"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.scatter(cdf.ENGINESIZE, cdf.CO2EMISSIONS, color='blue')\n",
+ "plt.xlabel(\"Engine size\")\n",
+ "plt.ylabel(\"Emission\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Creating train and test dataset\n",
+ "Train/Test Split involves splitting the dataset into training and testing sets respectively, which are mutually exclusive. After which, you train with the training set and test with the testing set. \n",
+ "This will provide a more accurate evaluation on out-of-sample accuracy because the testing dataset is not part of the dataset that have been used to train the model. Therefore, it gives us a better understanding of how well our model generalizes on new data.\n",
+ "\n",
+ "We know the outcome of each data point in the testing dataset, making it great to test with! Since this data has not been used to train the model, the model has no knowledge of the outcome of these data points. So, in essence, it is truly an out-of-sample testing.\n",
+ "\n",
+ "Let's split our dataset into train and test sets. Around 80% of the entire dataset will be used for training and 20% for testing. We create a mask to select random rows using the __np.random.rand()__ function: \n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 16,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "msk = np.random.rand(len(df)) < 0.8\n",
+ "train = cdf[msk]\n",
+ "test = cdf[~msk]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Train data distribution\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "In reality, there are multiple variables that impact the co2emission. When more than one independent variable is present, the process is called multiple linear regression. An example of multiple linear regression is predicting co2emission using the features FUELCONSUMPTION_COMB, EngineSize and Cylinders of cars. The good thing here is that multiple linear regression model is the extension of the simple linear regression model.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Coefficients: [[11.0479666 7.14624226 9.58182024]]\n"
+ ]
+ }
+ ],
+ "source": [
+ "from sklearn import linear_model\n",
+ "regr = linear_model.LinearRegression()\n",
+ "x = np.asanyarray(train[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB']])\n",
+ "y = np.asanyarray(train[['CO2EMISSIONS']])\n",
+ "regr.fit (x, y)\n",
+ "# The coefficients\n",
+ "print ('Coefficients: ', regr.coef_)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As mentioned before, __Coefficient__ and __Intercept__ are the parameters of the fitted line. \n",
+ "Given that it is a multiple linear regression model with 3 parameters and that the parameters are the intercept and coefficients of the hyperplane, sklearn can estimate them from our data. Scikit-learn uses plain Ordinary Least Squares method to solve this problem.\n",
+ "\n",
+ "#### Ordinary Least Squares (OLS)\n",
+ "OLS is a method for estimating the unknown parameters in a linear regression model. OLS chooses the parameters of a linear function of a set of explanatory variables by minimizing the sum of the squares of the differences between the target dependent variable and those predicted by the linear function. In other words, it tries to minimizes the sum of squared errors (SSE) or mean squared error (MSE) between the target variable (y) and our predicted output ($\\hat{y}$) over all samples in the dataset.\n",
+ "\n",
+ "OLS can find the best parameters using of the following methods:\n",
+ "* Solving the model parameters analytically using closed-form equations\n",
+ "* Using an optimization algorithm (Gradient Descent, Stochastic Gradient Descent, Newton’s Method, etc.)\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "
Prediction
\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Mean Squared Error (MSE) : 599.96\n",
+ "Variance score: 0.86\n"
+ ]
+ }
+ ],
+ "source": [
+ "y_hat= regr.predict(test[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB']])\n",
+ "x = np.asanyarray(test[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_COMB']])\n",
+ "y = np.asanyarray(test[['CO2EMISSIONS']])\n",
+ "print(\"Mean Squared Error (MSE) : %.2f\"\n",
+ " % np.mean((y_hat - y) ** 2))\n",
+ "\n",
+ "# Explained variance score: 1 is perfect prediction\n",
+ "print('Variance score: %.2f' % regr.score(x, y))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "__Explained variance regression score:__ \n",
+ "Let $\\hat{y}$ be the estimated target output, y the corresponding (correct) target output, and Var be the Variance (the square of the standard deviation). Then the explained variance is estimated as follows:\n",
+ "\n",
+ "$\\texttt{explainedVariance}(y, \\hat{y}) = 1 - \\frac{Var\\{ y - \\hat{y}\\}}{Var\\{y\\}}$ \n",
+ "The best possible score is 1.0, the lower values are worse.\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "
Practice
\n",
+ "Try to use a multiple linear regression with the same dataset, but this time use FUELCONSUMPTION_CITY and FUELCONSUMPTION_HWY instead of FUELCONSUMPTION_COMB. Does it result in better accuracy?\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Coefficients: [[11.23160902 6.45598471 6.94570618 2.0883399 ]]\n",
+ "Residual sum of squares (MSE): 610.81\n",
+ "Variance score (R^2): 0.86\n"
+ ]
+ }
+ ],
+ "source": [
+ "from sklearn import linear_model\n",
+ "import numpy as np\n",
+ "\n",
+ "# Membuat model regresi linear\n",
+ "regr = linear_model.LinearRegression()\n",
+ "\n",
+ "# Menentukan fitur dan target\n",
+ "x = np.asanyarray(train[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_CITY','FUELCONSUMPTION_HWY']])\n",
+ "y = np.asanyarray(train[['CO2EMISSIONS']])\n",
+ "\n",
+ "# Melatih model\n",
+ "regr.fit(x, y)\n",
+ "\n",
+ "# Menampilkan koefisien\n",
+ "print('Coefficients: ', regr.coef_)\n",
+ "\n",
+ "# Memprediksi nilai CO2EMISSIONS pada data test\n",
+ "y_ = regr.predict(np.asanyarray(test[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_CITY','FUELCONSUMPTION_HWY']]))\n",
+ "\n",
+ "# Menghitung residual sum of squares dan variance score\n",
+ "x_test = np.asanyarray(test[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_CITY','FUELCONSUMPTION_HWY']])\n",
+ "y_test = np.asanyarray(test[['CO2EMISSIONS']])\n",
+ "print(\"Residual sum of squares (MSE): %.2f\" % np.mean((y_ - y_test) ** 2))\n",
+ "print('Variance score (R^2): %.2f' % regr.score(x_test, y_test))"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Click here for the solution\n",
+ "\n",
+ "```python\n",
+ "regr = linear_model.LinearRegression()\n",
+ "x = np.asanyarray(train[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_CITY','FUELCONSUMPTION_HWY']])\n",
+ "y = np.asanyarray(train[['CO2EMISSIONS']])\n",
+ "regr.fit (x, y)\n",
+ "print ('Coefficients: ', regr.coef_)\n",
+ "y_= regr.predict(test[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_CITY','FUELCONSUMPTION_HWY']])\n",
+ "x = np.asanyarray(test[['ENGINESIZE','CYLINDERS','FUELCONSUMPTION_CITY','FUELCONSUMPTION_HWY']])\n",
+ "y = np.asanyarray(test[['CO2EMISSIONS']])\n",
+ "print(\"Residual sum of squares: %.2f\"% np.mean((y_ - y) ** 2))\n",
+ "print('Variance score: %.2f' % regr.score(x, y))\n",
+ "\n",
+ "```\n",
+ "\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",
+ "\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": 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": {
+ "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 = 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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\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": 55,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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mp6++ynXsc+csKynJsmbPNtfnzvnjJxIRkUBYsMCcK/I6n9gvkZGO9+Pizp9j7Mf5gN6WBdYs7sj7XBRgnpy/g2rMTEpKCgCxsbEAJCcns3//fjp16pS1T1RUFO3bt2ft2rVOj5GWlkZqaqrDJRDsme2KFaZbyRmXU7UrVDg/TdvezJNNZCR06AC9e5trdS2JiISnvMp9uNo/O3t9s/nzzXGqW3u4hfkAvMwIIDxqlQVNMmNZFqNHj6ZNmzY0atQIgP379wNQtWpVh32rVq2a9VhOkyZNIiYmJusSHx/v28DzEBlpLkeOuN7H5VTt4cPN9ccfw59/+ixGEREJXvmV+8iPPVEZOtQc526mUZxzrKENP3CFw36hXKssaJKZYcOGsWnTJubMmZPrMVuOwSeWZeXaZjdmzBhSUlKyLrt37/ZJvO4q8FTtBg2gUyfzDnNSRE9ERMKfN2qHWRYcPAhRnOEuzHRse6tMTgsWhOYCxkGRzNx77718/PHHJCUlERcXl7W9WrVqALlaYQ4cOJCrtcYuKiqK6Ohoh0sgFWqq9oh/3mxvvw1BOuBZRER8x5u1w/owm8ocYie1WERPp/u89lpoLmAc0GTGsiyGDRtGYmIiX331FXXr1nV4vG7dulSrVo3ly5dnbUtPT2fVqlW0bt3a3+EWSKHqw3TpAhddZFbTfucdn8YpIiLBx51yH+6xuC/SjMH8L0PJoFiee4faAsYBTWaGDh3K+++/z+zZsylXrhz79+9n//79nP6nWJzNZmPkyJE8/fTTLFy4kF9++YX+/ftTunRp+vTpE8jQ3Vao+jAREVmVGXnlFVMZ2AVv1R8QEZHg4U65j/zYbHBL5VVcmrGJU5TibQbl+5yQGxTs66lVeQGcXmbOnJm1T2ZmpjVu3DirWrVqVlRUlNWuXTvr559/dvs1AjU1OydnU7Xj492YCpeaalnR0eYJS5a4fezs0/FERCS0uVPuI68SIHv+1dOywNre6S6Pj5OUFJif2ZPzt82y3J3wFZpSU1OJiYkhJSUl4ONnMjLMSPF9+0w/aNu2bk6rHj0aXnrJDAheutThocRE0xSY869oz+BVTE9EJDzkPIccOgSjRjnOdoqMdGxJiY+HN8ck02XYhaZ1f/NmMi5uyJo1ZrCvO/NLZs82pUD8zZPzt5KZUJCcDBf+80b85Re49FLAvGHr1HE9bc9mM32tycmqRSMiEo5yJjitW8PatTm+NN8/yoxnuO46WLYs67krV5rBvvlJSjI1zfxNyUw2YZHMANx0k2mGGTTILEJJ8L8RRUQkwFJSTPPM8ePw+edmYsk/7F+I9+xxXpQv0F+IPTl/B8XUbHHD6NHm+r334MABoBA1bEREpGiwl/Zo2BA6d3Z4KJwWMFYyEypat4YWLSAtDaZNAwpZw0ZERMLbuXPns5WRI51OhwqXBYzVzRRK5s41o7CqVIGdO8koXjKomwhFRCSA5s+H//wHKlWCXbugVCmXuxZ4gooPqZspXN10k+n7PHAAZs8OqyZCERHxshdfNNf33JNnIgOhv4CxkplQUrz4+SJ6L74IlhU2TYQiIuJF69bB+vVQooRJZsKckplQM3gwlCkDmzfDihWASVh27DCzlmbPNtfJyUpkRESKrJdeMtd9+4KLtQzDiZKZUFO+PAwcaG7bmxAJ/SZCERHxkh07TEU8MFX1igAlM6Fo+HAzKOaLL2DLlkBHIyIiwcS+lt+110LjxoGOxi+UzISievWgZ09zO1vrjIiIFHEpKTB9urldRFplQMlM6LrvPnP93nuwf39gYxERkeDw5pvni+Rlq/Yb7pTMhKqrroJWrSA93b2VwkREJLylp5+v13H//RBRdE7xRecnDUf332+up06FkycDG4uIiATWvHmmimq1atCnT6Cj8SslM6GsRw+zmvbRozBjRqCjERGRQLEseO45c3v4cIiKCmw8fqZkJpRFRp5fgPKll8w6HCIiUvQsXw4//2zqkA0ZEuho/E7JTKjr1w8qVjRV8hYudHgoIwNWroQ5c8x1RkZAIhQREV97/nlzPWgQVKjgk5cI5nOKkplQV7o0DB1qbj/3XNaKk4mJUKcOdOxouk47djT3ExMDFqmIiPjCjz+alpmICLM6tg8E+zlFyUw4GDoUSpaE776DNWtITISbb4a//nLcbc8esz1Y3nwiIuIFL7xgrm+5xWQYXhYK5xQlM+GgShXT3QRYzz3PiBFZDTQO7NtGjgyu5kERESmg3bth7lxz2z7D1YsyMgiJc4qSmXAxejTYbNg+/YRyf7le4sCyzHv/1VcD/+YTEZFCmjLFTP5o3x6aN/f64desyd0ik539nLJmjddf2iNKZsLFRRdlLXHwAM/lu/uoUcHV3ykiIh46etRU/AV46CGfvMS+fd7dz1eUzISTf97MffmAOHbnu3sw9XeKiIiHpk6FEyfgsst8tnRB9ere3c9XlMyEk5Ytsdq1pwRnGc1L+e4eTP2dIiLigdOnzy9d8OCDYLP55GXatoW4ONeHt9kgPt7sF0hKZsKM7WHTOjOYN4nlSL77B0t/p4iIeGDmTDh4EGrXhl69fPYykZHnc6acCY39/pQpZr9AUjITbrp0gcsuoywneTh6qttPC3R/p4iIuOncufNF8u67D4oV8+nLJSTARx9BzZqO2+PizPaEBJ++vFuUzIQbm800OQL3R73CK8+edutpge7vFBERN330kan6XrEiDBjgl5dMSIAdOyApCWbPNtfJycGRyICSmfDUqxfUqYPt4EGGlp4ZEv2dIiLiBsuCZ581t4cPN2sx+UlkJHToAL17m+tAdy1lp2QmHBUrZpoegYgXn+eVF80ClMHc3ykiIm5YvtwsX5B9KRtRMhO2BgyASpUgOZkbz80P+v5OERFxg71VZvBg080kANgsy1mR4vylp6eTnJxMvXr1KObjwUeFkZqaSkxMDCkpKURHRwc6HP+aOBHGjTM1CH78kYxMG2vWmMG+1aubriW1yIiIhIj//Q+uvNK0vm/fDrVqBToin/Lk/O1xy8ypU6cYOHAgpUuX5tJLL2XXrl0ADB8+nGeeeaZgEYtvDBsGZcvCpk3w2WdB3d8pIiL5mDTJXN92W9gnMp7yOJkZM2YMP/30EytXrqRkyZJZ26+99lrmzZvn1eCkkGJj4e67ze2nnnK+UpiIiAS/X36BxYvNYEcfLV0QyjxOZhYtWsRrr71GmzZtsGUbUdqwYUO2b9/u1eDEC0aNgqgoWLcOVq8OdDQiIlIQ9p6Pm26CSy4JbCxByONk5uDBg1SpUiXX9pMnTzokNxIkqlc/X4fg6afz3T0jA1auhDlzzLWWORARCbA//zQfygBjxgQ2liDlcTLTokULlixZknXfnsC89dZbtGrVynuRifc88IAZILNsGXz3ncND2ZOXiRPNStodO0KfPuZaK2uLiPhf9s/mvSOehcxMU+H9iisCHVpQ8nga0qRJk+jSpQtbtmzh3LlzvPzyy2zevJl169axatUqX8QohVW3rslO3nvPDCD7JztJTIQRI+Cvv1w/1b6ytqZwi4j4R/bP5hrs4U9mAbDqqkdoH9jQgpbHLTOtW7fmm2++4dSpU9SrV49ly5ZRtWpV1q1bR7NmzXwRo3jDww+b64ULYcsWEhNNkpJXIgNaWVtExJ9yfjaP5kWiSGcNbej4eFu1lLtQ4DozoSIc6sxkZOCd+jAJCbBwIZm33U7tle/mm8jklJRkpnSLiIj3ZWSYrn37Z3Msh9lFLcpwiq58xlJbV+LizJpIRaG0htfrzKSmprp9Ee9KTPTiOJZ/Bo7ZZs+m+F9/evx0rawtIuI7a9Y4tpaP4GXKcIofuJwv6IJlwe7dZj9x5NaYmfLly+c7U8myLGw2Gxnqi/Aae3NjzrazAo9jadECOnXCtmwZD/MMd/GmR/FoZW0REd/J/oUxmhSG8woAT/MIYHO6nxhuJTNJSUm+jkNyyMgwA8CcdQJalqmbNHIk9OjhYXPj2LGwbBn9mcWTPMZu8q8iabOZdZy0sraIiO9k/8J4L69SnhQ205AF3ORyPzE0ZiZIrVxpupTyU5BxLFaHjthWreS/DGUYr+W5r71BTrOZRER8yz5mJuWv4yRTh4ocoQ8fMIc+wPkvlhozk1uBVs0+evQozz//PAMHDmTQoEG88MILHDlypEDBinPuNiMWpLnR9vhYAAYynerkfQCtrC0i4h+RkfDyy3A306jIEX6nPvPoBZz/YjllStFIZDzlcTKzatUq6tSpwyuvvMLRo0c5cuQIr7zyCnXr1lWdGS9ytxmxQM2NHTvCVVdRkjQmlH3O4aG4OJgwAWbPNq0+yclKZERE/CWhyykmxLwAmLEymZjMRV8s8+ZxN1OjRo1o3bo106ZNI/Kf9DAjI4N77rmHb775hl9++cUngRZUqHYz2Zsb9+xxPm6m0M2NS5dCly5YpUqx9oMd7DpTxeW0b69NDRcRkbxNmQKjRmHVqcPqt35n78HiRfZz15Pzt8fJTKlSpfjxxx+5+OKLHbZv3bqVyy+/nNOnT3sesQ+FajID52czgWNC45VxLJYFLVua5Q0efBCefdZlDDmrBMfFmaZQfUMQEfGiM2fgggvMN8c33oD/+79ARxRQPh0zc8UVV/Drr7/m2v7rr79y+eWXe3o4yUNCgklYatZ03O6V5kabzcxsAvjvf+Hw4Vy7uKoSbJ8arkqUIiJeNGOGSWTi46Ffv0BHE1LcSmY2bdqUdRk+fDgjRozg+eef5+uvv+brr7/m+eefZ9SoUYwcOdKjF1+9ejXdunWjRo0a2Gw2Fi1a5PB4//79sdlsDpcrr7zSo9cIdQkJsGOHGb/i9XEsN9wAl18OJ0+aps1s8psaDlriQETEa9LTz7eQP/QQREUFNp4Q41Y3U0REBDabjfx29bRo3ueff84333zDFVdcwU033cTChQvp2bNn1uP9+/fn77//ZubMmVnbSpQoQWxsrNuvEcrdTH6RmAg33QTR0SZL+ud368up4SIiksMbb8CQIWZg4p9/QsmSgY4o4Dw5f7tVNC85OdkrgeXUtWtXunbtmuc+UVFRVKtWzSevL0DPnnDZZbBpE7z0EjzxBODbqeEiIpJNejo89ZS5/fDDSmQKwK1kpnbt2r6Ow6WVK1dSpUoVypcvT/v27XnqqaeoUqWKy/3T0tJIS0vLuq/1ovIREQHjx5t+q5dfhlGjIDbWt1PDRUTkvJkzzaJL1asX+UG/BeVWMuPMli1b2LVrF+np6Q7bu3fvXuig7Lp27cott9xC7dq1SU5OZuzYsVx99dVs3LiRKBf9iZMmTWLChAlei6FI6NEDmjSBn37Kap1p29YMNM5variWOBAR8Uz2chc1KqbR7qmnzMpLY8aoVaaAPJ6a/eeff3LjjTfy888/O4yjsS9EWdCFJm02W64xMznt27eP2rVrM3fuXBJcjIB11jITHx+vMTP5WbjQtM6UK2dGHMfG+nZquIhIEZSz3MVdvM7r3M3p2BqU2rNdyUw2Pp2aPWLECOrWrcvff/9N6dKl2bx5M6tXr6Z58+asXLmyoDG7pXr16tSuXZtt27a53CcqKoro6GiHi7ihZ08zs+n4cXjxRcDHU8NFRIqYnOUuSpDGo5ixMg8eGUPiZ0pkCsrjZGbdunVMnDiRypUrExERQUREBG3atGHSpEkMHz7cFzFmOXz4MLt376a6Bmp4n80G48aZ26+8klV3xqdTw0VEighn5S4GMIN4/uIvajKdQSp3UQgeJzMZGRmULVsWgEqVKrF3717ADBLeunWrR8c6ceIEP/74Iz/++CNgZk39+OOP7Nq1ixMnTnD//fezbt06duzYwcqVK+nWrRuVKlXixhtv9DRscUePHrlaZ8CU0O7QAXr3NtdFraS2iEhhrVnjWIC0BGk8wtMATGIMZyjJ7t1mP/Gcx8lMo0aN2LRpEwAtW7Zk8uTJfPPNN0ycOJELLrjAo2Nt2LCBpk2b0rRpUwBGjx5N06ZNefzxx4mMjOTnn3+mR48eXHTRRfTr14+LLrqIdevWUa5cOU/DFnfYbGZmEzi0zoiISOHkLGMxkLcdWmVc7Sfu8Xg202OPPcbJkycBePLJJ7nhhhto27YtFStWZN68eR4dq0OHDnkW4lu6dKmn4Ulhde8OTZvCDz/Ac8/BM88EOiIRkZCXfXRESU5njZV5mkdIJ8rpfuI+j2czOXPkyBEqVKiQNaMpmKgCcAF8+il06walSplKlCpaKCJSKBkZUKeOKXcxwnqJlxjNTmpxEb+TTlRWuYvkZHXl2/l0NpMzsbGxQZnISAFdf71ZUfv0abXMiIh4QWSkqUtaxjrBGCYBMJHHsxIZMEvkKZEpGLdaZhISEpg1axbR0dEu67vYJQbZUspqmSmgFSvguuugRAn44w+ziquIiBTKL7dNotEHj7CNC2nIFs5RnPh4k8holqgjr6/NFBMTk9XyEhMTU/gIJfhdcw20bw+rVpk1Q15/PdARiYgEvezVfatXN1XSs1pbUlJo9NlzAJx9ZDzvNiqeex8pEI/GzFiWxa5du6hcuTKlS5f2ZVxeo5aZQlizBtq1g2LF4PffoW5dl7vm+Q8sIlIE5KzuC2YczMsv/9PqMn48TJgADRuaxX31IZknn42ZsSyL+vXrs2fPnkIFKCGibVvo1AnOnYOJE13ulphoBrZ17Ah9+pjrOnXMdhGRoiBndV+7PXvM9k/fOXy+fteECUpkvMyjZCYiIoL69etzWPVHio4nnjDX774LTooi5vcPrIRGRMKds+q+dvZtu+59zhQkvfxyDY7xAY9nM02ePJkHHniAX375xRfxSLD5179M7ZnMzPPLHfzDnX9glecWkXCXs7pvTlWs/fQ7/qq588QTEOGVicSSjce/0dtuu41vv/2WJk2aUKpUKWJjYx0uEobsXUzz5sE/S09A/v/AloXKc4tI2Muvau+jPEUZTnHowpam9IV4nccVgKdMmeKDMCSoNWliFmaaMwceeQQ++wxwv+y2ynOLSLjKyIC//3b9eB2SuYs3APjrnklUUk02n/A4menXr58v4pBgN3EizJ8Pn38Oq1dDu3Zul91WeW4RCUfOZi/lNIFxlOAsq6Ou46rhHf0XXBFTqI6706dPk5qa6nCRMHXhhTDon8XQxowBy6JtWzPt0NUXDZvN1Npr29Z/YYqI+IOryQ/ZNeJnbuN9AM5NfFoTmHzI42Tm5MmTDBs2jCpVqlC2bFkqVKjgcJEwNnasWa9p7VpYsiSrPDfkTmhUnltEwlVekx+ye5LHiMDir1Y3c/WDzfM95sqVpjd/5UpNnPCUx8nMgw8+yFdffcXUqVOJiopi+vTpTJgwgRo1avDuu+/6IkYJFjVqwPDhAJwYPoa5H2QQGwsffgg1azruGhcHH32kGYgiEn7ym/wAcCXr6MHHWBERxM14Is99Vaur8DweM/PJJ5/w7rvv0qFDBwYMGEDbtm258MILqV27Nh988AF9+/b1RZwSJD5p+BDtbK8Tk/wLn942hw+4jbg4UwuqcmVVABaR8Jf/pAaLSYwBwNa/P1xyics97d1VOVt57LW69KXQPR63zBw5coS6/5S1j46O5siRIwC0adOG1atXezc6CSqJidCjfwWesR4CzIqvxUlnzx7o1QuOHDGTnjp0UCIjIuErv0kNnVhGB1aRWTwqV32u7FSry3s8TmYuuOACduzYAUDDhg358MMPAdNiU758eW/GJkEk+z/dKwxnP1W5gGT+jzf1TyciRUpekx9sZGa1ynDPPVCrlsvjqFaX93iczNx555389NNPAIwZMyZr7MyoUaN44IEHvB6gBIfs/3SnKMMEzLeNx5lIOVL1TyciRUZekx/6MIcr+IGzpaOJeHRMnsdRrS7vcXvMzMiRIxk0aBCjRo3K2taxY0d+++03NmzYQL169WjSpIlPgpTAy/nPNJ1BjGQKF/M79/M845josJ+7q2hrtW0RCUUJCWY8S/Y6MyVIY1Lko5ABxR99yAwkzINqdXmPzbLym1xmXHLJJWzbto1mzZoxaNAgbr311nyX5A4GniwhLq6tXGlG2GeXwAIWcDMnKc2F/MF+qpOUZMbO5CwkFRdnvslkH8jmrOCUs/1ERIJV9i9kLda8yIXT7jMzP7dtg9Kl831unTpmsK+zM7HNZj4Tk5OL5pc8T87fbncz/fbbb6xevZrGjRtz//33U6NGDe644w4N+i0inPURJ5LAOq6kDKcYzwTi4+HQIfdW0dZq2yISDiIjzaSH3l2PceG8p8zGiRPzTWTsz1WtLu/waMzMVVddxdtvv83+/ft59dVX2bFjBx06dKB+/fo888wz7N2711dxSoA5/6ez8SCTARjIdN4c/RujRrkemW9ZMGQIvPeeuS7oCH4VlxKRoPPMM6ZZumFD8GDZH3t3lWp1FY7b3UyubN++nRkzZjBt2jROnDhBenq6t2LzCnUzeZezrqGlJXvQ6czHHGzTkypfL/TaayUlmW88+b2+uqZEJKB274b69SEtDT7+GLp18/gQGj+Ymyfnb4+L5mV38uRJVq1axapVqzh27BgXX3xxYQ4nISAhAXr0yPFPV3ESXP4plb9eRGu+YS1XeeW1cg46VnEpEQlKjz9uEpl27eCGGwp0CHt3lRRMgRaaXL16NXfeeSfVqlVjxIgRXHTRRaxZs4Zff/3V2/FJEMrqI7YXyGvcEAYMAGAyDwKFauzLkn0Ev4pLiUhQ+vlneOcdc3vyZNcr74pPuZ3M/PXXXzz11FPUr1+fDh068Ntvv/HSSy+xb98+ZsyYwVVXeefbuISoCROwSpfmKtZyMwsKdShnq22ruJSIBKX77zcfQDffDC1bBjqaIsvtbqY6depQsWJFbr/9dgYOHEiDBg18GZeEmho1sN1/P0ycyDM8xCd0I40ojw/jagS/ikuJSND54gtYtgyKFzcDgF3QeBjfc7tl5sMPP2TPnj08//zzSmTEuQcegOrVqcefPBrzWoEO4WoEv4pLiUhQOXcO7rvP3L73XqhXz+luWhHbPwo9mynYaTaTn82YAQMHYpUvzzez/mDniYqMGmXqz7h6p1WuDC+9ZKYm5lUpWMWlRCRovPGGqTERGwt//AEVKuTaxdWkBXsLtCYt5M0nRfNE3NKvH1x2GbZjx2jz1UT69oXXXzcPOSsKZbOZx/v2zXu1bRWXEpGgkZpqZjCBWRXbSSKjSQv+pWRGvCsyEl54wdyeOhV+/91rRaFUXEpEgsKzz8KBA6a2zJAhTnfRpAX/KlSdGRGnrr0Wrr8eliyBBx+ERYuc16cpwCA4bx1HRKRAdu2CF180tydPhhIlnO6mSQv+5XHLzIABAzh+/Hiu7SdPnmTAP7VGRHjuOZNhLF5s1hzASX2aAiYg3jqOiIjHHnkEzpyB9u3NNysXNGnBvzweABwZGcm+ffuoUqWKw/ZDhw5RrVo1zp0759UAC0sDgANo6FDT1dSkCWzcqKxDRELb+vXQqpW5vWEDNGvmcldNWig8nwwATk1NJSUlBcuyOH78OKmpqVmXo0eP8tlnn+VKcKSImzABypeHn34ys5xEREJVZqYZ0Qtw5515JjKgSQv+5nYyU758eWJjY7HZbFx00UVUqFAh61KpUiUGDBjA0KFDfRmrhJpKlWD8eHP70Ufh2LFARiMi4lJGhukRnzPHXOeaZfT++/Dtt1C2LDz9tFvH1KQF/3G7m2nVqlVYlsXVV1/NggULiI2NzXqsRIkS1K5dmxo1avgs0IJSN1OAnT0Ll10Gv/0Go0efn+kUAKrCKSLOJCaaRpfss4/i4kzLSkICcOIEXHSR+fB45hl46CGPjq/PnoLx5Pzt8ZiZnTt3Eh8fT0REaMzqVjITBL74Arp2hWLF4JdfIACrq+f7YSUiRZJbhe02PmpaY+rVg82bIcrzpVrEcz5NZgCOHTvGt99+y4EDB8jMzHR47I477vD0cD6lZCZI3HCDmap9/fXw6ad+fWlV4RQRZ+yDdF3Vg7HZoFW1ZL4+0gBbWhosXAg9e/ozxCLNp8nMJ598Qt++fTl58iTlypXDlm1kk81m48iRIwWL2keUzASJrVuhUSOznsnnn0OXLn55WXc+rDSjQKRoWrnSrJWUl/nczM0sgGuugeXLc4/mFZ/x6XIG9913X1atmWPHjnH06NGsS7AlMhJELr4Yhg83t0eNgvR0v7ysqnCKiCv5Faxrz0puZgGZtggz9UiJTNDyOJnZs2cPw4cPp3Tp0r6IR8LZ2LFmVcnffoNXX/XLS6oKp4i4klfBumKc5VXuBWBf9yGmZVmClsfJTOfOndmwYYMvYpFwV768mQkAZsq2HzIIVeEUEVfatjXdzM4aXO5hKo35hSMRFan21hP+D0484vHaTNdffz0PPPAAW7ZsoXHjxhQvXtzh8e7du3stOAlD/fvDG2+Yeg0PPgjvvefTl7N/WOVXhbNtW5+GISJByF7Y7uabzWeB/TOiCn8zEbMq9o7/m8QVlWPzOIoEA48HAOc1Jdtms5ERZOuZawBwEPruO2jZ0nxyrF7t80zCPpsJHBMazWYSEchdumEm/enPOxyt15wKW9drdkCA+HQAcGZmpstLsCUyEqRatIBBg8ztYcPMDCcfUhVOkfCVb+VeNyQkwI4dkJQEy8avpT/vAFDhg9eUyISIAtWZsTtz5gwlS5b0Zjxep5aZIHXokKmoefQovPaaWZTSx1SFUyS8eL0YZkaG+bL1ww8wYAC8/bbXYhXP+bRlJiMjgyeeeIKaNWtStmxZ/vzzTwDGjh3L2/rDi7sqVYInnzS3H3sMDh70+UtGRkKHDtC7t7lWIiMSuuzdxzlLL+zZY7YnJhbgoG+9ZRKZmBiYNCnXw95oBRLf8DiZeeqpp5g1axaTJ0+mRIkSWdsbN27M9OnTPTrW6tWr6datGzVq1MBms7Fo0SKHxy3LYvz48dSoUYNSpUrRoUMHNm/e7GnIEqzuugsuv9wsQOnhWiciUnRlZJgWGWf9CvZtI0d6mGwcPAiPPGJuP/EEVKni8HBioinA2bEj9OljruvUKWDSJF7ncTLz7rvv8uabb9K3b18is321veyyy/jtt988OtbJkydp0qQJr732mtPHJ0+ezIsvvshrr73Gd999R7Vq1bjuuus4fvy4p2FLMIqMhP/+19yeORO++Saw8YhISPBJMcwHHzTd3k2awN13Ozzkk1Yg8aoCFc278MILc23PzMzk7NmzHh2ra9euPPnkkyQ46dy0LIspU6bw6KOPkpCQQKNGjXjnnXc4deoUs2fP9jRsCVatW8PAgeb2kCFmlW0RkTwUthhmru6ilWtg1izz4LRpZlHcbPt6vRVIvM7jZObSSy9ljZN0d/78+TRt2tQrQQEkJyezf/9+OnXqlLUtKiqK9u3bs3btWpfPS0tLIzU11eEiQe7ZZ6FiRbOi9ssvBzoaEQlyhSmGmbO76LqOZ/njun9aYgYPhlatHPbXkiihweOieePGjeP2229nz549ZGZmkpiYyNatW3n33Xf51IurIe/fvx+AqlWrOmyvWrUqO3fudPm8SZMmMWHCBK/FIX5QsSJMnmxaaMaPh169ID4+0FGJSJAqaDFMe3dR9ueM4iUuPreZg1Ri/VXP0C3HsbQkSmjwuGWmW7duzJs3j88++wybzcbjjz/Or7/+yieffMJ1113n9QBtOepMW5aVa1t2Y8aMISUlJeuye/dur8ckPtC/P1x1FZw8adp0RURcsFfuhdxLEdjvT5niOGPRWXdRLXYyDvPl90GeY+jY2FzdRVoSJTR4nMyAWZ9p1apVnDhxglOnTvH11187dAd5Q7Vq1YDzLTR2Bw4cyNVak11UVBTR0dEOFwkBERGmrzoyEhYuhCVLAh2RiAQxT4thOusuepkRlOEUq2nLLPo57S7Ka/0mMNvj47UkSqAVKJnxh7p161KtWjWWL1+etS09PZ1Vq1bRunXrAEYmPtO4MYwaZW4PGwanTgU2HhEJatkr986eba6Tk50XzMvZDXQDn9CTxZylGHczDbA53a8grUDif26NmalQoUKeXTvZHTlyxO0XP3HiBH/88UfW/eTkZH788UdiY2OpVasWI0eO5Omnn6Z+/frUr1+fp59+mtKlS9OnTx+3X0NCzLhxMG+e+YSaMMEMDhYRccFeDDM/2buBynKc/2Kqjr/IaLZwqdP97OytQM6qDU+ZoiVRgoFbyxm88847WbcPHz7Mk08+SefOnWn1z6jvdevWsXTpUsaOHcso+zdrN6xcuZKOHTvm2t6vXz9mzZqFZVlMmDCBN954g6NHj9KyZUv++9//0qhRI7dfQ8sZhKBPPoHu3c2n1IYNprCeiEghZGSYWUx79sCL1khG8jJ/UpfG/MwpymQNGk5Odt3KoiVR/MuT87fHazPddNNNdOzYkWHDhjlsf+2111ixYkWuKr6BpmQmtNg/LC546BZqffsRVvPm2Nbnv2qtPmREJD+JifDsTd+yjiuJwKIzX7CMzlndRVp4Nrj4dG2mpUuX0qVLl1zbO3fuzIoVKzw9nEiW7PUfWn77CseIwbZhAz8Ndl4h2tnzVGZcRFxJ6HaWpXX+jwgs3qcvy+gMuB40LKHD42SmYsWKLFy4MNf2RYsWUbFiRa8EJUVPznLh+6nOQ5jxMvVmPsrnb+xy63l2KjMuIrm89BLld/yEFRtL3cQX8x00LKHD426mWbNmMXDgQLp06ZI1Zmb9+vV88cUXTJ8+nf79+/sizgJTN1Pws/dl50xIbGSyiva05Wu+LHk9HY5/QmQxW77Py3q+G33gIlJEbN9uZkyePm2WLujXL9ARST582s3Uv39/1q5dS/ny5UlMTGTBggXExMTwzTffBF0iI6HBVblwiwj+jzdJpzjXnFnCb0/Md+t5Wc9XmXERAfNhcPfdJpG5+mq4445ARyRe5vFyBgAtW7bkgw8+8HYsUkTlVQb8NxrwNI8wngnUm3IvDL/GLH+Qz/PcPb6IFAHvvAPLl0NUFLz+uusKeBKyCpTMZGZm8scff3DgwAEyMzMdHmvXrp1XApOiI78y4JMYwy3M59LULWZ52vfec+t57h5fRMLYvn3ni3FOnAj16wc2HvEJj8fMrF+/nj59+rBz505yPtVms5ERZOuga8xM8Mte/8HVonE3VP4fiw+1xpaZCZ9+Ctdf79bzNGZGpAizLLjxRli8GJo1g/XroViBvsNLAPh0zMyQIUNo3rw5v/zyC0eOHOHo0aNZF0+q/4rYuVMuvP+0ltjs367uugtSUlRmXETy9uGHJpEpXhxmzlQiE8Y8Tma2bdvG008/TYMGDShfvjwxMTEOF5GCyGvRuHnzIDYWPmw0kVM1LzRNMQ8+mO/zVDdCpAg7eBDuvdfcfuQRM5NJwpbH3UxXX301Dz74oNPCecFI3UyhJWcl30OHTHe3fdZSW1azmvbmzooVcM01Tp+nCsAiRVyfPjBnDjRqBBs3QokSgY5IPOTJ+dvjNrd7772X++67j/3799O4cWOKFy/u8Phll13m6SFFsmRfNC4xEf7zH8fxMGtox1Tu4R6mcrLPYMps3wRly7q92JyIhC63v7R8/LFJZCIiYMYMJTJFgMctMxERuXumbDYblmVpALB4TV4F8cpynF9oRG12kXnPUCL+m/dyByIS+hITna9a/fLLObqTDx82rTH798MDD8DkyX6PVbzDpwtN7ty5M8/Ha9eu7cnhfE7JTGhaudKsseTKNaxgBdeZO9m6m0Qk/NiXLcl5tnK6QGTv3jB3LjRoAN9/DyVLFvh11X0dWD5NZkKNkpnQNGeO6fLOy2sMZShToVYt2LQJNABdJOx4tGxJ4nzTNx0ZCevWQYsWBX5dt1uCxGd8OjUb4L333uOqq66iRo0aWS01U6ZMYfHixQU5nEgu7hS6e4hnOV2jHuzaBaNH+z4oEfE7d5ctWb/4b7NkAcCYMYVOZLSAbWjxOJmZNm0ao0eP5t///jfHjh3LGiNTvnx5pkyZ4u34pIhq29Z8C3JVddxmg9j4spSYPcvcmTEDlizxa4wiRU1GhukCnjPHXPtjiKR7y5FY1Jo0xIyXadIExo4t8OtlZJgWGWd9FvZtI0f652cX93mczLz66qu89dZbPProo0Rm6zxs3rw5P//8s1eDk6LL7YJ47ducb5UZNAhUuFHEJxITTXdPx46mC7hjR3Pfl60UGRnw99/573cb7xO/YZEpjvfuu4WavaQFbEOTx8lMcnIyTZs2zbU9KiqKkydPeiUoEfCgIN4TT8All5jZC8OGeT2OQHwbFQkmgeh2sSdP9sLfrsTxF6/Zhps748dDIcuDaAHb0ORxMlO3bl1+/PHHXNs///xzGjZs6I2YRLIkJMCOHZCUBLNnm+vk5BwD8EqVMqviRkaajGP2bK+9fiC+jYoEk0B0u7hKnnKKIJNZ9CPGOgb/+ldWZfDC0AK2Icry0IwZM6yaNWtac+fOtcqUKWPNmTPHevLJJ7NuB5uUlBQLsFJSUgIdivja+PGWBZYVE2NZO3cW+nALFliWzWYOmf1is5nLggWFD1kk2CUl5f4fcHZJSvLO6507Z1lxce695oTyL5gbpUtb1u+/e/X1nf3v2///4+PNfuJbnpy/PU5mLMuy3nzzTatWrVqWzWazbDabFRcXZ02fPr0gh/I5JTNFyNmzltWypfnE6dDBsjIyCnyo/D5Q9YEmRcXs2e4lFrNne+f13E2e3n1gk5VZooS588Yb3nnxf9i/yORMaPRFxr88OX8XaGr24MGD2blzJwcOHGD//v3s3r2bgQMHerPBSMRzxYrB++9DmTJmcMuLLxb4UBoEKGL4u9vFnbEoUZyh29y+2NLT4YYbYPBg77z4P7SAbegp8HroBw4cYOvWrdhsNmw2G5UrV/ZmXCIFc+GFZhrUoEFmpdzrrjNTNT2kQYAihr1Mwp49zsfN2IvWtW3rnddzJyl6ikcpv/tnqFIF3n7bdQ2HfxSkkm9CAvTooQrAocLjlpnU1FRuv/12atSoQfv27WnXrh01atTgtttuIyUlxRcxinhmwADo2RPOnoW+feH0aY8PoUGAIobbZRK8dJLPr8bUNXzJffzT6vr22yahyUNhBvHbF7Dt3dtcK5EJXh4nM4MGDeJ///sfS5Ys4dixY6SkpPDpp5+yYcMGBnu5qU+kQGw2ePNNqFoVNm82i815yJ2iffHx3vs2KhLM/NntklfyVIlDvMMd5s5dd5kupjyokm/R4fHaTGXKlGHp0qW0adPGYfuaNWvo0qVL0NWa0dpMRdgXX0DXrub2okWmzdgD9g9CcGxed7q4nUgR4M+FF3OvjWSxvGR3rj3zqakrtWGDGR+XR6xur+mkFpeg5NO1mSpWrEiMkwX9YmJiqFChgqeHE/GdLl3gvvvM7QED8i9akYMGAYo48me3S84aU78Pe9UkMiVKmFWx80hkQIP4ixqPk5nHHnuM0aNHsy/byMf9+/fzwAMPMLYQ62GI+MTTT0OzZmaZg759Pa7s5VbRPhHxiazkqcGP1H/zn+7i5593a1C/BvEXLR53MzVt2pQ//viDtLQ0atWqBcCuXbuIioqifv36Dvt+//333ou0gNTNJPzxBzRtCidOmHLn48YFOiIRcdfJk+YLydat0L276TLOZ/YSmOoMHTvmf/ikJJMwSfDx5Pzt8dTsnj17FjQukcC48EKYNg1uvx0mToSrr9bIXZFQMXy4SWRq1oQZM9xKZMD/U8olsDxumQk1apmRLP36mRV14+Lghx+gUqVARyQieZk923QP22zw1VceN6FoEH9o8+kAYIBjx44xffp0xowZw5EjRwDTpbRnz56CHE7EP157DS66yIwKvP12yMwMdEQi4sqvv8L//Z+5PXZsgfqCNIi/6PC4ZWbTpk1ce+21xMTEsGPHDrZu3coFF1zA2LFj2blzJ++++66vYi0QtcyIg02boGVLOHPGDA4eMybQEYlITidPmv/TzZtNt/CyZYWaOuXPKeXiPT5tmRk9ejT9+/dn27ZtlCxZMmt7165dWb16tefRivjTZZeZFhqAxx6DVasCG4+I5DZsmElkqlUzXU2FzDxUyTf8eZzMfPfdd9x11125ttesWZP9+/d7JSgRnxowAO64w3Qz3Xor/P13oCMSEbuZM2HWLIiIgDlzTCVvkXx4nMyULFmS1NTUXNu3bt2qxSYlNNhsMHUqNGwI+/cXqP6MiPjApk1wzz3m9hNPaM60uM3jZKZHjx5MnDiRs2fPAmCz2di1axcPP/wwN910k9cDFPGJMmXMCMDSpeHLL039GRHxiYwMU/dlzhxz7fS7Q0oK3HKLGc/WpQs8/LCfo5RQ5nEy8/zzz3Pw4EGqVKnC6dOnad++PRdeeCHlypXjqaee8kWMIr7RoAG89Za5/eST8PHHgY1HJAy5tWp1ZqYpnfD772YF1/feM91MIm4qcJ2Zr776iu+//57MzEyuuOIKrr32Wm/H5hWazST5GjECXnkFoqPhu+/M9G0RKTR7nZecZ5lcdV6eesoMyI+Kgq+/hubN/R6rBB9Pzt8qmidy9ixcc42Zu9mwIfzvf1C2bKCjEglpbq9aPe0LIrv922Q8b79tBuiL4MOp2ZmZmcyYMYMbbriBRo0a0bhxY7p37867775LmOdEEs6KF4cPPzQFKLZsMR+mej+LFIo7q1YX2/0nmb37mDv/939KZKTA3E5mLMuie/fuDBo0iD179tC4cWMuvfRSdu7cSf/+/bnxxht9GaeIb1WrBgsWmMRm/nyzMq+IFFh+q1GX4hSJJFD8+FH4179MV69IAbmdzMyaNYvVq1fz5Zdf8sMPPzBnzhzmzp3LTz/9xIoVK/jqq6+CrvqviEdatYKXXza3H37YVB0VkQKpXj2vRy3eZiCX8xPp5SubLxJRUf4KTcKQ28nMnDlzeOSRR+joZE31q6++mocffpgPPvjAq8GJ+N2QIaapOzMTevUysytExGP2VaudLXL9MM/Qm7mcpRiRC+abHUUKwe1kZtOmTXTp0sXl4127duWnn37ySlAiAWMvqNe6NRw7Bt27m2sR8Uhk5PmGzuwJTTc+5ikeBeCXu14j8ur2AYhOwo3bycyRI0eomkdZ6apVq3L06FGvBCUSUFFRZk5pXBxs3WoWdFGFYBGP5Vy1+lJ+4QP6EoHF9i5Dafp67qVxCsutAn0SdtxOZjIyMihWrJjLxyMjIzl37pxXghLxhzw/9KpWNUX0SpWCL76Ahx4KUJQioS0hAXbsgDWLDrO+cnfKcQKrQ0fqffyS11/LrQJ9EpbcrjMTERFB165diXIxSCstLY0vvviCjCBLg1VnpmjKyDBTQ/ftMwMR27Z1XCk3MdHUyss+dTQuzjSLJyRkO9D8+fCf/5jbM2bAnXf6JX6RsJKebpYoSEqCCy6Ab7+FihW9+hJuF+iTkOGTonl3uvkhPnPmTLf2c8f48eOZMGGCw7aqVat6tDq3kpmiJ79ExeMPvccfN4veFS8OS5ear3s55EyeWreGtWtdJ1MiRYZlwcCBZjXssmVh/Xq49FKvvoTbBfqS9X8YSjw5f7vuN8rBm0mKJy699FJWrFiRdT9S70TJg6tEZc8es33ePBg92nlNPMsyH3ojR0KPHtk+9MaPN7Oa5s0zWc66dXDJJQ6vmTN5iox07LZy2uojUhRMmmQSmYgIU5zSy4kMuFegb/dus58W4g5PQb+SV7FixahWrVrWpXLlyoEOSYJURoZJKlwlKgBDh7r/oZclIsJ8GLdqZWY2/fvfcPAgcD55ynnMnL2t9mRKffdSpMydC4+amUu89hp07eqTl8mvQJ+n+0noCfpkZtu2bdSoUYO6dety66238ueff+a5f1paGqmpqQ4XKRrc+Xb2Tw6Sr1wfeqVKweLFpr8/ORl69CDj5BmXyZOz1wbT6hNkw8pEfOObb6B/f3N79Gi4+26fvVTeBfo8309CT1AnMy1btuTdd99l6dKlvPXWW+zfv5/WrVtz+PBhl8+ZNGkSMTExWZf4+Hg/RiyB5M1vXU4/9CpXhiVLoHx5WLeOwzf0Y89fmW4f02mrj0g42r4devaEtDRzPXmyT18urwJ9YLbHx5v9JDwFdTLTtWtXbrrpJho3bsy1117LkiVLAHjnnXdcPmfMmDGkpKRkXXbv3u2vcCXA3P3WVblyIT70LrnE9BUVK0aVlR8ymQc9jlNN3RLWDhyAzp3h0CFo1gzef9/pqFtv1oNxVaAv+/0pUzT4N5wFdTKTU5kyZWjcuDHbtm1zuU9UVBTR0dEOFyka3P12NnXq+fs5Hwc3PvQ6djRjaID7eYHRvOBRnGrqlrB14oQZU7Z9u5le9MknUKZMrt18UQ8mZ4E+u7g4TcsuCkIqmUlLS+PXX3+lus4G4oS7385uvtkLH3q33UbmM6bp/AXupw/5r0umpm4Ja+npcNNNsHEjVKpkyhg4+ax2NWjeG4Pk7QX6kpJg9mxznZysRKYocLvOTCDcf//9dOvWjVq1anHgwAGefPJJVq1axc8//0zt2rXdOobqzBQ9zqZKx8ebRCb7h1p+hfXyZVls6z6a+p9O4SzFuJ4lLKeT013dLdxV6JhEAiEzE/r1M11KpUubLOJf/8q1m+rBiCd8UmcmEP766y969+7NoUOHqFy5MldeeSXr1693O5GRoikhwdSJyS8piIwsZM0Jm436i19gd7t9xH8zjwXcRAdW8j3NnNaZyZlM5eR2VWKRYDNmzPmxMR995DSRAdWDEd8J6mRm7ty5gQ5BQlShExV3RUQQ/+U7WF0PUi7pK74p14VNr67m8t4NPKoAnF+xP/X5S9B69tnzs5XefjvPWjKqByO+EtTJjEhIiIrCtmghXH01JTdu5F+PXgftv6ZDhzpuPd2dYn+DB0NMjEnQ1PwuQWPaNHj4YXN78mTT1YTr7lLVgxFfCakBwCJBKzrarK7dsKFpTrn2Wre/XubX9A5w5Ig5pFYAFm9OaS6U9983JbXBVPl94AEg75lKqgcjvqJkRsRbKlWC5cuhbl0zNfW66yCPAo92njSpa1mEos0XU5oLZNEiU93XsuDee81CrOQ/U2nxYtWDEd9QMiPiTTVqwIoV5nrzZjN+IJ8lNTxpUteyCMHHXy0lvpzS7JEVK6BXL/OD9utnsg+bza3uUvsirqoHI94W1FOzvUFTs8UTXpsavWULtGtnWmZatTI1N8qVc/madeqYk5In/41JSZrx4W2e/v39NQPNF1OaC/Re/+oruP56OHPG/IDz5kExM/Ry5UrTUpQf+/s25+u3bo1Hg+Yl/Hl0/rbCXEpKigVYKSkpgQ5FgtyCBZYVF2dZJqUwl7g4s71Avv/esipUMAe66irLSk3N87VtNnPJ/vp5XWbPLmBc4pSnf3/73yzn38X+dyzw+8aJpCT33hNJSe4dr0Dv9aQkyypVyuz8739b1pkzDg/Pnl3w963X//ckLHhy/lYyI2L58MS0YYNllS9vDta2rWUdP55nDDk/0L1x4pL8efr3P3cu77+VzWZZ8fFmP28oTKJQ2J/VsizLWrXKskqXNjt27WpZp0/n2qWgCZc/k0IJLZ6cv9XNJEWez6uSbthgpiKlpJiup88+c7pejT2WlSvhP/8xM5h8Eo8HikJF4oL8/T3tUiksb71egd7ra9aYsV8nT5oFJBctgpIlXR7bVXeps2OrIrDkxZPztwYAS5HnSVXSAmneHJYtw4qOhtWr+bvF9az57LjTgaKRkXDNNfDWW+aD3N8zPrIPZp04MUhmzvhYQf7+/i7+5q0pzR7/rKtWmYUjT540s/NcJDJQsJWrff6/J0WGkhkp8vxxYkr861/0iFpKCtFU/XUVxa7vRJNaR10mBoFYATjntN9x44Jg5owfFOTv7+/ibwVJFJzx6GddutS0yJw4YVoWFy92mcjYefq+VUVg8RYlM1Lk+frEZJ9S+8nBK7mGLzlMLK1Yz3t7r2bITQfzTGj8tQKwq2m/OYXj1PCC/P0DUfzNGwmuuz9ro+2LoXt3OH3azF765BMoVcrtON1936oisHiLxsxIkVeQvn5Pj509SWjEz6zgWqpygM00pF+NFfxvV/WAjQnIb9yCK+EyNbygf397AgiOz3N3hfTCxFvQcUzu/Kx3x87ltWO3YcvIMD/gBx9AiRJe/Rk8iUdjZooujZkR8YC3mvCdcTYm4Bca047V/EVNLmULc/e25bv5O9w+preKtNmPM36854kMhE/Tf0H//oHoCoTzi6j27u35Wl15/awAd1pv8+rhPtgyMsi87XbzJvNRIpNfPKoILB7x8cyqgNPUbHGXs6nR8fGFmxqa15TaOvxpbaeuZYF1snx1y/rppwLFWJB6HJ5OAy8KU8ML+vc/d878LmbPNtfemo7tS7l/1kzrEdvTWRumcZcVXzPDb9OiffG/J6FPU7OzUTeTeMLbU5Hzm1Jbnb18QRcu42ezLPbixdC+vdN97d0aOf9jPe3WcHUcd4Vz039RmIpuZ/9ZP16USe2XRzGCVwB4hocYwyRs/7yx/LXEQFH63Yt7PDl/K5kR8SF3xgQ0rHGMn+t2x/b1GoiKMqMmc5w9vFWPo6DjY7K/DmgNnXCRcSqNTyv1p8fpuQCM5CVeZmTW4+GcuErw05gZkSDhzpiAia+Ux7ZsqVmBLy0NbrkFXn/dYV9v1OPIyIBXXy14IgPmxDZvHsTG+n5hRfGx1FRS2t1Aj9NzSac4ffjAIZEB1XmR0FEs0AGIhDv7QFFnCxJOmWJv4ShldrrnHlMx7+67Yft2ePZZiIgodD0OZwsiuiMuDgYPhvr1TdP/oUMwapTvF1YUH9u5E264gdhffuEEZUggkeV0crl7Xu8/dQ9JMFAyI+Khgnx4JySYhpc8n1esGLzxhpkeM348PP+8SWjef5/q1Uu7FZuzehwFGSPz2GOmEnH2GBMTzTILOY9jL6SnrqcQ8d130K0b/P03abHV6HDkEzbSPM+nbNliWuFyvmf9tWq4SL58PBg54DSbSbzJb6v7vv++ZZUoYV6geXPr3O69Vlyc61W1XS1smN+CiN46jrcXVhQf+eij8ytfX3aZdS55V57vq5yX7O91LRApvubJ+VtjZkTc5KpKrk9K/PftC19+CRUrwoYNRLZuyayRPwKe1ePIb6yNt46jsRVBzrJMl+XNN5uqvl27wtdfE1knPs+6MznZ3+vz55sWGWetfeFYJVqCn5IZETdkZATgw7tNG/jf/+Dii2H3bq4Z25r1I+d6VKTNk8J23jhOuBTSCysnT5oKew8/bO4PGwYffwzlygGui/85Y3+vDx2q5FaCi5IZETcErGWiXj1Ytw46d4bTp/nXS73Z2etBklZkuLVek7tr2rz0kneOozV0gkxyMrRubaagFSsGU6eaKW3FHIdLZl9P6bHH8j6kZcHBg+69vJJb8RclMyJuCGjLRIUKsGRJ1jfriBeeo8OzXend+Ui+5ezdXRDx3nu9cxxvLqwohbRiBTRvDps2QZUq8NVXZpacC/ZlEho29F4ISm7FX5TMiLgh4C0TkZEwaZL5hl26NCxfbk5UGzbk+zRvrH2jNXRCSGamea907gxHjkCLFrBxo9uZprvv4cqVldxK8FAyI+KGoGmZ+M9/TLfTBRec70J49dU85117a0FEV8exzyRPS1MRvYA7eBCuvx4eecQkNf37w+rV5o/tJnff61Onnr+f83FQciv+peUMRNxkn80EjrlDQEr8HzsGAwbAwoXm/k03wdtvm/WdXPBWcbPsx9m2zdT4U52RIPD113DrrWbKUcmS8N//wp13ujdNKQd33+vO6szEx2cvBilScFqbKRslM+JNQfXhbVmmVeb+++HsWahbF+bOhX/9yy8v762FL6WQMjJg8mQYO9bcvuQS+PBDaNy4UId1972uCsDiK0pmslEyI94WdB/e331nup927DCBPP646WYo5rsC395a+FLOK9D7ascOuOOO89PobrsNpk2DsmUDF5OIlyiZyUbJjBQJR4+adZ3mmtWPufJKeO89uPBCn7zcypXQsWP++yUlmRkykjePlwWwLHj3XTMN7fhxk7y88ooZI1OAbiWRYKRVs0WKmgoVzDLWH3xgxs2sXw+XXw5vvunZokxu8sZU9YwMkxQV9dW3Pa4sfeiQaYnr398kMlddBT/9VODxMSLhQMmMSID45GTepw9s2oTVvoOp/HrXXRxtfh0Z2/70wsHPK+xU9cRE003VsaMJuWNHc9+rS0KEAI8qS1uWebM0aGAGJBUrBk89BatWmdltIkWYkhmRAPDlyTxxQy1q//Elo3mBU5Siwvdfkn5xIzb1f9FrzR+Fmaru1zWugpy7laW/TfwLunc3b5ZDh6BRI9P69sgjGsQigpIZEb/z5cncfuzdeyJ4idE05me+oiOlrNNc9s59HGnQ2nRJFFJBi+gFZI2rIJZfd10EGQxhGs37NYRPP4XixWHiRFMEr1kz/wQpEgKUzIj4kS9P5s6O/Sf1uIYvGcRbHCOG2G3fYl1xBQwfbmrVFEJBivFp9W1HeXXXtWQ9/6Ml07iH4qePm0HdP/5opmCXKOG3GEVCgZIZET/y5cnc9bFtvM0gGrKFD7kFW2amqU9z0UUwc6apFFtA2RcodGfhS1+scRWMA4lzxpSe7jxGZ911lTnAdAaynlY0ZyOptmgyp7xiiuJ5c+EkkTDiu0IUIpKLLxeszO85+6hBLz6k0pgVXL3wXvjtN1NF+I034IUXzKyYArAvUOgOb69x5fGUZj9wFlNkpGOSlT3Gl182XYNRpHEP/2UsT1CBYwDMpD9Vpj/D9QOqunw91YIRAawwl5KSYgFWSkpKoEMRsZKSLMu0v+R9SUry8bHT0izruecsq2zZ8w/06GFZW7Z488fN5dw5y4qLsyybzXlsNptlxceb/fKzYIHz49hs5rJggU9/FI9iyjPGjAzr2+HvWbsia2ftsJGmVs8q3+T7MyxYYH6f2Y8dFxeYn13E2zw5fyuZEfEjb57MvXLsPXssa/Bgy4qIMDtFRJj7e/Z47WfOyX7CzxmnJ0mI/WfNK1ko6O+xoPKLKVeMZFp9Ki+1Mps2zdp4plINa/3gt6ykFefyjT0YkzkRb1Iyk42SGQk23jiZe/3YmzdbVvfu558QFWVZw4ZZ1u7dBQ8mnzhznvjj493/2X3ZwlVQ7sYEmVYnvrC+pvX5jdHRlvXUU5Z18qRbrxWMyZyIt3ly/tYAYBE/K8gsIJ8fu2FDWLzYDL5o0wbS0uC116BePbj7bti5s+BBuYjTnYHDrgb3+nLsUUHl/1oW/2YJ67mSpXThKtZyhii2dhkB27ebmjGlS7v1WpoVJuJIA4BFAiAhAXr08M3AzUIdu00bWL3aZA4TJ5rr11+H6dPhlltg1Cho0aLwQZL/wOG8Bvd6OpDYH4NkXcUUxRl6M4eRTKEJmwA4RSleZwjP8QBzHqrOxZU8e61gTOZEAsoPLUUBpW4mkUJYtcqyrr3WsQ+jdWvLmj/fss6e9dnL5jce5MMP3R8f5K9BsjnHLFVhvzWOcdZ+qmS98HHKWM/ygFWF/YXqCgrGbjYRb/Pk/K1Vs0Ukf99/b5pE5syBs2fNtrg4s9jhgAFQt67XXiojwyzt4KobxWYzL/3ii2a9RTCn7uyPg+lWAzPtOeenXPZ9vDmFO/GjTN64ZQUDmU5PFlEC87vaRTyvci/TGcQxKhT69e2/oz17cv9scP53lJysadoSujw5fyuZERH37dsHU6earqdDh85vv+YaGDjQ9G+5Oe7DlZUrzVpV+UlKgiNHcndFxcebpRR69HAvKfLKCT85Gd59F2bMgF27sjavpyUvMYrFEQmkZRbPFWNhEin70hXgOpkLVK0dEW9QMpONkhkRH0hLMwOGp0+HFSvOn01Ll4Zu3UyTSdeuUKqUx4eeM8esp5if2bOhd2/X42E8SYrcLfrnYOdOmD8fPvwQvvvu/Pby5cnsexvfXz6QbWUup3p1aN0a1q71/pgdZ+OKvJEoiQQDJTPZKJkR8bEdO8yyCO+9Z1oo7MqWhX//2yQ1XbpAtWpuHc5bSYinSVG+MjNNd9vnn5tFH7/99vxjERFw9dVw551w440FSuIKShWAJVwpmclGyYyIn1gWbNhgWio+/NChuwWApk1NYtOhg1k0sVw5p4fJbzwIQOXK8NJLZgq6q5N3oZMiyzKJ2tdfw/LlsHQpHDhw/nGbDdq3N61QN90EVark/2IBooRHQlHYJTNTp07lueeeY9++fVx66aVMmTKFtm3buvVcJTMiAWBZpuViyRLTkrFhg+PjERHQpImZCn7lleb2xRdDMVMtwtV4EGdcrcXk8SDZY8fg559N68s335jL3r2OTypbFq691iRl3bu73doUSMG4fpWIO8IqmZk3bx633347U6dO5aqrruKNN95g+vTpbNmyhVq1auX7fCUzIkHgwAHTsrFsmUkSsndH2UVFmeJ9l10G9evz7aG6PPVBXf53sC5/UxWw5X4OeQ94zZkUFSedWuyiHn9Sl2RG9Uzm4owtsGmT88KAxYtDs2bQrp1JYFq3hhIlCv578DP7z++v2Vwi3hRWyUzLli254oormDZtWta2Bg0a0LNnTyZNmpTv85XMiAShPXtMUvP117Bxo0kmTpxwuXtGsRIcyKzEgcxKHKISh6nIScqQTgnSiCKdKEqXi2TIgHQizqWbAcppaZCSwuGthzi2/RDlzx2iAkeJII+PvFq1TDLVqpVpNWrRwq/jX7zJ3Snumr4twcqT83dQVwBOT09n48aNPPzwww7bO3XqxNq1a50+Jy0tjbS0tKz7qampPo1RRAqgZk0z1sReKCYz04xP2bTJdPVs327OssnJ8NdfRJ5Lpzp7qc5e18c8Dryce3PFfy52GVGliKhXF1vduqY+zkUXmW6uxo2hQgXv/YwB5smSBwWazSUSRII6mTl06BAZGRlUrVrVYXvVqlXZv3+/0+dMmjSJCRMm+CM8EfGWiAi44AJz6dnT8bH0dBa/vo8JIw5j2mXMpRSniSKNKNIoQTrFOEfnbiVoeHmU6bIqUQJiYqBSpfOXypWJrFTpfD9LAYTKYFoteSBFSVAnM3a2HB88lmXl2mY3ZswYRo8enXU/NTWV+Ph4n8YnIj5UogQxl9XmB2rnu2vSaGjYwXehhNJgWk/XrxIJZUG9analSpWIjIzM1Qpz4MCBXK01dlFRUURHRztcRCS0tW1rkgZXDSo2mykW5+YkxwKxD6bN2XWzZ4/Znpjou9cuiGD4nYn4S1AnMyVKlKBZs2YsX77cYfvy5ctp3bp1gKISEX+LjDStH5D75Gy/P2WK77p7MjJMi4yz6RL2bSNHmv2CRaB/ZyL+FNTJDMDo0aOZPn06M2bM4Ndff2XUqFHs2rWLIUOGBDo0EfGjhAQzlbhmTcftcXG+n2LsyWDaYBLI35mIPwX9mJlevXpx+PBhJk6cyL59+2jUqBGfffYZtWvn338uIuElIcEsIOnvAbihPJg2UL8zEX8K+jozhaU6MyJSWD5ftFJEcvHk/B303UwiIoGmwbQiwU3JjIhIPjSYViS4KZkREXEhI8N0Mc2ZA7GxZjFwDaYVCT5BPwBYRCQQXBXIe/FFqFxZg2lFgomSGRGRHFytNr1nD/TqZVpievcOTGwikptmM4mIXwTbmkau4gmm1aaD7Xcm4k9hs2q2iISHYFvTKK94YmODY7XpYPudiQQzDQAWCQPZB6quXBlcZfWDbU2j/OJZvNi94/iyQF6w/c5Egp26mURCXDB/gw+mLht346lUCQ4ezP9YviqQF2y/M5FAUdE8kSIiWL/B21uKxo8PrjWN3Flj6eBBM1spUAXyQnUdKJFAUjIjEqKCdSXnxETTstCxIzz5pHvP8deaRu6+Tt++5joQBfJCeR0okUBRMiMSooLxG7yrlqL8VK/um3gK+jo9evh+tWlX45zcjdFfvzORUKDZTCIhKti+wefVUuSKffyHv9Y0sq+xtGeP8zizxxMZ6bvVpvMa59Sjh/sxioihZEYkRAXbN/j8WopyCsSaRvY1lm6+2bx+9mTBWTyRkd4f5JtXQb6bbzYtP57EKCLqZhIJWcG2krOnLUCBWtMoIcH3XUiuuDvOyR/dXCLhRC0zIiHK01YGX3O3Beixx+Caa5x32fir4m1Cgu+6kPLiyTinQMUoEoqUzIiEMHsrg7PxF1Om+PcbvLvjUcaPd35C9ne9HF90IeXH03FOgYhRJBSpm0kkxCUkwI4dpojb7NnmOjnZ/10R9pYi8HxKc7DWy/G2YBvnJBIuVAFYRLzKWQtLfLzrlqKiVPHW/rPm13oVDj+rSGGpArCIBIynLUXBWC/HVwrTeiUirmnMjIh4nSdjPYKtXo6v+WOck78GUosECyUzIhJQRXEciS9nKgXzwqMivqIxMyISUBpH4j2uCvLZu7BUo0ZCicbMiEjI0DgS7wjWhUdF/EHJjIgEnLer8rpaxDGcFaWB1CI5acyMiAQFb40jKapjRoraQGqR7JTMiEjQKGzFW3cWcQzXhKYoDqQWsVM3k4iEhaI+ZiTYFh4V8SclMyISFor6mBENpJaiTMmMiIQFjRnx/kBqkVChMTMiEhY0ZsTwZUE+kWClZEZEwoJ9zEh+xfeKwpiRwg6kFgk16mYSkbCgMSMiRZeSGREJGxozIlI0qZtJRMKKxoyIFD1KZkQk7GjMiEjRom4mERERCWlKZkRERCSkKZkRERGRkKZkRkREREKakhkREREJaUpmREREJKQpmREREZGQpmRGREREQpqSGREREQlpYV8B2Ppn+dzU1NQARyIiIiLusp+37efxvIR9MnP8+HEA4uPjAxyJiIiIeOr48ePExMTkuY/NciflCWGZmZns3buXcuXKYbPZAh1OwKWmphIfH8/u3buJjo4OdDhhTb9r/9Hv2n/0u/afov67tiyL48ePU6NGDSIi8h4VE/YtMxEREcTFxQU6jKATHR1dJP85AkG/a//R79p/9Lv2n6L8u86vRcZOA4BFREQkpCmZERERkZCmZKaIiYqKYty4cURFRQU6lLCn37X/6HftP/pd+49+1+4L+wHAIiIiEt7UMiMiIiIhTcmMiIiIhDQlMyIiIhLSlMyIiIhISFMyI6SlpXH55Zdjs9n48ccfAx1O2NmxYwcDBw6kbt26lCpVinr16jFu3DjS09MDHVrYmDp1KnXr1qVkyZI0a9aMNWvWBDqksDNp0iRatGhBuXLlqFKlCj179mTr1q2BDqtImDRpEjabjZEjRwY6lKClZEZ48MEHqVGjRqDDCFu//fYbmZmZvPHGG2zevJmXXnqJ119/nUceeSTQoYWFefPmMXLkSB599FF++OEH2rZtS9euXdm1a1egQwsrq1atYujQoaxfv57ly5dz7tw5OnXqxMmTJwMdWlj77rvvePPNN7nssssCHUpQ09TsIu7zzz9n9OjRLFiwgEsvvZQffviByy+/PNBhhb3nnnuOadOm8eeffwY6lJDXsmVLrrjiCqZNm5a1rUGDBvTs2ZNJkyYFMLLwdvDgQapUqcKqVato165doMMJSydOnOCKK65g6tSpPPnkk1x++eVMmTIl0GEFJbXMFGF///03gwcP5r333qN06dKBDqdISUlJITY2NtBhhLz09HQ2btxIp06dHLZ36tSJtWvXBiiqoiElJQVA72MfGjp0KNdffz3XXnttoEMJemG/0KQ4Z1kW/fv3Z8iQITRv3pwdO3YEOqQiY/v27bz66qu88MILgQ4l5B06dIiMjAyqVq3qsL1q1ars378/QFGFP8uyGD16NG3atKFRo0aBDicszZ07l++//57vvvsu0KGEBLXMhJnx48djs9nyvGzYsIFXX32V1NRUxowZE+iQQ5a7v+vs9u7dS5cuXbjlllsYNGhQgCIPPzabzeG+ZVm5ton3DBs2jE2bNjFnzpxAhxKWdu/ezYgRI3j//fcpWbJkoMMJCRozE2YOHTrEoUOH8tynTp063HrrrXzyyScOH/gZGRlERkbSt29f3nnnHV+HGvLc/V3bP4z27t1Lx44dadmyJbNmzSIiQt8lCis9PZ3SpUszf/58brzxxqztI0aM4Mcff2TVqlUBjC483XvvvSxatIjVq1dTt27dQIcTlhYtWsSNN95IZGRk1raMjAxsNhsRERGkpaU5PCZKZoqsXbt2kZqamnV/7969dO7cmY8++oiWLVsSFxcXwOjCz549e+jYsSPNmjXj/fff1weRF7Vs2ZJmzZoxderUrG0NGzakR48eGgDsRZZlce+997Jw4UJWrlxJ/fr1Ax1S2Dp+/Dg7d+502HbnnXdyySWX8NBDD6lrzwmNmSmiatWq5XC/bNmyANSrV0+JjJft3buXDh06UKtWLZ5//nkOHjyY9Vi1atUCGFl4GD16NLfffjvNmzenVatWvPnmm+zatYshQ4YEOrSwMnToUGbPns3ixYspV65c1pikmJgYSpUqFeDowku5cuVyJSxlypShYsWKSmRcUDIj4mPLli3jjz/+4I8//siVKKphtPB69erF4cOHmThxIvv27aNRo0Z89tln1K5dO9ChhRX71PcOHTo4bJ85cyb9+/f3f0Ai2aibSUREREKaRiCKiIhISFMyIyIiIiFNyYyIiIiENCUzIiIiEtKUzIiIiEhIUzIjIiIiIU3JjIiIiIQ0JTMiIiIS0pTMiBQBNpuNRYsWBToMt4wfP57LL7880GF4XYcOHRg5cqTb+69cuRKbzcaxY8dc7jNr1izKly9f6NhEQp2SGZEg1r9/f3r27BnoMEKeOyf9F154gZiYGE6dOpXrsTNnzlC+fHlefPHFAseQmJjIE088UeDni4hrSmZERIA77riD06dPs2DBglyPLViwgFOnTnH77bd7fNyzZ88CEBsbS7ly5Qodp4jkpmRGJIR06NCB4cOH8+CDDxIbG0u1atUYP368wz7btm2jXbt2lCxZkoYNG7J8+fJcx9mzZw+9evWiQoUKVKxYkR49erBjx46sx+0tQhMmTKBKlSpER0dz1113kZ6enrWPZVlMnjyZCy64gFKlStGkSRM++uijrMft3SRffvklzZs3p3Tp0rRu3ZqtW7c6xPLMM89QtWpVypUrx8CBAzlz5kyueGfOnEmDBg0oWbIkl1xyCVOnTs16bMeOHdhsNhITE+nYsSOlS5emSZMmrFu3LiuOO++8k5SUFGw2GzabLdfvDKBy5cp069aNGTNm5HpsxowZdO/encqVK/PQQw9x0UUXUbp0aS644ALGjh2blbDA+W6yGTNmcMEFFxAVFYVlWbm6md5//32aN29OuXLlqFatGn369OHAgQO5Xvubb76hSZMmlCxZkpYtW/Lzzz/n2ie7Tz75hGbNmlGyZEkuuOACJkyYwLlz5/J8jkjIs0QkaPXr18/q0aNH1v327dtb0dHR1vjx463ff//deueddyybzWYtW7bMsizLysjIsBo1amR16NDB+uGHH6xVq1ZZTZs2tQBr4cKFlmVZ1smTJ6369etbAwYMsDZt2mRt2bLF6tOnj3XxxRdbaWlpWa9btmxZq1evXtYvv/xiffrpp1blypWtRx55JCuWRx55xLrkkkusL774wtq+fbs1c+ZMKyoqylq5cqVlWZaVlJRkAVbLli2tlStXWps3b7batm1rtW7dOusY8+bNs0qUKGG99dZb1m+//WY9+uijVrly5awmTZpk7fPmm29a1atXtxYsWGD9+eef1oIFC6zY2Fhr1qxZlmVZVnJysgVYl1xyifXpp59aW7dutW6++Wardu3a1tmzZ620tDRrypQpVnR0tLVv3z5r37591vHjx53+vpcsWWLZbDbrzz//zNqWnJxs2Ww267PPPrMsy7KeeOIJ65tvvrGSk5Otjz/+2Kpatar17LPPZu0/btw4q0yZMlbnzp2t77//3vrpp5+szMxMq3379taIESOy9nv77betzz77zNq+fbu1bt0668orr7S6du2a9bj999egQQNr2bJl1qZNm6wbbrjBqlOnjpWenm5ZlmXNnDnTiomJyXrOF198YUVHR1uzZs2ytm/fbi1btsyqU6eONX78eOdvMJEwoWRGJIg5S2batGnjsE+LFi2shx56yLIsy1q6dKkVGRlp7d69O+vxzz//3CGZefvtt62LL77YyszMzNonLS3NKlWqlLV06dKs142NjbVOnjyZtc+0adOssmXLWhkZGdaJEyeskiVLWmvXrnWIZeDAgVbv3r0tyzp/Ml6xYkXW40uWLLEA6/Tp05ZlWVarVq2sIUOGOByjZcuWDslMfHy8NXv2bId9nnjiCatVq1aWZZ1PZqZPn571+ObNmy3A+vXXXy3Lyn3Sd+XcuXNWzZo1rccffzxr2+OPP27VrFnTOnfunNPnTJ482WrWrFnW/XHjxlnFixe3Dhw44LBfzmQmp2+//dYCshIt++9v7ty5WfscPnzYKlWqlDVv3jynP1fbtm2tp59+2uG47733nlW9evW8f3CREFcsQA1CIlJAl112mcP96tWrZ3VP/Prrr9SqVYu4uLisx1u1auWw/8aNG/njjz9yjd84c+YM27dvz7rfpEkTSpcu7XCcEydOsHv3bg4cOMCZM2e47rrrHI6Rnp5O06ZNXcZbvXp1AA4cOECtWrX49ddfGTJkiMP+rVq1IikpCYCDBw+ye/duBg4cyODBg7P2OXfuHDExMW69ziWXXIK7IiMj6devH7NmzWLcuHHYbDbeeecd+vfvT2RkJAAfffQRU6ZM4Y8//uDEiROcO3eO6Ohoh+PUrl2bypUr5/laP/zwA+PHj+fHH3/kyJEjZGZmArBr1y4aNmzo8Puwi42N5eKLL+bXX391esyNGzfy3Xff8dRTT2Vty8jI4MyZM5w6dcrh7ykSTpTMiISY4sWLO9y32WxZJ0LLsnLtb7PZHO5nZmbSrFkzPvjgg1z75ncCzvl6S5YsoWbNmg6PR0VFuYzXHov9+fmx7/fWW2/RsmVLh8fsyYU3Xie7AQMGMGnSJL766ivAJBd33nknAOvXr+fWW29lwoQJdO7cmZiYGObOncsLL7zgcIwyZcrk+RonT56kU6dOdOrUiffff5/KlSuza9cuOnfu7DAuyZWcf1O7zMxMJkyYQEJCQq7HSpYsme9xRUKVkhmRMNKwYUN27drF3r17qVGjBkDWQFi7K664gnnz5mUN7HXlp59+4vTp05QqVQowJ/KyZcsSFxdHhQoViIqKYteuXbRv377A8TZo0ID169dzxx13ZG1bv3591u2qVatSs2ZN/vzzT/r27Vvg1ylRogQZGRlu7VuvXj3at2/PzJkzswbu1qtXDzCDcWvXrs2jjz6atf/OnTs9jue3337j0KFDPPPMM8THxwOwYcMGp/uuX7+eWrVqAXD06FF+//13l61NV1xxBVu3buXCCy/0OCaRUKZkRiSMXHvttVx88cXccccdvPDCC6SmpjqceAH69u3Lc889R48ePZg4cSJxcXHs2rWLxMREHnjggawuqvT0dAYOHMhjjz3Gzp07GTduHMOGDSMiIoJy5cpx//33M2rUKDIzM2nTpg2pqamsXbuWsmXL0q9fP7fiHTFiBP369aN58+a0adOGDz74gM2bN3PBBRdk7TN+/HiGDx9OdHQ0Xbt2JS0tjQ0bNnD06FFGjx7t1uvUqVOHEydO8OWXX2Z1n+XV5ZK9W2v69OlZ2y+88EJ27drF3LlzadGiBUuWLGHhwoVuxZBdrVq1KFGiBK+++ipDhgzhl19+cVmDZuLEiVSsWJGqVavy6KOPUqlSJZe1hx5//HFuuOEG4uPjueWWW4iIiGDTpk38/PPPPPnkkx7HKRIqNDVbJIxERESwcOFC0tLS+Ne//sWgQYMcxk8AlC5dmtWrV1OrVi0SEhJo0KABAwYM4PTp0w4tNddccw3169enXbt2/Oc//6Fbt24OU5qfeOIJHn/8cSZNmkSDBg3o3Lkzn3zyCXXr1nU73l69evH444/z0EMP0axZM3bu3Mndd9/tsM+gQYOYPn06s2bNonHjxrRv355Zs2Z59DqtW7dmyJAh9OrVi8qVKzN58uQ897/pppuIiooiKirKocumR48ejBo1imHDhnH55Zezdu1axo4d63YcdpUrV2bWrFnMnz+fhg0b8swzz/D888873feZZ55hxIgRNGvWjH379vHxxx9TokQJp/t27tyZTz/9lOXLl9OiRQuuvPJKXnzxRWrXru1xjCKhxGY562QXkSKtf//+HDt2LGSWQBCRok0tMyIiIhLSlMyIiIhISFM3k4iIiIQ0tcyIiIhISFMyIyIiIiFNyYyIiIiENCUzIiIiEtKUzIiIiEhIUzIjIiIiIU3JjIiIiIQ0JTMiIiIS0v4fcr932Z0A1hcAAAAASUVORK5CYII=\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": 56,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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T7OuOQG+lxGksJxNCCKlDSE2j0UClUiE/P5/zd4iIiO6Q8Hsa5m85iSea18fqMV2kjmNS3e9vu52zQ0RERPbh1nwdxxwQYNkhIiKiezpuLDsNHG9yMsCyQ0RERPegLdfj7M0LCnJkh4iIiJzO2cuFKDcIqDxc0cDPQ+o4NcKyQ0RERFW6/WKC97uDgb1i2SEiIqIqHb/o2JOTAZYdIiIiugfjyE5rB52cDLDsEBERURX0BoFTlxx7cjLwAGWnrKwMKSkpKC8vt2YeIiIishNpV4tQotPDw1WByEBvqePUmMVlp7i4GOPHj4enpydatWqFzMxMAMC0adPw7rvvWj0gERERScN4CKt5iA8UcsecnAzUoOzMmTMHR44cwe7du+Hu7m5a3qdPH2zYsMGq4YiIiEg6xisnt3bAO53fzuIbgW7evBkbNmzAI488YnYKWsuWLXHu3DmrhiMiIiLp3H7auSOzeGTnypUrqF+/fqXlRUVFDnv+PREREZkTQtx2TyzHHtmxuOx06dIFW7duNb02FpyPP/4YXbt2tV4yIiIikkx2filuFOvgIpfhoWDHnZwM1OAwVnx8PJ566imcPHkS5eXl+Oc//4kTJ07gjz/+QFJSki0yEhERUS07frHiEFbT+t5QuigkTvNgLB7Z6datG37//XcUFxejSZMm2LFjB9RqNf744w906tTJFhmJiIiolpkmJzvwxQSNLB7ZAYA2bdpg7dq11s5CREREduKkk0xOBqpZdjQaTbV36Ovr+B8KERFRXXfrnlh1ZGTHz8/vvmdaCSEgk8mg1+utEoyIiIikcVlTihxNKeSyOjSys2vXLlvnICIiIjtxOOsGAOAhtQ+8lDWa8WJXqvUb9OzZ09Y5iIiIyE4cuVl22jX0kzSHtdSoruXl5WH16tU4deoUZDIZWrRogbFjx8Lf39/a+YiIiKiWGUd22of7SZrDWiw+9TwpKQkRERH417/+hby8PFy/fh3/+te/EBkZyevsEBEROTiDQeDohYozsersyM6UKVMwbNgwrFy5EgpFxUWG9Ho9Jk+ejClTpuD48eNWD0lERES149yVQhRqy+HhqsBDase+crKRxSM7586dw4wZM0xFBwAUCgXi4uJ4I1AiIiIHZzyE1aaBCi4Ki2uCXbL4t+jYsSNOnTpVafmpU6fQvn17a2QiIiIiiRy5cAMA0C7M8a+vY1Stw1hHjx41PZ82bRqmT5+O1NRUPPLIIwCAvXv34t///jfeffdd26QkIiKiWmGanBxWT9ogViQTQoj7bSSXyyGTyXC/TR31ooIajQYqlQr5+fm8AjQREdVZpTo9Ws/bjnKDwG+ze6NhPU+pI91Tdb+/qzWyk5aWZrVgREREZJ9OZOej3CAQ6O2GBn4eUsexmmqVnUaNGtk6BxEREUnscFbFKeftw+5/myhHUuNrQJ88eRKZmZkoKyszWz5w4MAHDkVERES1z9munGxkcdk5f/48nn32WRw7dsxsHo+xATrinB0iIiJyvisnG1l86vn06dMRGRmJy5cvw9PTEydOnEBycjI6d+6M3bt32yAiERER2dr1ojJkXi8GALRt4CdtGCuzeGTnjz/+wC+//IKgoCDI5XLI5XJ0794d8fHxmDZtGg4dOmSLnERERGRDxkNYjQO9oPJ0lTaMlVk8sqPX6+HtXXH56MDAQGRnZwOomMSckpJi3XRERERUK25dX8dP0hy2YPHITuvWrXH06FE0btwY0dHRWLJkCdzc3LBq1So0btzYFhmJiIjIxm5dOdlP0hy2YHHZeeONN1BUVAQAePvtt9G/f3/06NEDAQEB2LBhg9UDEhERkW0JIUyHsTiyAyAmJsb0vHHjxjh58iSuX7+OevXqOdU5+URERHVF5vVi5BXr4KaQo3mIj9RxrK7G19m5nb+/vzV2Q0RERBIwztdpEeoLpYtC2jA2UK2yM2TIECQkJMDX1xdDhgy557YbN260SjAAKC8vx/z58/H5558jJycHISEhGDNmDN544w3I5RVzq4UQWLBgAVatWoW8vDxER0fj3//+N1q1amW1HERERM7sYEYeAKCDEx7CAqpZdlQqlekQlUpVe7d8X7x4Mf7zn/9g7dq1aNWqFfbv34+xY8dCpVJh+vTpAIAlS5Zg6dKlSEhIwEMPPYS3334bTz75JFJSUuDj43xDcURERNa2L72i7HSJcM4jNdW667mREAKZmZkICgqCp6ft74Tav39/qNVqrF692rRs6NCh8PT0xGeffQYhBEJDQxEbG4vZs2cDALRaLdRqNRYvXoyJEydW6+fwrudERFRXaUp1aL9gBwwC+PO1J6D2dZc6UrVV9/vbouvsCCEQFRWFixcvPnDA6ujevTt+/vlnnDlzBgBw5MgR/Pbbb3j66acBVNyNPScnB3379jW9R6lUomfPntizZ0+V+9VqtdBoNGYPIiKiuuhQ5g0YBBDu7+lQRccSFk1QlsvliIqKwrVr1xAVFWWrTCazZ89Gfn4+mjdvDoVCAb1ej3feeQd///vfAQA5OTkAALVabfY+tVqNjIyMKvcbHx+PBQsW2C44ERGRg9iXdh0A0DminsRJbMfiKygvWbIEM2fOxPHjx22Rx8yGDRuwbt06fPHFFzh48CDWrl2L999/H2vXrjXb7s5T3oUQ9zwNfs6cOcjPzzc9srKybJKfiIjI3u1Lryg7zjpfB6jBqef/+Mc/UFxcjHbt2sHNzQ0eHh5m669fv261cDNnzsSrr76KF154AQDQpk0bZGRkID4+HqNHj0ZwcDAAmM7UMsrNza002nM7pVIJpVJptZxERESOqKzcYDrtnGXnNsuWLbNBjLsrLi42nWJupFAoYDAYAACRkZEIDg5GYmIiOnToAAAoKytDUlISFi9eXGs5iYiIHNHx7Hxoyw2o5+mKJkFeUsexGYvLzujRo22R464GDBiAd955B+Hh4WjVqhUOHTqEpUuXYty4cQAqDl/FxsZi0aJFiIqKQlRUFBYtWgRPT08MHz681nISERE5ov3pxvk6/k59F4QHuoJySUkJdDqd2TJrnrr90Ucf4c0338TkyZORm5uL0NBQTJw4EXPnzjVtM2vWLJSUlGDy5Mmmiwru2LGD19ghIiK6j1vX13HeycmAhdfZAYCioiLMnj0bX331Fa5du1ZpvV6vt1q42sLr7BARUV0jhEDHtxKRV6zDxsnd0DHc8QqPTa6zA1SMpPzyyy9YsWIFlEolPvnkEyxYsAChoaH49NNPHyg0ERER1Y5zV4qQV6yDu6scrUNr7+4IUrD4MNaWLVvw6aefolevXhg3bhx69OiBpk2bolGjRvj8888xYsQIW+QkIiIiKzLO12kf5gc3F4vHPhyKxb/d9evXERkZCaBifo7xVPPu3bsjOTnZuumIiIjIJpz9fli3s7jsNG7cGOnp6QCAli1b4quvvgJQMeLj5+dnzWxERERkI/szbp2J5ewsLjtjx47FkSNHAFRcidg4d+fll1/GzJkzrR6QiIiIrCtXU4qMa8WQy4CO4X5Sx7G5as/ZiY2NxYsvvoiXX37ZtKx37944ffo09u/fjyZNmqBdu3Y2CUlERETWYzyE1TzYFz7urhKnsb1qj+z89NNPaNeuHR5++GGsWrXKdKfw8PBwDBkyhEWHiIjIQdy6H5bjnW5eE9UuO6dPn0ZycjLatGmDV155BaGhoRg1ahQnJRMRETkY43ydLpHOP18HsHDOzqOPPorVq1cjJycHH330EdLT09GrVy9ERUXh3XffRXZ2tq1yEhERkRVoSnU4mV1xdKZzI5adKnl6emLs2LFITk7G2bNn8fzzz2PJkiWIiIiwcjwiIiKypr/OX4dBAJGBXghWuUsdp1Y80FWEioqKkJSUhKSkJNy4cQNNmjSxVi4iIiKygT3nKm711K1JgMRJak+Nyk5ycjLGjh2L4OBgTJ8+HQ899BB+/fVXnDp1ytr5iIiIyIr2nLsKAOjWJFDiJLWn2qeeX7hwAWvXrkVCQgLOnTuH6OhofPjhh3jhhRfg7e1ty4xERERkBVcLtTidUwAAeKRx3ZivA1hQdiIiIhAQEICRI0di/PjxaNGihS1zERERkZX9cfMQVosQXwR4KyVOU3uqXXa++uorDBw4EC4uFt87lIiIiOxAXZyvA1hQdoYMGWLLHERERGRjxvk6jzatW2XHue/pTkRERACAC3nFyLhWDIVcVifudH47lh0iIqI6wHgIq11DVZ24H9btWHaIiIjqgD9M83XqzinnRhaXnXHjxqGgoKDS8qKiIowbN84qoYiIiMh6hBD4PdV4fZ26NV8HqEHZWbt2LUpKSiotLykpwaeffmqVUERERGQ9564UIbdACzcXOTo2qht3Or9dtc/G0mg0EEJACIGCggK4u9+6n4Zer8e2bdtQv359m4QkIiKimjOehdW5UT24uyokTlP7ql12/Pz8IJPJIJPJ8NBDD1VaL5PJsGDBAquGIyIioge3J7Vivs6jTevefB3AgrKza9cuCCHw+OOP49tvv4W//63T1tzc3NCoUSOEhobaJCQRERHVjN4g8Mf5irLTtQ7O1wEsKDs9e/YEAKSlpSEsLAxyOU/kIiIisnenLmmQX6KDt9IFbRuopI4jCYvv/dCoUSPcuHEDf/31F3Jzc2EwGMzWjxo1ymrhiIiI6MEYz8KKjvSHi6JuDlRYXHa2bNmCESNGoKioCD4+PpDJZKZ1MpmMZYeIiMiOJJ+9AgDoVkfn6wA1OPV8xowZpmvt3LhxA3l5eabH9evXbZGRiIiIaqBIW46/0iq+m3s3C5I4jXQsLjsXL17EtGnT4OnpaYs8REREZCW/p16FTi8Q7u+JyEAvqeNIxuKyExMTg/3799siCxEREVnR7jMVh7B6NQsym3ZS11g8Z+eZZ57BzJkzcfLkSbRp0wauruY3Exs4cKDVwhEREVHNCCGw+3QuAKB3s7p90V+Ly86ECRMAAAsXLqy0TiaTQa/XP3gqIiIieiBncwuRnV8KNxc5HmlcN6+vY2Rx2bnzVHMiIiKyP7tTKkZ1ujYOgIdb3btFxO0e6IT70tJSa+UgIiIiK9p1+tZ8nbrO4rKj1+vx1ltvoUGDBvD29sb58+cBAG+++SZWr15t9YBERERkmYJSHfZnGE85r9vzdYAalJ133nkHCQkJWLJkCdzc3EzL27Rpg08++cSq4YiIiMhyv6deg04vEBHgiYg6fMq5kcVl59NPP8WqVaswYsQIKBS3jgG2bdsWp0+ftmo4IiIislzSmYr5Or04qgOghhcVbNq0aaXlBoMBOp3OKqGIiIioZoQQnK9zB4vLTqtWrfDrr79WWv7111+jQ4cOVglFRERENZNyuQA5mlIoecq5icVlZ968eZg6dSoWL14Mg8GAjRs3YsKECVi0aBHmzp1r9YAXL17EP/7xDwQEBMDT0xPt27fHgQMHTOuFEJg/fz5CQ0Ph4eGBXr164cSJE1bPQURE5Ah2p9y88WeTALi71u1Tzo0sLjsDBgzAhg0bsG3bNshkMsydOxenTp3Cli1b8OSTT1o1XF5eHh599FG4urrixx9/xMmTJ/HBBx/Az8/PtM2SJUuwdOlSLF++HPv27UNwcDCefPJJFBQUWDULERGRI9h1mvN17iQTQgipQ1Tl1Vdfxe+//37Xw2ZAxahOaGgoYmNjMXv2bACAVquFWq3G4sWLMXHixGr9HI1GA5VKhfz8fPj6+lotPxERUW3SlOrQcWEiyg0CyTN7IzzAuW/aXd3v7we6qKCtff/99+jcuTOee+451K9fHx06dMDHH39sWp+WloacnBz07dvXtEypVKJnz57Ys2dPlfvVarXQaDRmDyIiIke363Quyg0CTYK8nL7oWKJat4uoV69ete+Wev369QcKdLvz589j5cqViIuLw2uvvYa//voL06ZNg1KpxKhRo5CTkwMAUKvVZu9Tq9XIyMiocr/x8fFYsGCB1XISERHZgx0nLgMAYloFS5zEvlSr7Cxbtsz0/Nq1a3j77bcRExODrl27AgD++OMPbN++HW+++aZVwxkMBnTu3BmLFi0CAHTo0AEnTpzAypUrMWrUKNN2dxYxIcQ9y9mcOXMQFxdneq3RaBAWFmbV7ERERLWpVKfHrpv3w2LZMVetsjN69GjT86FDh2LhwoWYOnWqadm0adOwfPly7Ny5Ey+//LLVwoWEhKBly5Zmy1q0aIFvv/0WABAcXPEPMycnByEhIaZtcnNzK4323E6pVEKpVFotJxERkdR+O3sVxWV6hKjc0bahSuo4dsXiOTvbt2/HU089VWl5TEwMdu7caZVQRo8++ihSUlLMlp05cwaNGjUCAERGRiI4OBiJiYmm9WVlZUhKSkK3bt2smoWIiMiebT9RMbWjb0t1taee1BUWl52AgABs2rSp0vLNmzcjIMC6Fy96+eWXsXfvXixatAipqan44osvsGrVKkyZMgVAxeGr2NhYLFq0CJs2bcLx48cxZswYeHp6Yvjw4VbNQkREZK/K9QbsPMX5OlWp1mGs2y1YsADjx4/H7t27TXN29u7di59++snqNwLt0qULNm3ahDlz5mDhwoWIjIzEsmXLMGLECNM2s2bNQklJCSZPnoy8vDxER0djx44d8PHxsWoWIiIie7UvPQ95xTr4ebri4Uh/qePYnRpdZ+fPP//Ev/71L5w6dQpCCLRs2RLTpk1DdHS0LTLaHK+zQ0REjmz+9yeQsCcdf+vUEO8/107qOLWmut/fFo/sAEB0dDQ+//zzGocjIiIi6xBCIPEkD2HdS43KjsFgQGpqKnJzc2EwGMzWPfbYY1YJRkRERPd3/KIGF2+UwNNNgR5RgVLHsUsWl529e/di+PDhyMjIwJ1HwGQyGfR6vdXCERER0b0Zz8Lq+VAQb/xZBYvLzqRJk9C5c2ds3boVISEhPL2NiIhIQj/dLDs8hFU1i8vO2bNn8c0336Bp06a2yENERETVdO5KIVJzC+Eil6F3c97lvCoWX2cnOjoaqamptshCREREFjAewuraJAAqD1eJ09gvi0d2XnrpJcyYMQM5OTlo06YNXF3NP9y2bdtaLRwRERFVbduxSwB4COt+LC47Q4cOBQCMGzfOtEwmk5luvskJykRERLZ37kohjl/UwEUuw9NtQu7/hjrM4rKTlpZmixxERERkge8PZwMAekQFwt/LTeI09s3ismO8CScRERFJQwiB749UlJ2B7UMlTmP/LJ6gDACfffYZHn30UYSGhiIjIwMAsGzZMnz33XdWDUdERESVHbuYj7SrRXB3lePJlpyvcz8Wl52VK1ciLi4OTz/9NG7cuGGao+Pn54dly5ZZOx8RERHd4bubh7D6tFDDW1mjmyHUKRaXnY8++ggff/wxXn/9dSgUt67U2LlzZxw7dsyq4YiIiMic3iDww9GKsjOofQOJ0zgGi8tOWloaOnToUGm5UqlEUVGRVUIRERHR3f2Zdg2XNVr4urvgsYd4L6zqsLjsREZG4vDhw5WW//jjj2jZsqU1MhEREVEVjGdhPd0mBEoX3gurOiw+0Ddz5kxMmTIFpaWlEELgr7/+wpdffon4+Hh88skntshIREREALTletOFBHkWVvVZXHbGjh2L8vJyzJo1C8XFxRg+fDgaNGiAf/7zn3jhhRdskZGIiIgAJJ+5Ck1pOer7KBEdGSB1HIdRoyncEyZMwIQJE3D16lUYDAbUr8+bjxEREdnad4cvAgAGtAuFQi6TOI3jqPH5arm5uUhJSYFMJoNMJkNQUJA1cxEREdFtirTl2HnqMgBgEA9hWcTiCcoajQYjR45EaGgoevbsicceewyhoaH4xz/+gfz8fFtkJCIiqvO2HruEUp0BkYFeaNNAJXUch2Jx2XnxxRfx559/YuvWrbhx4wby8/Pxww8/YP/+/ZgwYYItMhIREdV5X+3LAgD8rVNDyGQ8hGUJiw9jbd26Fdu3b0f37t1Ny2JiYvDxxx/jqaeesmo4IiIiAlJzC7E/Iw9yWUXZIctYPLITEBAAlary8JlKpUK9evWsEoqIiIhu+Xp/xahO72b1ofZ1lziN47G47LzxxhuIi4vDpUuXTMtycnIwc+ZMvPnmm1YNR0REVNfp9AZ8e/ACAOD5LmESp3FMFh/GWrlyJVJTU9GoUSOEh4cDADIzM6FUKnHlyhX897//NW178OBB6yUlIiKqg345nYurhWUI9Fbi8ea81EtNWFx2Bg8ebIMYREREdDfGiclDOzaAq8LiAzKEGpSdefPm2SIHERER3eGyphS7UnIBAM915iGsmqpRRbxx4wY++eQTzJkzB9evXwdQccjq4sWLVg1HRERUl31z4AIMAujcqB6a1veWOo7Dsnhk5+jRo+jTpw9UKhXS09MxYcIE+Pv7Y9OmTcjIyMCnn35qi5xERER1isEg8NXNs7CGcWLyA7F4ZCcuLg5jxozB2bNn4e5+6/S3fv36ITk52arhiIiI6qo/064j41oxvJUueKZtiNRxHJrFZWffvn2YOHFipeUNGjRATk6OVUIRERHVdcZRnQHtQuDpVuNbWRJqUHbc3d2h0WgqLU9JSeHNQImIiKzgaqEWW49WXM9uWJdwidM4PovLzqBBg7Bw4ULodDoAgEwmQ2ZmJl599VUMHTrU6gGJiIjqmi//zESZ3oB2YX5oH+YndRyHZ3HZef/993HlyhXUr18fJSUl6NmzJ5o2bQofHx+88847tshIRERUZ+j0Bqz7MwMAMLZbhLRhnITFBwF9fX3x22+/4ZdffsHBgwdhMBjQsWNH9OnTxxb5iIiI6pSfjufgskaLQG8lnm7DicnWUOMZT48//jgef/xxa2YhIiKq89buSQcAjIgOh5sLr5hsDRaVHYPBgISEBGzcuBHp6emQyWSIjIzE3/72N4wcORIymcxWOYmIiJzesQv52J+RBxe5DCOiOTHZWqpdGYUQGDhwIF588UVcvHgRbdq0QatWrZCRkYExY8bg2WeftWVOIiIip5dwc1TnmbYhqO/rfu+NqdqqPbKTkJCA5ORk/Pzzz+jdu7fZul9++QWDBw/Gp59+ilGjRlk9JBERkbO7WqjFliPZAIDRnJhsVdUe2fnyyy/x2muvVSo6QMX8nVdffRWff/65VcPdKT4+HjKZDLGxsaZlQgjMnz8foaGh8PDwQK9evXDixAmb5iAiIrK29X/dPN28oQodeLq5VVW77Bw9ehRPPfVUlev79euHI0eOWCXU3ezbtw+rVq1C27ZtzZYvWbIES5cuxfLly7Fv3z4EBwfjySefREFBgc2yEBERWZNOb8C6vZkAKkZ1OAfWuqpddq5fvw61Wl3lerVajby8PKuEulNhYSFGjBiBjz/+GPXq1TMtF0Jg2bJleP311zFkyBC0bt0aa9euRXFxMb744gubZCEiIrK2bccuIUdTikBvN94HywaqXXb0ej1cXKqe4qNQKFBeXm6VUHeaMmUKnnnmmUrX8klLS0NOTg769u1rWqZUKtGzZ0/s2bOnyv1ptVpoNBqzBxERkRSEEFi5+xwAYOQjEVC6KCRO5HyqPUFZCIExY8ZAqVTedb1Wq7VaqNutX78eBw8exL59+yqtM9549M4RJ7VajYyMjCr3GR8fjwULFlg3KBERUQ3sSsnF6ZwCeLkpMLpbI6njOKVql53Ro0ffdxtrn4mVlZWF6dOnY8eOHXB3r/oUvDuPbQoh7nm8c86cOYiLizO91mg0CAsLe/DAREREFlqxq2JUZ3h0OPw83SRO45yqXXbWrFljyxx3deDAAeTm5qJTp06mZXq9HsnJyVi+fDlSUlIAVIzwhITcOsaZm5t7z/lFSqWyyhEqIiKi2vJX2nXsz8iDm0KOF3s0ljqO07Lr61A/8cQTOHbsGA4fPmx6dO7cGSNGjMDhw4fRuHFjBAcHIzEx0fSesrIyJCUloVu3bhImJyIiur8Vu1MBAEM7NYSaFxG0mRrfG6s2+Pj4oHXr1mbLvLy8EBAQYFoeGxuLRYsWISoqClFRUVi0aBE8PT0xfPhwKSITERFVy4nsfOxOuQK5DJjUk6M6tmTXZac6Zs2ahZKSEkyePBl5eXmIjo7Gjh074OPjI3U0IiKiKhnPwHqmbSgaBXhJnMa5yYQQQuoQUtNoNFCpVMjPz4evr6/UcYiIyMmlXy3C4x/shkEA26b1QMtQfvfURHW/v+16zg4REZEz+m/yORgE0LtZEItOLWDZISIiqkVZ14vxzYELAIDJvZtKnKZuYNkhIiKqRct2noVOL9AjKhBdIvyljlMnsOwQERHVktTcAmw6VDGq80rfZhKnqTtYdoiIiGrJ0sQzMAggppUa7cL8pI5TZ7DsEBER1YJjF/Kx7VgOZDJgBkd1ahXLDhERUS14f0fFLY4Gt2+Ah9S8FlxtYtkhIiKysb/SriPpzBW4yGWI7RMldZw6h2WHiIjIhoQQeG/7aQDAsC5hvFqyBFh2iIiIbGh3yhXsS8+D0kWOlx7nqI4UWHaIiIhsRKc34O2tJwEAo7tFIFjFO5tLgWWHiIjIRj77IwPnrhQhwMsNU3i1ZMmw7BAREdnAtUItPtx5BgDwSkwzqDxcJU5Ud7HsEBER2cDSxDMoKC1HyxBfPN85TOo4dRrLDhERkZWduqTBl39lAgDmDWgJhVwmcaK6jWWHiIjIioQQWLjlJAwCeKZNCKIbB0gdqc5j2SEiIrKi7Sdy8Mf5a1C6yPFqv+ZSxyGw7BAREVlNSZkeb289BQCY+FhjhPl7SpyIAJYdIiIiq/lw5xlcyCtBqModk3o1kToO3cSyQ0REZAXHL+bjk1/PAwDefrY1PN1cJE5ERiw7RERED6hcb8Dsb4/CIIAB7ULxeHO11JHoNiw7RERED2j1b2k4ka2BysMVc/u3lDoO3YFlh4iI6AFkXCvC0sSKKyW//kwLBPkoJU5Ed2LZISIiqiEhBF7bdAzacgO6NQnAc50aSh2J7oJlh4iIqIa+3n8Bv6dWXFNn0bNtIJPxSsn2iGWHiIioBjKvFWPBlhMAgJeffAgRgV4SJ6KqsOwQERFZqFxvQOyGQygq0+PhCH9M6NFY6kh0Dyw7REREFlqx+xwOZt6Aj9IFHzzfjjf6tHMsO0RERBY4lJmHf/58FgCwcHAr3hLCAbDsEBERVVORthwvbzgMvUFgQLtQDG7fQOpIVA0sO0RERNW0cMtJpF8rRqjKHW8Pas2zrxwEyw4REVE1bD50ERv2Z0EmAz54vj1Unq5SR6JqYtkhIiK6j1OXNHh141EAwNTeTdG1SYDEicgSLDtERET3kF+iw/+tO4BSnQE9ogIR2+chqSORhVh2iIiIqmAwCMz46gjSrxWjgZ8H/vVCB55m7oBYdoiIiKqwMukcdp66DDeFHCv/0RH1vNykjkQ1wLJDRER0F7+evYIPdqQAABYOaoW2Df2kDUQ1xrJDRER0h7OXCzD584MwCGBY5zC88HC41JHoAbDsEBER3eZKgRZjE/ahoLQcnRvVw4JBraSORA/IrstOfHw8unTpAh8fH9SvXx+DBw9GSkqK2TZCCMyfPx+hoaHw8PBAr169cOLECYkSExGRIysp0+PFT/fjQl4JGgV4YtWoznB3VUgdix6QXZedpKQkTJkyBXv37kViYiLKy8vRt29fFBUVmbZZsmQJli5diuXLl2Pfvn0IDg7Gk08+iYKCAgmTExGRozEYBF7ecBhHsm7Az9MVa8Z0gT8nJDsFmRBCSB2iuq5cuYL69esjKSkJjz32GIQQCA0NRWxsLGbPng0A0Gq1UKvVWLx4MSZOnFit/Wo0GqhUKuTn58PX19eWvwIREdmpRdtOYVXyebgp5Fj3YjQejvSXOhLdR3W/v+16ZOdO+fn5AAB//4q/gGlpacjJyUHfvn1N2yiVSvTs2RN79uypcj9arRYajcbsQUREddeq5HNYlXweAPDec21ZdJyMw5QdIQTi4uLQvXt3tG7dGgCQk5MDAFCr1WbbqtVq07q7iY+Ph0qlMj3CwsJsF5yIiOzaZ3szsGjbaQDAzJhmGMQ7mTsdhyk7U6dOxdGjR/Hll19WWnfnXWeFEPe8E+2cOXOQn59vemRlZVk9LxER2b9vD1zAm5uPAwAm92qCKb2bSpyIbMFF6gDV8dJLL+H7779HcnIyGjZsaFoeHBwMoGKEJyQkxLQ8Nze30mjP7ZRKJZRKpe0CExGR3fvx2CXM/OYIAGBMtwjMjGkmcSKyFbse2RFCYOrUqdi4cSN++eUXREZGmq2PjIxEcHAwEhMTTcvKysqQlJSEbt261XZcIiJyELtO52La+kMwCOC5Tg0xt3/Lex4RIMdm1yM7U6ZMwRdffIHvvvsOPj4+pnk4KpUKHh4ekMlkiI2NxaJFixAVFYWoqCgsWrQInp6eGD58uMTpiYjIHv10PAcvfXkQOr1A/7YheHdoW8h5c0+nZtdlZ+XKlQCAXr16mS1fs2YNxowZAwCYNWsWSkpKMHnyZOTl5SE6Oho7duyAj49PLaclIiJ7t+nQBbzy9VHoDQJPtwnGh8Pa8y7mdYBDXWfHVnidHSIi5/f5nxl4Y/NxCAEM7dgQi4e2gYvCrmdz0H1U9/vbrkd2iIiIrOHj5PN4Z9spAMCoro0wf0ArHrqqQ1h2iIjIaRkMAu/+dNp0wcD/69UEs2KacTJyHcOyQ0RETqmkTI+XNxzGTycqTm6ZGdOM19Gpo1h2iIjI6eQWlGLC2v04ciEfbgo53nuuLa+MXIex7BARkVM5c7kAY9fsw8UbJfDzdMWqkZ15r6s6jmWHiIicxrZjlzDz6yMoKtMjIsATa8Y+jMhAL6ljkcRYdoiIyOHp9AYs/vE0PvktDQDwSGN/rBzRCfW83CRORvaAZYeIiBxabkEppn5+CH+lXwcATHysMWbGNOM1dMiEZYeIiBzWntSriN1wGLkFWngrXfD+c23xVOuQ+7+R6hSWHSIicjjacj3e356Cj3+tOGz1kNob//lHJzQO8pY4Gdkjlh0iInIop3M0iF1/GKdzCgAAw6PD8cYzLeDpxq80ujv+zSAiIoegNwis+T0NS7anoKzcgAAvNywe2hZ9WqqljkZ2jmWHiIjs3slsDeZsPIojF/IBAI83r4/FQ9siyEcpcTJyBCw7RERkt0p1evzz57P4OPk8yg0CPu4ueO3pFnihSxjvb0XVxrJDRER2KenMFcz77jjSrxUDAJ5qFYwFg1pB7esucTJyNCw7RERkV85fKcQ7W0/h59O5AAC1rxILB7VGTKtgiZORo2LZISIiu6Ap1eGjn88iYU86dHoBF7kMo7tFYHqfKPi6u0odjxwYyw4REUmqVKfHur0ZWLH7HK4XlQEAejcLwhv9W6IJr5tDVsCyQ0REkigrN+Cr/Vn46JezuKzRAgCaBHnhzf4t0atZfYnTkTNh2SEiolpVVm7A5kMXsXxXKjKvV0w+buDngelPRGFIxwa8pxVZHcsOERHViiJtOb78KxOf/JqGHE0pACDQW4mpvZvg79HhULooJE5Izoplh4iIbOpKgRbr9mZg7R/puFGsAwDU91FiQo/GGPFIOG/zQDbHv2FERGQTh7NuYO2edPxwNBs6vQAARAR4YmLPJhjSsQFHcqjWsOwQEZHVFJeVY+vRS1j3ZyaOZN0wLe8Q7odxj0bi6TYhUMh55WOqXSw7RET0QIQQOJx1A1/tz8KWI5dQqC0HALgp5OjfLgRjukWgbUM/aUNSncayQ0RENZJ1vRjfH8nGd4cv4szlQtPyRgGeeL5zGIZ1CUOgN2/USdJj2SEiomrLLSjFj8dy8N3hiziYecO0XOkix9NtQvB85zBER/pDzkNVZEdYdoiI6J4yrhVh+4kcbD9xGQcz8yAq5hpDJgO6Ng7AoPaheKp1CFQevKUD2SeWHSIiMqPTG3AwIw+7z1zBrtO5OJ1TYLa+fZgfBrQLRf+2IbwDOTkElh0iIkLmtWLsOXcVyWev4NezV1FQWm5ap5DL8Ehjf8S0CsaTLdUIUXlImJTIciw7RER1UPaNEuxLv47fU69iz7lruJBXYra+nqcrej4UhF7N6qNXsyD4ebpJlJTowbHsEBE5uXK9AWdzC3EgIw/70q9jf3oeLt4wLzcuchnah/nh0aaB6NUsCG0b+vF6OOQ0WHaIiJyIEAKZ14tx/KIGRy7cwOGsGzh2IR8lOr3Zdgq5DC1DfNG1SQC6NQlAlwh/eCn5lUDOiX+ziYgcVKlOj7OXC3E6R4OTlzQ4ka3BqWwNCrTllbb1VrqgXZgKXSL80SXCH+3D/FhuqM7g33QiIjtXpC3H+StFOHelEOeuFOLs5UKkXC5AxrUiGETl7d0UcjQL9kG7MBXah9VD+zAVGgd689o3VGex7BAR2YGCUh0u5JUg41oxMq4VIf1aEdKuFiH9ajFyNKVVvq+epyuaBfugebAvWjdQoVWoL5rW94arQl6L6YnsG8sOEZGNGQwCV4u0yMkvRfaNEmTfuPlnfgmyrpcgK68YN4p199xHoLcbGgd5o0mQN5oEeaF5sC8eCvZGkLcSMhlHbIjuhWWHiKiGtOV6XC8qw7XCMlwp1OKKRosrhVrkakqRW6BFjqYUl/Mrnpff7XjTHep5uiLc3xONArwQEeiFiICK502CvHjqN9EDYNkhojpPCIGiMj00JTrkl+hwo1iH/JIy3CjW4UaJDnnFZcgrKsP1oorn14vKcLVQa3bhvfuRyYBAbyUa+HmggZ8HQlTuCPHzQFg9D4T5eyLM3xPenDBMZBNO82/WihUr8N577+HSpUto1aoVli1bhh49ekgdi4hsxGAQKNHpKx5lehSVlaNIq0fxzT+LtOUoKitHobYchaXlKNKWo0BbjoLSchSU6lB487mmRAdNaTn01Rh5uRsXuQz+Xm4I9Faivq8SQd5KBPlUPIJ93aFWuSPY1x1BPkrOoyGSiFOUnQ0bNiA2NhYrVqzAo48+iv/+97/o168fTp48ifDwcKnjETkVIQR0egGd3oByvUCZ3oBygwG6cgGdwQCdvuJ5md6AsnIDyvQG6G7+WVZe8dDqDdDq9CjTG6DVGaAtN0Bbroe23IBSnR5a3c0/b74uLdejuEyP0jK9qeCU6gxW/91cFTL4urvCz9MVfp5u8PNwhcrDFfW83ODv5YZ6nm7w96pYF+itRKC3G3zdXXmWE5Gdkwkhava/M3YkOjoaHTt2xMqVK03LWrRogcGDByM+Pv6+79doNFCpVMjPz4evr6/VcuUVlaGorPIwt7U+8Tv3I1B5x5W3udt+RDW2qby2qn3fvtyYybjsXuvutt/bt7m1f3GXnyVM2whx63cSt20jULHBnctuvc/4/Oafty83vadinUFU/V6DoWKZQQjTcoO47TUqRiWMy3Bz21vbAHqDMC0TouK53lDxXH/be/UGAb0QMBjuvdz4Wm8wf5Sb/Wm49VpvXF6xrNxYbm6utzcergp4uingpXQx+9Nb6QJvpQu8bv7p7e4CH/eK577urvBxd4Gvhyt83StKjburnJN9iRxIdb+/HX5kp6ysDAcOHMCrr75qtrxv377Ys2fPXd+j1Wqh1WpNrzUajU2yvbcjBV/8mWmTfRPZExe5DC4KGdwUcri5yOGmkMPltueuLnIoFXK4usigdFHATSGH0lVu+tPdRQGlq7xinYsc7i5yuLsqbj7kULoq4OmqgIebAh43l3u4VRQcdxcFR1aI6J4cvuxcvXoVer0earXabLlarUZOTs5d3xMfH48FCxbYPJurXAZ31+odo5fh/v+xvtv/cN656G7/V1ppSU33c4/3Gbe/229x632ySvuR3baN7Lb1t+/n9izGp3dub9yXWY47lstue59Zhpvr5PJb62Q3d3zrPbdtd3OBcZ1cJjPbr0wmg/zm+op1spvbVWwjlxu3uW07+e2vZTdfV1zSX34zrEIug0IuM/1Mhey27W4+V8hvLVcY3y+XweXmfoz7cJHLbz1XVLzH5bbXxvXG58Yy46owPjcWmor3cTSEiOyZw5cdozv/YyuEqPI/wHPmzEFcXJzptUajQVhYmNUzLRjUGgsGtbb6fomIiKj6HL7sBAYGQqFQVBrFyc3NrTTaY6RUKqFUKmsjHhEREUnM4c+DdHNzQ6dOnZCYmGi2PDExEd26dZMoFREREdkLhx/ZAYC4uDiMHDkSnTt3RteuXbFq1SpkZmZi0qRJUkcjIiIiiTlF2Rk2bBiuXbuGhQsX4tKlS2jdujW2bduGRo0aSR2NiIiIJOYU19l5ULa6zg4RERHZTnW/vx1+zg4RERHRvbDsEBERkVNj2SEiIiKnxrJDRERETo1lh4iIiJwayw4RERE5NZYdIiIicmosO0REROTUWHaIiIjIqTnF7SIelPEi0hqNRuIkREREVF3G7+373QyCZQdAQUEBACAsLEziJERERGSpgoICqFSqKtfz3lgADAYDsrOz4ePjA5lMJnUcyWk0GoSFhSErK4v3CrMxfta1h5917eFnXXvq+mcthEBBQQFCQ0Mhl1c9M4cjOwDkcjkaNmwodQy74+vrWyf/5ZECP+vaw8+69vCzrj11+bO+14iOEScoExERkVNj2SEiIiKnxrJDlSiVSsybNw9KpVLqKE6Pn3Xt4Wdde/hZ1x5+1tXDCcpERETk1DiyQ0RERE6NZYeIiIicGssOEREROTWWHSIiInJqLDtULVqtFu3bt4dMJsPhw4eljuN00tPTMX78eERGRsLDwwNNmjTBvHnzUFZWJnU0p7FixQpERkbC3d0dnTp1wq+//ip1JKcTHx+PLl26wMfHB/Xr18fgwYORkpIidaw6IT4+HjKZDLGxsVJHsUssO1Qts2bNQmhoqNQxnNbp06dhMBjw3//+FydOnMCHH36I//znP3jttdekjuYUNmzYgNjYWLz++us4dOgQevTogX79+iEzM1PqaE4lKSkJU6ZMwd69e5GYmIjy8nL07dsXRUVFUkdzavv27cOqVavQtm1bqaPYLZ56Tvf1448/Ii4uDt9++y1atWqFQ4cOoX379lLHcnrvvfceVq5cifPnz0sdxeFFR0ejY8eOWLlypWlZixYtMHjwYMTHx0uYzLlduXIF9evXR1JSEh577DGp4zilwsJCdOzYEStWrMDbb7+N9u3bY9myZVLHsjsc2aF7unz5MiZMmIDPPvsMnp6eUsepU/Lz8+Hv7y91DIdXVlaGAwcOoG/fvmbL+/btiz179kiUqm7Iz88HAP49tqEpU6bgmWeeQZ8+faSOYtd4I1CqkhACY8aMwaRJk9C5c2ekp6dLHanOOHfuHD766CN88MEHUkdxeFevXoVer4darTZbrlarkZOTI1Eq5yeEQFxcHLp3747WrVtLHccprV+/HgcPHsS+ffukjmL3OLJTB82fPx8ymeyej/379+Ojjz6CRqPBnDlzpI7ssKr7Wd8uOzsbTz31FJ577jm8+OKLEiV3PjKZzOy1EKLSMrKeqVOn4ujRo/jyyy+ljuKUsrKyMH36dKxbtw7u7u5Sx7F7nLNTB129ehVXr1695zYRERF44YUXsGXLFrMvBL1eD4VCgREjRmDt2rW2jurwqvtZG/9jlZ2djd69eyM6OhoJCQmQy/n/Iw+qrKwMnp6e+Prrr/Hss8+alk+fPh2HDx9GUlKShOmc00svvYTNmzcjOTkZkZGRUsdxSps3b8azzz4LhUJhWqbX6yGTySCXy6HVas3W1XUsO1SlzMxMaDQa0+vs7GzExMTgm2++QXR0NBo2bChhOudz8eJF9O7dG506dcK6dev4Hyorio6ORqdOnbBixQrTspYtW2LQoEGcoGxFQgi89NJL2LRpE3bv3o2oqCipIzmtgoICZGRkmC0bO3YsmjdvjtmzZ/PQ4R04Z4eqFB4ebvba29sbANCkSRMWHSvLzs5Gr169EB4ejvfffx9XrlwxrQsODpYwmXOIi4vDyJEj0blzZ3Tt2hWrVq1CZmYmJk2aJHU0pzJlyhR88cUX+O677+Dj42OaE6VSqeDh4SFxOufi4+NTqdB4eXkhICCARecuWHaI7MCOHTuQmpqK1NTUSkWSg68PbtiwYbh27RoWLlyIS5cuoXXr1ti2bRsaNWokdTSnYjy1v1evXmbL16xZgzFjxtR+IKKbeBiLiIiInBpnPxIREZFTY9khIiIip8ayQ0RERE6NZYeIiIicGssOEREROTWWHSIiInJqLDtERETk1Fh2iIiIyKmx7BARgIq7gm/evFnqGNUyf/58tG/fXuoYVterVy/ExsZWe/vdu3dDJpPhxo0bVW6TkJAAPz+/B85G5MhYdogc3JgxYzB48GCpYzi86pSCDz74ACqVCsXFxZXWlZaWws/PD0uXLq1xho0bN+Ktt96q8fuJ6O5YdoiIqmnUqFEoKSnBt99+W2ndt99+i+LiYowcOdLi/ep0OgCAv78/fHx8HjgnEZlj2SFyMr169cK0adMwa9Ys+Pv7Izg4GPPnzzfb5uzZs3jsscfg7u6Oli1bIjExsdJ+Ll68iGHDhqFevXoICAjAoEGDkJ6eblpvHFFasGAB6tevD19fX0ycOBFlZWWmbYQQWLJkCRo3bgwPDw+0a9cO33zzjWm98TDMzz//jM6dO8PT0xPdunVDSkqKWZZ3330XarUaPj4+GD9+PEpLSyvlXbNmDVq0aAF3d3c0b94cK1asMK1LT0+HTCbDxo0b0bt3b3h6eqJdu3b4448/TDnGjh2L/Px8yGQyyGSySp8ZAAQFBWHAgAH43//+V2nd//73PwwcOBBBQUGYPXs2HnroIXh6eqJx48Z48803TYUGuHUY7n//+x8aN24MpVIJIUSlw1jr1q1D586d4ePjg+DgYAwfPhy5ubmVfvbvv/+Odu3awd3dHdHR0Th27FilbW63ZcsWdOrUCe7u7mjcuDEWLFiA8vLye76HyKEJInJoo0ePFoMGDTK97tmzp/D19RXz588XZ86cEWvXrhUymUzs2LFDCCGEXq8XrVu3Fr169RKHDh0SSUlJokOHDgKA2LRpkxBCiKKiIhEVFSXGjRsnjh49Kk6ePCmGDx8umjVrJrRarennent7i2HDhonjx4+LH374QQQFBYnXXnvNlOW1114TzZs3Fz/99JM4d+6cWLNmjVAqlWL37t1CCCF27dolAIjo6Gixe/duceLECdGjRw/RrVs30z42bNgg3NzcxMcffyxOnz4tXn/9deHj4yPatWtn2mbVqlUiJCREfPvtt+L8+fPi22+/Ff7+/iIhIUEIIURaWpoAIJo3by5++OEHkZKSIv72t7+JRo0aCZ1OJ7RarVi2bJnw9fUVly5dEpcuXRIFBQV3/by3bt0qZDKZOH/+vGlZWlqakMlkYtu2bUIIId566y3x+++/i7S0NPH9998LtVotFi9ebNp+3rx5wsvLS8TExIiDBw+KI0eOCIPBIHr27CmmT59u2m716tVi27Zt4ty5c+KPP/4QjzzyiOjXr59pvfHza9GihdixY4c4evSo6N+/v4iIiBBlZWVCCCHWrFkjVCqV6T0//fST8PX1FQkJCeLcuXNix44dIiIiQsyfP//uf8GInADLDpGDu1vZ6d69u9k2Xbp0EbNnzxZCCLF9+3ahUChEVlaWaf2PP/5oVnZWr14tmjVrJgwGg2kbrVYrPDw8xPbt200/19/fXxQVFZm2WblypfD29hZ6vV4UFhYKd3d3sWfPHrMs48ePF3//+9+FELe+rHfu3Glav3XrVgFAlJSUCCGE6Nq1q5g0aZLZPqKjo83KTlhYmPjiiy/MtnnrrbdE165dhRC3ys4nn3xiWn/ixAkBQJw6dUoIUbkUVKW8vFw0aNBAzJ0717Rs7ty5okGDBqK8vPyu71myZIno1KmT6fW8efOEq6uryM3NNdvuzrJzp7/++ksAMBUx4+e3fv160zbXrl0THh4eYsOGDXf9vXr06CEWLVpktt/PPvtMhISE3PsXJ3JgLhINKBGRDbVt29bsdUhIiOnwx6lTpxAeHo6GDRua1nft2tVs+wMHDiA1NbXS/JHS0lKcO3fO9Lpdu3bw9PQ0209hYSGysrKQm5uL0tJSPPnkk2b7KCsrQ4cOHarMGxISAgDIzc1FeHg4Tp06hUmTJplt37VrV+zatQsAcOXKFWRlZWH8+PGYMGGCaZvy8nKoVKpq/ZzmzZujuhQKBUaPHo2EhATMmzcPMpkMa9euxZgxY6BQKAAA33zzDZYtW4bU1FQUFhaivLwcvr6+Zvtp1KgRgoKC7vmzDh06hPnz5+Pw4cO4fv06DAYDACAzMxMtW7Y0+zyM/P390axZM5w6dequ+zxw4AD27duHd955x7RMr9ejtLQUxcXFZv88iZwFyw6RE3J1dTV7LZPJTF+UQohK28tkMrPXBoMBnTp1wueff15p2/t9Qd/587Zu3YoGDRqYrVcqlVXmNWYxvv9+jNt9/PHHiI6ONltnLB/W+Dm3GzduHOLj4/HLL78AqCgfY8eOBQDs3bsXL7zwAhYsWICYmBioVCqsX78eH3zwgdk+vLy87vkzioqK0LdvX/Tt2xfr1q1DUFAQMjMzERMTYzYvqip3/jM1MhgMWLBgAYYMGVJpnbu7+333S+SIWHaI6piWLVsiMzMT2dnZCA0NBQDTRF2jjh07YsOGDaaJx1U5cuQISkpK4OHhAaDii97b2xsNGzZEvXr1oFQqkZmZiZ49e9Y4b4sWLbB3716MGjXKtGzv3r2m52q1Gg0aNMD58+cxYsSIGv8cNzc36PX6am3bpEkT9OzZE2vWrDFNLG7SpAmAisnCjRo1wuuvv27aPiMjw+I8p0+fxtWrV/Huu+8iLCwMALB///67brt3716Eh4cDAPLy8nDmzJkqR6s6duyIlJQUNG3a1OJMRI6KZYeojunTpw+aNWuGUaNG4YMPPoBGozH7YgaAESNG4L333sOgQYOwcOFCNGzYEJmZmdi4cSNmzpxpOgRWVlaG8ePH44033kBGRgbmzZuHqVOnQi6Xw8fHB6+88gpefvllGAwGdO/eHRqNBnv27IG3tzdGjx5drbzTp0/H6NGj0blzZ3Tv3h2ff/45Tpw4gcaNG5u2mT9/PqZNmwZfX1/069cPWq0W+/fvR15eHuLi4qr1cyIiIlBYWIiff/7ZdHjuXod0bj9s9sknn5iWN23aFJmZmVi/fj26dOmCrVu3YtOmTdXKcLvw8HC4ubnho48+wqRJk3D8+PEqr8GzcOFCBAQEQK1W4/XXX0dgYGCV116aO3cu+vfvj7CwMDz33HOQy+U4evQojh07hrffftvinESOgKeeE9UxcrkcmzZtglarxcMPP4wXX3zRbP4GAHh6eiI5ORnh4eEYMmQIWrRogXHjxqGkpMRspOeJJ55AVFQUHnvsMTz//PMYMGCA2Snbb731FubOnYv4+Hi0aNECMTEx2LJlCyIjI6udd9iwYZg7dy5mz56NTp06ISMjA//3f/9nts2LL76ITz75BAkJCWjTpg169uyJhIQEi35Ot27dMGnSJAwbNgxBQUFYsmTJPbcfOnQolEollEql2SGhQYMG4eWXX8bUqVPRvn177NmzB2+++Wa1cxgFBQUhISEBX3/9NVq2bIl3330X77///l23fffddzF9+nR06tQJly5dwvfffw83N7e7bhsTE4MffvgBiYmJ6NKlCx555BEsXboUjRo1sjgjkaOQibsdwCciuo8xY8bgxo0bDnOLCSKquziyQ0RERE6NZYeIiIicGg9jERERkVPjyA4RERE5NZYdIiIicmosO0REROTUWHaIiIjIqbHsEBERkVNj2SEiIiKnxrJDRERETo1lh4iIiJza/wNdhxie1akKtAAAAABJRU5ErkJggg==\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.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": [
+ "
"
+ ]
+ },
+ "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": 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": [
+ "
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+ "\n",
+ "
\n",
+ " \n",
+ "
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+ "
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+ "
Year
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+ "
Value
\n",
+ "
\n",
+ " \n",
+ " \n",
+ "
\n",
+ "
0
\n",
+ "
1960
\n",
+ "
5.918412e+10
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+ "
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+ "
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+ "
1
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+ "
1961
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+ "
4.955705e+10
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+ "
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+ "
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+ "
2
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+ "
1962
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+ "
4.668518e+10
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+ "
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+ "
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+ "
3
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+ "
1963
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+ "
5.009730e+10
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+ "
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+ "
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+ "
4
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+ "
1964
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+ "
5.906225e+10
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+ "
\n",
+ "
\n",
+ "
5
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+ "
1965
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+ "
6.970915e+10
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+ "
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+ "
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+ "
6
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+ "
1966
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+ "
7.587943e+10
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+ "
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+ "
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+ "
7
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+ "
1967
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+ "
7.205703e+10
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+ "
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+ "
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+ "
8
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+ "
1968
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+ "
6.999350e+10
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+ "
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+ "
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+ "
9
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+ "
1969
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+ "
7.871882e+10
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+ "
\n",
+ " \n",
+ "
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+ "
"
+ ],
+ "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": [
+ "
"
+ ]
+ },
+ "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": [
+ "
"
+ ]
+ },
+ "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": [
+ "[]"
+ ]
+ },
+ "execution_count": 63,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
"
+ ]
+ },
+ "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": [
+ "
\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",
+ "##
"
+ ]
+ },
+ "metadata": {},
+ "output_type": "display_data"
+ }
+ ],
+ "source": [
+ "plt.scatter(cdf.ENGINESIZE, cdf.CO2EMISSIONS, color='blue')\n",
+ "plt.xlabel(\"Engine size\")\n",
+ "plt.ylabel(\"Emission\")\n",
+ "plt.show()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "#### Creating train and test dataset\n",
+ "Train/Test Split involves splitting the dataset into training and testing sets respectively, which are mutually exclusive. After which, you train with the training set and test with the testing set.\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 18,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "msk = np.random.rand(len(df)) < 0.8\n",
+ "train = cdf[msk]\n",
+ "test = cdf[~msk]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "
Polynomial regression
\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "Sometimes, the trend of data is not really linear, and looks curvy. In this case we can use Polynomial regression methods. In fact, many different regressions exist that can be used to fit whatever the dataset looks like, such as quadratic, cubic, and so on, and it can go on and on to infinite degrees.\n",
+ "\n",
+ "In essence, we can call all of these, polynomial regression, where the relationship between the independent variable x and the dependent variable y is modeled as an nth degree polynomial in x. Lets say you want to have a polynomial regression (let's make 2 degree polynomial):\n",
+ "\n",
+ "\n",
+ "$$y = b + \\theta_1 x + \\theta_2 x^2$$\n",
+ "\n",
+ "\n",
+ "\n",
+ "Now, the question is: how we can fit our data on this equation while we have only x values, such as __Engine Size__? \n",
+ "Well, we can create a few additional features: 1, $x$, and $x^2$.\n",
+ "\n",
+ "\n",
+ "\n",
+ "__PolynomialFeatures()__ function in Scikit-learn library, drives a new feature sets from the original feature set. That is, a matrix will be generated consisting of all polynomial combinations of the features with degree less than or equal to the specified degree. For example, lets say the original feature set has only one feature, _ENGINESIZE_. Now, if we select the degree of the polynomial to be 2, then it generates 3 features, degree=0, degree=1 and degree=2: \n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 19,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "array([[ 1. , 2. , 4. ],\n",
+ " [ 1. , 2.4 , 5.76],\n",
+ " [ 1. , 3.5 , 12.25],\n",
+ " ...,\n",
+ " [ 1. , 3.2 , 10.24],\n",
+ " [ 1. , 3. , 9. ],\n",
+ " [ 1. , 3.2 , 10.24]])"
+ ]
+ },
+ "execution_count": 19,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "from sklearn.preprocessing import PolynomialFeatures\n",
+ "from sklearn import linear_model\n",
+ "train_x = np.asanyarray(train[['ENGINESIZE']])\n",
+ "train_y = np.asanyarray(train[['CO2EMISSIONS']])\n",
+ "\n",
+ "test_x = np.asanyarray(test[['ENGINESIZE']])\n",
+ "test_y = np.asanyarray(test[['CO2EMISSIONS']])\n",
+ "\n",
+ "\n",
+ "poly = PolynomialFeatures(degree=2)\n",
+ "train_x_poly = poly.fit_transform(train_x)\n",
+ "train_x_poly"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "**fit_transform** takes our x values, and output a list of our data raised from power of 0 to power of 2 (since we set the degree of our polynomial to 2). \n",
+ "\n",
+ "The equation and the sample example is displayed below. \n",
+ "\n",
+ "\n",
+ "$$\n",
+ "\\begin{bmatrix}\n",
+ " v_1\\\\\\\\\\\\\n",
+ " v_2\\\\\\\\\n",
+ " \\vdots\\\\\\\\\n",
+ " v_n\n",
+ "\\end{bmatrix}\\longrightarrow \\begin{bmatrix}\n",
+ " [ 1 & v_1 & v_1^2]\\\\\\\\\n",
+ " [ 1 & v_2 & v_2^2]\\\\\\\\\n",
+ " \\vdots & \\vdots & \\vdots\\\\\\\\\n",
+ " [ 1 & v_n & v_n^2]\n",
+ "\\end{bmatrix}\n",
+ "$$\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "$$\n",
+ "\\begin{bmatrix}\n",
+ " 2.\\\\\\\\\n",
+ " 2.4\\\\\\\\\n",
+ " 1.5\\\\\\\\\n",
+ " \\vdots\n",
+ "\\end{bmatrix} \\longrightarrow \\begin{bmatrix}\n",
+ " [ 1 & 2. & 4.]\\\\\\\\\n",
+ " [ 1 & 2.4 & 5.76]\\\\\\\\\n",
+ " [ 1 & 1.5 & 2.25]\\\\\\\\\n",
+ " \\vdots & \\vdots & \\vdots\\\\\\\\\n",
+ "\\end{bmatrix}\n",
+ "$$\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n",
+ "\n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "It looks like feature sets for multiple linear regression analysis, right? Yes. It Does. \n",
+ "Indeed, Polynomial regression is a special case of linear regression, with the main idea of how do you select your features. Just consider replacing the $x$ with $x_1$, $x_1^2$ with $x_2$, and so on. Then the 2nd degree equation would be turn into:\n",
+ "\n",
+ "$$y = b + \\theta_1 x_1 + \\theta_2 x_2$$\n",
+ "\n",
+ "Now, we can deal with it as a 'linear regression' problem. Therefore, this polynomial regression is considered to be a special case of traditional multiple linear regression. So, you can use the same mechanism as linear regression to solve such problems. \n",
+ "\n",
+ "\n",
+ "\n",
+ "so we can use __LinearRegression()__ function to solve it:\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 20,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Coefficients: [[ 0. 50.57406358 -1.44659762]]\n",
+ "Intercept: [106.21698993]\n"
+ ]
+ }
+ ],
+ "source": [
+ "clf = linear_model.LinearRegression()\n",
+ "train_y_ = clf.fit(train_x_poly, train_y)\n",
+ "# The coefficients\n",
+ "print ('Coefficients: ', clf.coef_)\n",
+ "print ('Intercept: ',clf.intercept_)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "As mentioned before, __Coefficient__ and __Intercept__ , are the parameters of the fit curvy line. \n",
+ "Given that it is a typical multiple linear regression, with 3 parameters, and knowing that the parameters are the intercept and coefficients of hyperplane, sklearn has estimated them from our new set of feature sets. Lets plot it:\n"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 21,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Text(0, 0.5, 'Emission')"
+ ]
+ },
+ "execution_count": 21,
+ "metadata": {},
+ "output_type": "execute_result"
+ },
+ {
+ "data": {
+ "image/png": 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\n",
+ "text/plain": [
+ "
\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",
+ "##