F133aX29nYNGTJExhh99NFHuuOOO/TAAw/otttui0c/AQAAgE6i2ppr1apVmjdvnu68807t3btXPp9PjY2NwTB7xx13aM2aNfHqKwAAABAiqt0MpkyZooEDB+rxxx8P+/qPfvQjHThwQEuXLo1ZB2ON3QwAAEBc+f1SdbXk80k5OVJxseRy2d0rR4nboQlvvPGGpk6d2uXrU6dO1WuvvRbNJQEAAPoOr1cqKJDGj5euuSbws6Ag0I64iCrM7t69WwUFBV2+XlhYGHKgAgAAQNLweqUrr5R27Qptb2gItBNo4yKqMPv555+rf//+Xb7er18/tba29rhTAAAAjuL3S7NnS+FWb3a0lZcH6hBTUe9m8Pvf/17HH3982NcOP9IWAAAgaVRXd56RPZwxUn19oK6kpNe6lQyiCrMnnXSSFi9efMwaAACApOLzxbYOEYsqzO7YsSNO3QAAAHCwnJzY1iFiUYXZzz//XC+//LIuv/xySdLcuXPV0tLy5cVSU3XfffcpPT09tr0EAABIZMXFkscTuNkr3LpZywq8Xlzc+33r46IKs3/84x/1P//zP8Ewu3DhQp1++uk67rjjJEn/+te/NHToUM2ZMyf2PQUAAEhULpe0YEFg1wLLCg20lhX4OX8++83GQVS7GTz77LO6/vrrQ9qWLFmiVatWadWqVfr1r3+t559/PqYdBAAAcISyMqmyUho2LLTd4wm0l5XZ068+LqqZ2ffff1/Dhw8PPk9PT1dKypd5+Nxzz9XNN98cu94BAAA4SVmZNGkSJ4D1oqjCbFNTk1JTv3zLRx99FPJ6e3t7yBpaAACApONysf1WL4pqmYHH49Hbb7/d5ev//Oc/5fF4etwpAAAAIBJRhdnLLrtMd911lz7//PNOr3322We699579e1vfztmnQMAAACOxjIm3P4R4e3evVtnn322+vfvr5kzZ2r48OGyLEv/+te/tHDhQrW1tammpkbZ2dnx7HOPNDc3y+12q6mpSZmZmXZ3BwAAAEeIJq9FtWY2Oztb69ev149//GPdcccd6sjBlmXpkksu0aJFixI6yAIAAKBviSrMSlJhYaFWrlypjz/+WFu3bpUknXLKKcrKyop55wAAAICjiTrMdsjKytK5554by74AAAAkLr+fLbcSULfDLAAAQNLweqXZs6Vdu75s83gCp35xGIKtotrNAAAAIOl4vYFjag8PspLU0BBo93rt6RckEWYBAAC65vcHZmTDbf7U0VZeHqiDLQizAAAAXamu7jwjezhjpPr6QB1sQZgFAADois8X2zrEHGEWAACgKzk5sa1DzBFmAQAAulJcHNi1wLLCv25ZUl5eoA62IMwCAAB0xeUKbL8ldQ60Hc/nz2e/WRsRZgEAAI6mrEyqrJSGDQtt93gC7ewzaysOTQAAADiWsjJp0iROAEtAhFkAAIBIuFxSSYndvcARWGYAAAAAxyLMAgAAwLEIswAAAHAswiwAAAAcizALAAAAxyLMAgAAwLEIswAAAHAswiwAAAAcy/Ywu2jRIhUWFio9PV2jRo1SdXV1RO9bt26dUlNTdfbZZ8e3gwAAAEhYtobZZcuWqby8XHfeeadqampUXFysCRMmaOfOnUd9X1NTk6ZNm6ZvfvObvdRTAAAAJCLLGGPs+vAxY8Zo5MiRevTRR4NtI0aM0OTJk1VRUdHl+77//e/r1FNPlcvl0osvvqja2tqIP7O5uVlut1tNTU3KzMzsSfcBAAAQB9HkNdtmZltbW7Vp0yaVlpaGtJeWlmr9+vVdvu/pp5/Wtm3bdPfdd0f0OS0tLWpubg55AAAAoG+wLczu3btXfr9f2dnZIe3Z2dlqbGwM+54tW7bojjvu0LPPPqvU1NSIPqeiokJutzv4yMvL63HfAQAAkBhsvwHMsqyQ58aYTm2S5Pf7dc011+jee+/V8OHDI77+3Llz1dTUFHzU19f3uM8AAABIDJFNb8bBiSeeKJfL1WkWds+ePZ1mayXpwIED2rhxo2pqajRz5kxJUnt7u4wxSk1N1UsvvaSLLrqo0/vS0tKUlpYWny8BAAAAW9k2M9u/f3+NGjVKVVVVIe1VVVUaN25cp/rMzEy99dZbqq2tDT5mzJihr33ta6qtrdWYMWN6q+sAAABIELbNzErSnDlzNHXqVI0ePVpjx47VE088oZ07d2rGjBmSAksEGhoa9MwzzyglJUVFRUUh7x8yZIjS09M7tQMAACA52Bpmp0yZon379um+++6Tz+dTUVGRVqxYofz8fEmSz+c75p6zAAAASF627jNrB/aZBQAASGyO2GcWAAAA6CnCLAAAAByLMAsAAADHIswCAADAsWzdzQAAAMBWfr9UXS35fFJOjlRcLLlcdvcKUSDMAgCA5OT1SrNnS7t2fdnm8UgLFkhlZfb1C1FhmQEAAEg+Xq905ZWhQVaSGhoC7V6vPf1C1AizAAAgufj9gRnZcFvtd7SVlwfqkPAIswAAILlUV3eekT2cMVJ9faAOCY8wCwAAkovPF9s62IowCwAAkktOTmzrYCvCLAAASC7FxYFdCywr/OuWJeXlBeqQ8AizAAAgubhcge23pM6BtuP5/PnsN+sQhFkAAJB8ysqkykpp2LDQdo8n0M4+s47BoQkAACA5lZVJkyZxApjDEWYBAEDycrmkkhK7e4EeYJkBAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxCLMAAABwLMIsAAAAHIswCwAAAMcizAIAAMCxUu3uAAAAQMz5/VJ1teTzSTk5UnGx5HLZ3SvEAWEWAAD0LV6vNHu2tGvXl20ej7RggVRWZl+/EBcsMwAAAH2H1ytdeWVokJWkhoZAu9drT78QN4RZAADQN/j9gRlZYzq/1tFWXh6oQ59BmAUAAH1DdXXnGdnDGSPV1wfq0GcQZgEAQN/g88W2Do5AmAUAAH1DTk5s6+AIhFkAANA3FBcHdi2wrPCvW5aUlxeoQ59BmAUAAH2DyxXYfkvqHGg7ns+fz36zfQxhFgAA9B1lZVJlpTRsWGi7xxNoZ5/ZPodDEwAAQN9SViZNmsQJYEmCMAsAAPoel0sqKbG7F+gFLDMAAACAYxFmAQAA4FiEWQAAADgWYRYAAACOxQ1gAADAGfx+dihAJ4RZAACQ+LxeafZsadeuL9s8nsAhCewdm9RYZgAAABKb1ytdeWVokJWkhoZAu9drT7+QEAizAAAgcfn9gRlZYzq/1tFWXh6oQ1IizAIAgMRVXd15RvZwxkj19YE6JCXCLAAASFw+X2zr0OcQZgEAQOLKyYltHfocwiwAAEhcxcWBXQssK/zrliXl5QXqkJQIswAAIHG5XIHtt6TOgbbj+fz57DebxAizAAAgsZWVSZWV0rBhoe0eT6CdfWaTmu1hdtGiRSosLFR6erpGjRql6qPcjej1enXJJZdo8ODByszM1NixY/X3v/+9F3sLAABsUVYm7dghrVolLVkS+FlXR5CFvWF22bJlKi8v15133qmamhoVFxdrwoQJ2rlzZ9j6NWvW6JJLLtGKFSu0adMmjR8/XhMnTlRNTU0v9xwAAMSM3y+tXi0tXRr42dWesS6XVFIiXX114CdLCyDJMibcLsS9Y8yYMRo5cqQeffTRYNuIESM0efJkVVRURHSN008/XVOmTNFdd90VUX1zc7PcbreampqUmZnZrX4DAIAY4ZhahBFNXrNtZra1tVWbNm1SaWlpSHtpaanWr18f0TXa29t14MABZWVldVnT0tKi5ubmkAcAAEgAHFOLGLAtzO7du1d+v1/Z2dkh7dnZ2WpsbIzoGg8++KAOHjyoq666qsuaiooKud3u4CMvL69H/QYAADHAMbWIEdtvALOO2GbDGNOpLZylS5fqnnvu0bJlyzRkyJAu6+bOnaumpqbgo76+vsd9BgAAPcQxtYiRVLs++MQTT5TL5eo0C7tnz55Os7VHWrZsmW644QY9//zzuvjii49am5aWprS0tB73FwAAxBDH1CJGbJuZ7d+/v0aNGqWqqqqQ9qqqKo0bN67L9y1dulTXXnutlixZom9/+9vx7iYAAIgHjqlFjNg2MytJc+bM0dSpUzV69GiNHTtWTzzxhHbu3KkZM2ZICiwRaGho0DPPPCMpEGSnTZumBQsW6LzzzgvO6h533HFyu922fQ8AABCljmNqGxrCr5u1rMDrHFOLY7B1zeyUKVM0f/583XfffTr77LO1Zs0arVixQvn5+ZIkn88Xsufs448/rra2Nt18883KyckJPmbPnm3XVwAAAN3BMbWIEVv3mbUD+8wCAJBAwu0zm5cXCLLsM5u0oslrti4zAAAAfZTfH9iJwOcLrHstLg4/y1pWJk2aFFktEAZhFgAAxFa0p3p1HFMLdIPt+8wCAIA+hFO90MsIswAAIDY41Qs2IMwCAIDY4FQv2IAwCwAAYoNTvWADbgADAACRO9ouBZzqBRswMwsAACLj9UoFBdL48dI11wR+FhR8eVNXx6leRx6C0MGyAnvIcqoXYogwCwAAji2SXQo41Qs2IMwCAICji2aXgrIyqbJSGjYstM7jCbRzqhdijDWzAADg6KLZpaCkhFO90KsIswAA4Og3dnVnlwJO9UIvIcwCAJDsjnX8LLsUIIGxZhYAgGQWyY1d7FKABEaYBQAgWUV6Y5fELgVIWIRZAAD6Kr9fWr1aWro08NPvD309mhu72KUACYo1swAA9EXHWgcrRX9jF7sUIAERZgEA6Gs61sEeuXygYx1sx0xqd27sYpcCJBiWGQAA0JdEc8ABN3ahDyDMAgDgNEdbCxvNOliOn0UfQJgFAMBJvF6poEAaP1665prAz4KCQLvUvXWw3NgFB2PNLAAAieBoJ3B1iGQtbHfWwXJjFxzMMibcopq+q7m5WW63W01NTcrMzLS7OwAARLbzgN8fmIHtagmBZQXes3WrdPLJgYAb7j/xHXV1dYRVJKxo8hrLDAAAiKdj7fUayQlcUuRrYdevZx0skgphFgCAeDnW+tZodh6IZi0s62CRRFgzCwBAPESyvjUrK/KdB6JdC8s6WCQJwiwAALF2rBlXywrMuFZURHY9n0+66qrAzOqx1sIevicsBxwgCbDMAACAaB1rHWyk61s/+iiyz8vJYU9YoAuEWQAAonGsdbBS5OtbBw+O7gQu1sICnRBmAQCIVKQ7D0S6vnXYsOhnW8vKpB07pFWrpCVLAj/r6giySFrsMwsAQCQi3ee1ri7wvKAg8r1ew+0zm5cXCLKEVCShaPIaN4ABANDhaKdwRboOtro6cNPVggWB2VrLCg204WZc2XkA6DbCLAAA0rFP4Ypmn1fpy/Wt4a4ZbsaVnQeAbiHMAgAQyZ6w0e7zKjHjCvQC1swCAJJbpGtht26VTj458nWwALotmrzGbgYAgOQW6VrY9evZ5xVIQIRZAEByi2YtLPu8AgmHNbMAgL7taDsUSNGvhWUdLJBQCLMAgL7rWDsUSIEg6vEcey1sxylcEjsPAAmEZQYAgL4p0tO6XC7WwgIORpgFAPQ9fn9gRjbcTGtHW3l5oE5iLSzgYCwzAAAklmOtcY2kLtrTuiTWwgIORZgFACSOSNa4RlIX7WldHVgLCzgOYRYAEH+RzLZGcgpXWVn8TusC4EicAAYACBXpX/NHWhvJbGu0p3BxWhfQp3ECGAAkKr9fWr1aWro08LPjBqRE+WyvNxAqx4+Xrrkm8LOg4Ms7/6OtjXRHgUjXuC5axGldAEIQZgGgt0QTFGMdemMZPCOtjWZHgUjXuG7bFlkdp3UBSYNlBgDQUz1ZD9oxS3h4uIr0JqhYfvakSZH9NX9dXeB5JLVPPy1dfHH4msOtWhX4OX78sWsffli69dbIrtlxI1c0yyYAJIRo8hphFgC60tvrQevqpL/8JbahN9LPjkfwnDdPuv/+Y9ctWSJddVWgn8da48paWCApsGYWQN8QzV+1R1obaZ0d60FXr478r+Xj8dmR8PkiXxIQqZycyE/h6t+ftbAAQhBmgb4kHjcX2XXNWN+IFG2dHetBV6+OfeiNR/CMdDurkpLALOmRobODZUl5eYEZbynyNa6shQVwOJNkmpqajCTT1NRkd1eQ7NrajFm1ypglSwI/29p6Vrt8uTEejzGBOBN4eDyB9t64ZqTfJ5JrLl9ujGWF1kiBNsvqXm2kdW1tnft3ZH1enjEvv9x1zeGPVasCj0hq582LbV00n/3yy4HvHe53dPj3bmv78ncUSW3H7/3I2nBjGe0/S9H8GQLgKNHkNcIsEAk7g2esw188rhnp94nkmpGGycND1bFqW1oiv2asg+eSJZGHv0gDcjw+O9rgGW3tkb//vLyu/0cLQNIjzB4FYbaH4jFjkujXtDN4xjr8xeOaTpjxfPjhyK+5ZElsA+WqVaG/96OFv1iH3mg++2j/DHcVPKOpZRYVQBQIs0fR62E21kHNzpAYzexbLMOfnde0M3jGI/zF+podfzUdyfeJx4xnpMFz5szIrxmPv5Y/2j9zR4a/WIbeaD+7Qzz+PQMAUSDMHkWvhtlYBzU7Q2Ks1yU64Zp2B894hD87127GY8YzHjOzibAeNFahtzufDQAJgDB7FL0WZmMd1JxwQ0w06xKdcE27g2c8wl+srxmPIB2PG5E6xjzSmcxEWA8aq9ALAA7kqDD7yCOPmIKCApOWlmZGjhxp1qxZc9T61atXm5EjR5q0tDRTWFhoHn300ag+r1fCbKxDld0hMR6zX064pt3BMx7hL9bX7M4SB7tuRIp2JtMp60GZbQXQBzkmzD733HOmX79+ZvHixWbz5s1m9uzZJiMjw3zwwQdh67dv324GDBhgZs+ebTZv3mwWL15s+vXrZyorKyP+zF4Js7EOVXaHxHisS3TCNe0OnvEIf7G+ZrRrN+2+ESnamUyCIgDYwjFh9txzzzUzZswIaTvttNPMHXfcEbb+pz/9qTnttNNC2qZPn27OO++8iD+zV8JsrEOV3SHRCbOo8bim3cHTmPiEv1hfM1FmPNmbFAD6DEeE2ZaWFuNyuYzX6w1pnzVrlvnGN74R9j3FxcVm1qxZIW1er9ekpqaa1tbWsO/5/PPPTVNTU/BRX18f8S+n2/razGw81iU65Zp2B89oa3uyM0VPrsmMJwAghhwRZhsaGowks27dupD2n//852b48OFh33Pqqaean//85yFt69atM5LMhx9+GPY9d999t5HU6dEra2ZjFarsDnTGxGddopOuafe+m/EIf7G+JgEVABAjjgqz69evD2m///77zde+9rWw7zn11FPNAw88ENK2du1aI8n4fL6w77FlZtaY2IcquwNdR32s1yU65Zp2B08AAJKII8Jsby0zOJLt+8z2JFTZHeiMccbhDvG6JgAA6BXR5DXLGGNkkzFjxmjUqFFatGhRsO3rX/+6Jk2apIqKik71t99+u/72t79p8+bNwbYf//jHqq2t1YYNGyL6zObmZrndbjU1NSkzM7PnX+JY/H6pulry+aScHKm4WHK54l8Xr2sCAADEWTR5zdYwu2zZMk2dOlWPPfaYxo4dqyeeeEKLFy/WO++8o/z8fM2dO1cNDQ165plnJEl1dXUqKirS9OnTddNNN2nDhg2aMWOGli5dqiuuuCKiz+z1MAsAAICoRJPXUnupT2FNmTJF+/bt03333Sefz6eioiKtWLFC+fn5kiSfz6edO3cG6wsLC7VixQrdeuuteuSRR5Sbm6vf/va3EQdZAAAA9C22zszagZlZAACAxBZNXkvppT4BAAAAMUeYBQAAgGMRZgEAAOBYhFkAAAA4FmEWAAAAjkWYBQAAgGMRZgEAAOBYhFkAAAA4lq0ngNmh44yI5uZmm3sCAACAcDpyWiRneyVdmD1w4IAkKS8vz+aeAAAA4GgOHDggt9t91JqkO862vb1dH374oU444QRZltUrn9nc3Ky8vDzV19dzhG4CYnwSG+OT+BijxMb4JDbGJzxjjA4cOKDc3FylpBx9VWzSzcympKTI4/HY8tmZmZn8g5rAGJ/ExvgkPsYosTE+iY3x6exYM7IduAEMAAAAjkWYBQAAgGMRZntBWlqa7r77bqWlpdndFYTB+CQ2xifxMUaJjfFJbIxPzyXdDWAAAADoO5iZBQAAgGMRZgEAAOBYhFkAAAA4FmEWAAAAjkWYjcCaNWs0ceJE5ebmyrIsvfjiiyGv7969W9dee61yc3M1YMAAXXrppdqyZUun62zYsEEXXXSRMjIyNHDgQJWUlOizzz4Lvv7JJ59o6tSpcrvdcrvdmjp1qvbv3x/nb9c39HSMduzYIcuywj6ef/75YB1j1D2x+DPU2NioqVOnaujQocrIyNDIkSNVWVkZUsP4dF8sxmjbtm367ne/q8GDByszM1NXXXWVdu/eHVLDGEWvoqJC//Zv/6YTTjhBQ4YM0eTJk/Xee++F1BhjdM899yg3N1fHHXecSkpK9M4774TUtLS06JZbbtGJJ56ojIwMfec739GuXbtCahif7onVGD3xxBMqKSlRZmamLMsK+7tnjDojzEbg4MGDOuuss7Rw4cJOrxljNHnyZG3fvl1/+ctfVFNTo/z8fF188cU6ePBgsG7Dhg269NJLVVpaqjfeeENvvvmmZs6cGXJE2zXXXKPa2lqtXLlSK1euVG1traZOndor39HpejpGeXl58vl8IY97771XGRkZmjBhQvBajFH3xOLP0NSpU/Xee+/pr3/9q9566y2VlZVpypQpqqmpCdYwPt3X0zE6ePCgSktLZVmWXnnlFa1bt06tra2aOHGi2tvbg9dijKL36quv6uabb9Zrr72mqqoqtbW1qbS0NOTPx69+9Ss99NBDWrhwod58800NHTpUl1xyiQ4cOBCsKS8v1wsvvKDnnntOa9eu1aeffqrLL79cfr8/WMP4dE+sxujQoUO69NJL9bOf/azLz2KMwjCIiiTzwgsvBJ+/9957RpJ5++23g21tbW0mKyvLLF68ONg2ZswYM2/evC6vu3nzZiPJvPbaa8G2DRs2GEnmX//6V2y/RB/X3TE60tlnn22uv/764HPGKDa6Oz4ZGRnmmWeeCblWVlaW+f3vf2+MYXxiqTtj9Pe//92kpKSYpqamYM3HH39sJJmqqipjDGMUK3v27DGSzKuvvmqMMaa9vd0MHTrU/OIXvwjWfP7558btdpvHHnvMGGPM/v37Tb9+/cxzzz0XrGloaDApKSlm5cqVxhjGJ5a6M0aHW7VqlZFkPvnkk5B2xig8ZmZ7qKWlRZKUnp4ebHO5XOrfv7/Wrl0rSdqzZ49ef/11DRkyROPGjVN2drYuvPDC4OtSYObW7XZrzJgxwbbzzjtPbrdb69ev76Vv0zdFMkZH2rRpk2pra3XDDTcE2xij+Ih0fC644AItW7ZMH3/8sdrb2/Xcc8+ppaVFJSUlkhifeIpkjFpaWmRZVsjG7+np6UpJSQnWMEax0dTUJEnKysqSJNXV1amxsVGlpaXBmrS0NF144YXB3+umTZv0xRdfhNTk5uaqqKgoWMP4xE53xigSjFF4hNkeOu2005Sfn6+5c+fqk08+UWtrq37xi1+osbFRPp9PkrR9+3ZJ0j333KObbrpJK1eu1MiRI/XNb34zuOassbFRQ4YM6XT9IUOGqLGxsfe+UB8UyRgd6cknn9SIESM0bty4YBtjFB+Rjs+yZcvU1tamQYMGKS0tTdOnT9cLL7ygk08+WRLjE0+RjNF5552njIwM3X777Tp06JAOHjyon/zkJ2pvbw/WMEY9Z4zRnDlzdMEFF6ioqEiSgr+77OzskNrs7Ozga42Njerfv7++8pWvHLWG8em57o5RJBij8AizPdSvXz8tX75c77//vrKysjRgwACtXr1aEyZMkMvlkqTgerHp06fruuuu0znnnKOHH35YX/va1/TUU08Fr2VZVqfrG2PCtiNykYzR4T777DMtWbIkZFa2A2MUe5GOz7x58/TJJ5/o5Zdf1saNGzVnzhx973vf01tvvRWsYXziI5IxGjx4sJ5//nn97W9/0/HHHy+3262mpiaNHDkyZBwZo56ZOXOm/vnPf2rp0qWdXjvydxjJ7/XIGsan52I9Rse6Rnev05ek2t2BvmDUqFGqra1VU1OTWltbNXjwYI0ZM0ajR4+WJOXk5EiSvv71r4e8b8SIEdq5c6ckaejQoZ3u+pWkjz76qNP/ySF6xxqjw1VWVurQoUOaNm1aSDtjFD/HGp9t27Zp4cKFevvtt3X66adLks466yxVV1frkUce0WOPPcb4xFkkf4ZKS0u1bds27d27V6mpqRo4cKCGDh2qwsJCSfwZ6qlbbrlFf/3rX7VmzRp5PJ5g+9ChQyUFZu06/nsjBZa4dfxehw4dqtbWVn3yySchs7N79uwJ/g0U49NzPRmjSDBG4TEzG0Nut1uDBw/Wli1btHHjRk2aNEmSVFBQoNzc3E7bdLz//vvKz8+XJI0dO1ZNTU164403gq+//vrrampqCvmrbvRMV2N0uCeffFLf+c53NHjw4JB2xij+uhqfQ4cOSVLI7h9SYN1mx998MD69I5I/QyeeeKIGDhyoV155RXv27NF3vvMdSYxRdxljNHPmTHm9Xr3yyivB/znoUFhYqKFDh6qqqirY1traqldffTX4ex01apT69esXUuPz+fT2228Haxif7ovFGEWCMeqCLbedOcyBAwdMTU2NqampMZLMQw89ZGpqaswHH3xgjDHmz3/+s1m1apXZtm2befHFF01+fr4pKysLucbDDz9sMjMzzfPPP2+2bNli5s2bZ9LT083WrVuDNZdeeqk588wzzYYNG8yGDRvMGWecYS6//PJe/a5OFYsxMsaYLVu2GMuyzP/93/+F/RzGqHt6Oj6tra3mlFNOMcXFxeb11183W7duNb/5zW+MZVnmf//3f4N1jE/3xeLP0FNPPWU2bNhgtm7dav70pz+ZrKwsM2fOnJAaxih6P/7xj43b7TarV682Pp8v+Dh06FCw5he/+IVxu93G6/Wat956y1x99dUmJyfHNDc3B2tmzJhhPB6Pefnll80//vEPc9FFF5mzzjrLtLW1BWsYn+6J1Rj5fD5TU1NjFi9ebCSZNWvWmJqaGrNv375gDWPUGWE2Ah1bZBz5+OEPf2iMMWbBggXG4/GYfv36mZNOOsnMmzfPtLS0dLpORUWF8Xg8ZsCAAWbs2LGmuro65PV9+/aZH/zgB+aEE04wJ5xwgvnBD37QaVsOhBerMZo7d67xeDzG7/eH/RzGqHtiMT7vv/++KSsrM0OGDDEDBgwwZ555Zqetuhif7ovFGN1+++0mOzvb9OvXz5x66qnmwQcfNO3t7SE1jFH0wo2LJPP0008Ha9rb283dd99thg4datLS0sw3vvEN89Zbb4Vc57PPPjMzZ840WVlZ5rjjjjOXX3652blzZ0gN49M9sRqju++++5jXYYw6s4wxJl6zvgAAAEA8sWYWAAAAjkWYBQAAgGMRZgEAAOBYhFkAAAA4FmEWAAAAjkWYBQAAgGMRZgEAAOBYhFkAAAA4FmEWABKIMUYXX3yxvvWtb3V6bdGiRXK73dq5c6cNPQOAxESYBYAEYlmWnn76ab3++ut6/PHHg+11dXW6/fbbtWDBAp100kkx/cwvvvgiptcDgN5EmAWABJOXl6cFCxbotttuU11dnYwxuuGGG/TNb35T5557ri677DIdf/zxys7O1tSpU7V3797ge1euXKkLLrhAAwcO1KBBg3T55Zdr27Ztwdd37Nghy7L05z//WSUlJUpPT9d///d/2/E1ASAmLGOMsbsTAIDOJk+erP379+uKK67Qf/3Xf+nNN9/U6NGjddNNN2natGn67LPPdPvtt6utrU2vvPKKJGn58uWyLEtnnHGGDh48qLvuuks7duxQbW2tUlJStGPHDhUWFqqgoEAPPvigzjnnHKWlpSk3N9fmbwsA3UOYBYAEtWfPHhUVFWnfvn2qrKxUTU2NXn/9df39738P1uzatUt5eXl67733NHz48E7X+OijjzRkyBC99dZbKioqCobZ+fPna/bs2b35dQAgLlhmAAAJasiQIfrRj36kESNG6Lvf/a42bdqkVatW6fjjjw8+TjvtNEkKLiXYtm2brrnmGn31q19VZmamCgsLJanTTWOjR4/u3S8DAHGSancHAABdS01NVWpq4F/V7e3tmjhxon75y192qsvJyZEkTZw4UXl5eVq8eLFyc3PV3t6uoqIitba2htRnZGTEv/MA0AsIswDgECNHjtTy5ctVUFAQDLiH27dvn9599109/vjjKi4uliStXbu2t7sJAL2KZQYA4BA333yzPv74Y1199dV64403tH37dr300ku6/vrr5ff79ZWvfEWDBg3SE088oa1bt+qVV17RnDlz7O42AMQVYRYAHCI3N1fr1q2T3+/Xt771LRUVFWn27Nlyu91KSUlRSkqKnnvuOW3atElFRUW69dZb9etf/9rubgNAXLGbAQAAAByLmVkAAAA4FmEWAAAAjkWYBQAAgGMRZgEAAOBYhFkAAAA4FmEWAAAAjkWYBQAAgGMRZgEAAOBYhFkAAAA4FmEWAAAAjkWYBQAAgGMRZgEAAOBY/w99KbzwXu7KKQAAAABJRU5ErkJggg==\n", - "text/plain": [ - "
" - ] - }, - "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": 10, - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "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": 11, - "metadata": { - "tags": [] - }, - "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": 12, - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "text/plain": [ - "[]" - ] - }, - "execution_count": 12, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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\n", 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" - ] - }, - "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": 13, - "metadata": { - "tags": [] - }, - "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": 14, - "metadata": { - "tags": [] - }, - "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": 15, - "metadata": { - "tags": [] - }, - "outputs": [ - { - "data": { - "image/png": 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\n", 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" - ] - }, - "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": 18, - "metadata": { - "tags": [] - }, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Mean absolute error: 0.03\n", - "Residual sum of squares (MSE): 0.00\n", - "R2-score: 0.95\n" - ] - } - ], - "source": [ - "# memisahkan data 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", - "# membangun model, menggunakan training\n", - "popt, pcov = curve_fit(sigmoid, train_x, train_y)\n", - "\n", - "# prediksi menggunakan testing\n", - "y_hat = sigmoid(test_x, *popt)\n", - "\n", - "# evaluasi\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))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "
Click here for the solution\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", - "
\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "

Want to learn more?

\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: SPSS Modeler\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 Watson Studio\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", - "Joseph Santarcangelo\n", - "\n", - "\n", - "##

© IBM Corporation 2020. All rights reserved.

\n", - "\n", - "\n", - "\n", - "\n", - "\n" - ] - } - ], - "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 -}