notebook/07-06-Linear-Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "---\n",
    "---\n",
    "\n",
    "# In Depth: Linear Regression\n",
    "\n",
    "---\n",
    "---\n",
    "\n",
    "![image.png](img/chengjun.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "notes"
    }
   },
   "source": [
    "<!--BOOK_INFORMATION-->\n",
    "\n",
    "*This notebook contains an excerpt from the [Python Data Science Handbook](http://shop.oreilly.com/product/0636920034919.do) by Jake VanderPlas; the content is available [on GitHub](https://github.com/jakevdp/PythonDataScienceHandbook).*\n",
    "\n",
    "*The text is released under the [CC-BY-NC-ND license](https://creativecommons.org/licenses/by-nc-nd/3.0/us/legalcode), and code is released under the [MIT license](https://opensource.org/licenses/MIT). If you find this content useful, please consider supporting the work by [buying the book](http://shop.oreilly.com/product/0636920034919.do)!*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Naive Bayes (discussed earlier in [In Depth: Naive Bayes Classification](05.05-Naive-Bayes.ipynb)) is a good starting point for classification tasks.\n",
    "\n",
    "**Linear regression models** are a good starting point for regression tasks.\n",
    "- can be fit very quickly,  \n",
    "- are very interpretable.\n",
    "    \n",
    "The simplest form of a linear regression model (i.e., fitting a straight line to data) \n",
    "- Extended to model more complicated data behavior.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-01T01:16:44.860603Z",
     "start_time": "2024-08-01T01:16:44.855980Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns; sns.set()\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Simple Linear Regression\n",
    "\n",
    "We will start with the most familiar linear regression, a straight-line fit to data.\n",
    "A straight-line fit is a model of the form\n",
    "$$\n",
    "y = ax + b\n",
    "$$\n",
    "where $a$ is commonly known as the *slope*, and $b$ is commonly known as the *intercept*.\n",
    "\n",
    "Consider the following data, which is scattered about a line with a slope of 2 and an intercept of -5:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-01T01:17:41.567441Z",
     "start_time": "2024-08-01T01:17:41.416643Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# generate training set\n",
    "rng = np.random.RandomState(1)\n",
    "x = 10 * rng.rand(50)\n",
    "y = 2 * x - 5 + rng.randn(50)\n",
    "# generate test set\n",
    "xtest = np.linspace(0, 10, 1000)\n",
    "ytest = 2*xtest -5\n",
    "# plot training set\n",
    "plt.scatter(x, y);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We can use Scikit-Learn's ``LinearRegression`` estimator to fit this data and construct the best-fit line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-01T01:18:50.579295Z",
     "start_time": "2024-08-01T01:18:49.396118Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "model = LinearRegression(fit_intercept=True)\n",
    "model.fit(x[:, np.newaxis], y)\n",
    "# predict ypred for the test set.\n",
    "ypred = model.predict(xtest[:, np.newaxis])\n",
    "# plot training set as scatter plot\n",
    "plt.scatter(x, y)\n",
    "# plot the predicted result as a strait line\n",
    "plt.plot(xtest, ypred);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The slope and intercept of the data are contained in the model's fit parameters, which in Scikit-Learn are always marked by a trailing underscore.\n",
    "Here the relevant parameters are ``coef_`` and ``intercept_``:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-01T01:19:15.984618Z",
     "start_time": "2024-08-01T01:19:15.981036Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model slope:     2.027208810360695\n",
      "Model intercept: -4.998577085553202\n"
     ]
    }
   ],
   "source": [
    "print(\"Model slope:    \", model.coef_[0])\n",
    "print(\"Model intercept:\", model.intercept_) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We see that the results are very close to the inputs, as we might hope."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Model evaluation for regression**\n",
    "\n",
    "- RMSE\n",
    "- R Square\n",
    "\n",
    "https://scikit-learn.org/stable/modules/model_evaluation.html#scoring-parameter"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-01T01:23:04.580772Z",
     "start_time": "2024-08-01T01:23:04.578073Z"
    },
    "code_folding": [],
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# Root mean square error 均方根误差,亦称标准误差\n",
    "# https://en.wikipedia.org/wiki/Root-mean-square_deviation\n",
    "def rmse(y_test, y_pred): \n",
    "    mse = np.mean((y_test - y_pred) ** 2)\n",
    "    rmse = mse ** 0.5 \n",
    "    return rmse"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-01T01:25:25.955822Z",
     "start_time": "2024-08-01T01:25:25.951914Z"
    },
    "code_folding": [],
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# R square\n",
    "# https://en.wikipedia.org/wiki/Coefficient_of_determination\n",
    "def R2(y_test, y_pred): \n",
    "    residuals_sum_of_squares = np.sum((y_pred - y_test)**2)\n",
    "    total_sum_of_squares = np.sum((y_test - np.mean(y_test))**2)\n",
    "    return 1 - residuals_sum_of_squares/total_sum_of_squares\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-01T01:27:18.549098Z",
     "start_time": "2024-08-01T01:27:18.545186Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE: 0.1584\n",
      "R2 score: 0.9992\n"
     ]
    }
   ],
   "source": [
    "print('RMSE: %.4f' % rmse(ytest, ypred))\n",
    "print('R2 score: %.4f' % R2(ytest, ypred)) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-01T01:28:04.409522Z",
     "start_time": "2024-08-01T01:28:04.407019Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.metrics import mean_squared_error, r2_score, explained_variance_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-01T01:28:15.180483Z",
     "start_time": "2024-08-01T01:28:15.176068Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "RMSE: 0.1584\n",
      "R2 score: 0.9992\n",
      "Variance score: 0.9998\n"
     ]
    }
   ],
   "source": [
    "print('RMSE: %.4f' % mean_squared_error(ytest, ypred) ** 0.5)\n",
    "print('R2 score: %.4f' % r2_score(ytest, ypred))\n",
    "print('Variance score: %.4f' % explained_variance_score(ytest, ypred))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "The ``LinearRegression`` estimator is much more capable than this, however—in addition to simple straight-line fits, it can also handle multidimensional linear models of the form\n",
    "$$\n",
    "y = a_0 + a_1 x_1 + a_2 x_2 + \\cdots\n",
    "$$\n",
    "where there are multiple $x$ values.\n",
    "Geometrically, this is akin to fitting a plane to points in three dimensions, or fitting a hyper-plane to points in higher dimensions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "**Building some example data using NumPy**\n",
    "\n",
    "The <font color = 'red'>multidimensional nature of such regressions</font> makes them more difficult to visualize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-01T01:34:22.579169Z",
     "start_time": "2024-08-01T01:34:22.575602Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "rng = np.random.RandomState(1)\n",
    "X = 10 * rng.rand(100, 3) #three features\n",
    "y = 0.5 + np.dot(X, [1.5, -2., 1.])\n",
    "# y is constructed from three random X features"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "we can use the single ``LinearRegression`` estimator to fit lines, planes, or hyperplanes to our data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-07T02:26:03.759024Z",
     "start_time": "2021-08-07T02:26:03.741217Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5000000000000144\n",
      "[ 1.5 -2.   1. ]\n"
     ]
    }
   ],
   "source": [
    "model.fit(X, y)\n",
    "print(model.intercept_)\n",
    "print(model.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Basis Function Regression 基函数回归\n",
    "\n",
    "One trick you can use to adapt linear regression to nonlinear relationships between variables\n",
    "- to transform the data according to *basis functions*.\n",
    "\n",
    "We have seen one version of this before, in the ``PolynomialRegression`` pipeline used in [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) and [Feature Engineering](05.04-Feature-Engineering.ipynb).\n",
    "\n",
    "The idea is to take our multidimensional linear model:\n",
    "$$\n",
    "y = a_0 + a_1 x_1 + a_2 x_2 + a_3 x_3 + \\cdots\n",
    "$$\n",
    "and build the $x_1, x_2, x_3,$ and so on, from our single-dimensional input $x$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "That is, we let $x_n = f_n(x)$, where $f_n()$ is some function that transforms our data.\n",
    "\n",
    "For example, if $f_n(x) = x^n$, our model becomes a polynomial regression:\n",
    "$$\n",
    "y = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + \\cdots\n",
    "$$\n",
    "\n",
    "Notice that this is *still a linear model*\n",
    "- the linearity refers to the fact that the coefficients $a_n$ never multiply or divide each other.\n",
    "- What we have effectively done is taken our one-dimensional $x$ values and projected them into a higher dimension, so that a linear fit can fit more complicated relationships between $x$ and $y$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Polynomial basis functions 多项式基函数\n",
    "\n",
    "> polynomial, Synonym: multinomial, 多项式\n",
    "\n",
    "This polynomial projection is useful enough that it is built into Scikit-Learn, using the ``PolynomialFeatures`` transformer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-01T01:37:59.473485Z",
     "start_time": "2024-08-01T01:37:59.468394Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.,  4.,  8.],\n",
       "       [ 3.,  9., 27.],\n",
       "       [ 4., 16., 64.]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "x = np.array([2, 3, 4])\n",
    "poly = PolynomialFeatures(3, include_bias=False)\n",
    "poly.fit_transform(x[:, None])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We see here that the transformer has converted our one-dimensional array into a three-dimensional array by taking the exponent of each value.\n",
    "- This new, higher-dimensional data representation can then be plugged into a linear regression.\n",
    "- As we saw in [Feature Engineering](05.04-Feature-Engineering.ipynb), the cleanest way to accomplish this is to use a pipeline.\n",
    "\n",
    "Let's make a 7th-degree polynomial model in this way:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-01T01:38:09.245290Z",
     "start_time": "2024-08-01T01:38:09.240140Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.pipeline import make_pipeline\n",
    "poly_model = make_pipeline(PolynomialFeatures(7),\n",
    "                           LinearRegression())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "With this transform in place, we can use the linear model to fit much more complicated relationships between $x$ and $y$. \n",
    "\n",
    "For example, here is a sine wave with noise:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Our linear model, through the use of 7th-order polynomial basis functions, can provide an excellent fit to this non-linear data!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-01T01:38:37.004351Z",
     "start_time": "2024-08-01T01:38:36.833933Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(1)\n",
    "x = 10 * rng.rand(50)\n",
    "y = np.sin(x) + 0.1 * rng.randn(50)\n",
    "xfit = np.linspace(0, 10, 1000)\n",
    "\n",
    "poly_model.fit(x[:, np.newaxis], y)\n",
    "yfit = poly_model.predict(xfit[:, np.newaxis])\n",
    "\n",
    "plt.scatter(x, y)\n",
    "plt.plot(xfit, yfit);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Gaussian basis functions 高斯基函数\n",
    "\n",
    "Of course, other basis functions are possible.\n",
    "For example, one useful pattern is to fit a model that is not a sum of polynomial bases, but a sum of Gaussian bases.\n",
    "The result might look something like the following figure:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "\n",
    "<img src = \"img/figures/05.06-gaussian-basis.png\" width = \"400px\">\n",
    "\n",
    "<center>[figure source in Appendix](#Gaussian-Basis)</center>\n",
    "\n",
    "<font size = '4pt'>The shaded regions in the plot are the scaled basis functions, and when added together they reproduce the smooth curve through the data.</font>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "\n",
    "These Gaussian basis functions are not built into Scikit-Learn, \n",
    "- but we can write a custom transformer that will create them\n",
    "- Scikit-Learn transformers are implemented as Python classes; \n",
    "    - reading Scikit-Learn's source is a good way to see how they can be created:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The simplest case of a normal distribution is known as the ''standard normal distribution''.\n",
    "\n",
    "$$\n",
    "f(x \\mid \\mu, \\sigma^2) = \\frac{1}{\\sqrt{2\\pi\\sigma^2} } e^{ -\\frac{(x-\\mu)^2}{2\\sigma^2} } \\sim  e^{ -0.5 (\\frac{x-\\mu}{\\sigma})^2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-01T01:41:59.119546Z",
     "start_time": "2024-08-01T01:41:59.114565Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.base import BaseEstimator, TransformerMixin\n",
    "\n",
    "class GaussianFeatures(BaseEstimator, TransformerMixin):\n",
    "    \"\"\"Uniformly spaced Gaussian features for one-dimensional input\"\"\"\n",
    "    def __init__(self, N, sigma_factor=2.0):\n",
    "        self.N = N\n",
    "        self.sigma_factor = sigma_factor\n",
    "    \n",
    "    @staticmethod\n",
    "    def _gauss_basis(x, mu, sigma, axis=None):\n",
    "        arg = (x - mu) / sigma\n",
    "        return np.exp(-0.5 * np.sum(arg ** 2, axis))\n",
    "        \n",
    "    def fit(self, X, y=None):\n",
    "        # create N centers spread along the data range\n",
    "        self.mu_ = np.linspace(X.min(), X.max(), self.N)\n",
    "        self.sigma_ = self.sigma_factor * (self.mu_[1] - self.mu_[0])\n",
    "        return self\n",
    "        \n",
    "    def transform(self, X):\n",
    "        return self._gauss_basis(X[:, :, np.newaxis], self.mu_,\n",
    "                                 self.sigma_, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-08-01T01:42:02.198425Z",
     "start_time": "2024-08-01T01:42:02.006696Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rng = np.random.RandomState(1)\n",
    "x = 10 * rng.rand(50)\n",
    "y = np.sin(x) + 0.1 * rng.randn(50)\n",
    "xfit = np.linspace(0, 10, 1000)\n",
    "\n",
    "gauss_model = make_pipeline(GaussianFeatures(20),\n",
    "                            LinearRegression())\n",
    "gauss_model.fit(x[:, np.newaxis], y)\n",
    "yfit = gauss_model.predict(xfit[:, np.newaxis])\n",
    "\n",
    "plt.scatter(x, y)\n",
    "plt.plot(xfit, yfit)\n",
    "plt.xlim(0, 10);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "There is nothing magic about polynomial basis functions: \n",
    "- You should have some sort of intuition about **the generating process of your data**; \n",
    "- If you think one basis or another might be appropriate, you can use them as well."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Regularization 正则化\n",
    "\n",
    "The introduction of basis functions into our linear regression makes the model much more flexible, \n",
    "- but it also can very quickly lead to over-fitting (refer back to [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) for a discussion of this).\n",
    "\n",
    "For example, if we choose too many Gaussian basis functions, we end up with results that don't look so good:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-07T02:47:05.947237Z",
     "start_time": "2021-08-07T02:47:05.570010Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = make_pipeline(GaussianFeatures(30),\n",
    "                      LinearRegression())\n",
    "model.fit(x[:, np.newaxis], y)\n",
    "\n",
    "plt.scatter(x, y)\n",
    "plt.plot(xfit, model.predict(xfit[:, np.newaxis]))\n",
    "\n",
    "plt.xlim(0, 10)\n",
    "plt.ylim(-5, 1.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "With the data projected to the 30-dimensional basis, the model has far too much flexibility and goes to extreme values between locations where it is constrained by data.\n",
    "\n",
    "We can see the reason for this if we plot the coefficients of the Gaussian bases with respect to their locations:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-07T02:51:14.172435Z",
     "start_time": "2021-08-07T02:51:13.606230Z"
    },
    "code_folding": [
     0
    ],
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def basis_plot(model, title=None):\n",
    "    fig, ax = plt.subplots(2, sharex=True)\n",
    "    model.fit(x[:, np.newaxis], y)\n",
    "    ax[0].scatter(x, y)\n",
    "    ax[0].plot(xfit, model.predict(xfit[:, np.newaxis]))\n",
    "    ax[0].set(xlabel='x', ylabel='y', ylim=(-5, 1.5))\n",
    "    \n",
    "    if title:\n",
    "        ax[0].set_title(title)\n",
    "\n",
    "    ax[1].plot(model.steps[0][1].mu_,\n",
    "               model.steps[1][1].coef_)\n",
    "    ax[1].set(xlabel='basis location',\n",
    "              ylabel='coefficient',\n",
    "              xlim=(0, 10))\n",
    "    \n",
    "model = make_pipeline(GaussianFeatures(30), LinearRegression())\n",
    "basis_plot(model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "This is typical over-fitting behavior when basis functions overlap: \n",
    "- the coefficients of adjacent basis functions blow up and cancel each other out.\n",
    "\n",
    "We know that such behavior is problematic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "It would be nice if we could limit such spikes expliticly in the model \n",
    "- by **penalizing large values of the model parameters**.\n",
    "\n",
    "Such a penalty is known as *regularization*, and comes in several forms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Ridge regression ($L_2$ Regularization) 岭回归\n",
    "\n",
    "\n",
    "*ridge regression* or $L_2$ *regularization*, sometimes also called *Tikhonov regularization*.\n",
    "- Perhaps the most common form of regularization\n",
    "\n",
    "This proceeds by penalizing the **sum of squares** (2-norms) of the model coefficients; \n",
    "- The penalty on the model fit would be \n",
    "$$\n",
    "P = \\alpha\\sum_{n=1}^N \\theta_n^2\n",
    "$$\n",
    "\n",
    "where $\\alpha$ is a free parameter that controls the strength of the penalty.\n",
    "\n",
    "This type of penalized model is built into Scikit-Learn with the ``Ridge`` estimator:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-07T02:51:20.941566Z",
     "start_time": "2021-08-07T02:51:20.348376Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "model = make_pipeline(GaussianFeatures(30), Ridge(alpha=0.1))\n",
    "basis_plot(model, title='Ridge Regression')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "The $\\alpha$ parameter is essentially a knob controlling the complexity of the resulting model.\n",
    "- In the limit $\\alpha \\to 0$, we recover the standard linear regression result; \n",
    "- in the limit $\\alpha \\to \\infty$, all model responses will be suppressed.\n",
    "\n",
    "One advantage of ridge regression in particular is that it can be computed very efficiently\n",
    "- at hardly more computational cost than the original linear regression model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Lasso regression ($L_1$ regularization) 套索回归\n",
    "\n",
    "Lasso regression involves penalizing the **sum of absolute values** (1-norms) of regression coefficients:\n",
    "$$\n",
    "P = \\alpha\\sum_{n=1}^N |\\theta_n|\n",
    "$$\n",
    "Though this is conceptually very similar to ridge regression, the results can differ surprisingly: \n",
    "- for example, due to geometric reasons lasso regression tends to favor *sparse models* where possible: \n",
    "    - it preferentially sets model coefficients to exactly zero.\n",
    "\n",
    "We can see this behavior in duplicating the ridge regression figure, but using L1-normalized coefficients:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-08-07T02:53:26.159489Z",
     "start_time": "2021-08-07T02:53:25.643902Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "model = make_pipeline(GaussianFeatures(30), Lasso(alpha=0.01))\n",
    "basis_plot(model, title='Lasso Regression')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "With the lasso regression penalty, **the majority of the coefficients are exactly zero**, \n",
    "- with the functional behavior being modeled by a small subset of the available basis functions.\n",
    "\n",
    "As with ridge regularization, the $\\alpha$ parameter tunes the strength of the penalty, and should be determined via, for example, cross-validation (refer back to [Hyperparameters and Model Validation](05.03-Hyperparameters-and-Model-Validation.ipynb) for a discussion of this)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Example: Predicting Bicycle Traffic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "To predict the number of bicycle trips across Seattle's Fremont Bridge based on weather, season, and other factors.\n",
    "\n",
    "We have seen this data already in [Working With Time Series](03.11-Working-with-Time-Series.ipynb).\n",
    "\n",
    "- we will join the bike data with another dataset, and \n",
    "- try to determine the extent to which weather and seasonal factors—temperature, precipitation, and daylight hours—affect the volume of bicycle traffic through this corridor.\n",
    "\n",
    "- the NOAA makes available their daily [weather station data](http://www.ncdc.noaa.gov/cdo-web/search?datasetid=GHCND) (I used station ID USW00024233) \n",
    "- we can easily use Pandas to join the two data sources.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We will perform a simple linear regression to relate weather and other information to bicycle counts, in order to estimate how a change in any one of these parameters affects the number of riders on a given day.\n",
    "\n",
    "In particular, this is an example of how the tools of Scikit-Learn can be used in a statistical modeling framework, in which the parameters of the model are assumed to have interpretable meaning.\n",
    "\n",
    "Let's start by loading the two datasets, indexing by date:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:51:22.442283Z",
     "start_time": "2020-05-28T09:51:22.440027Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [],
   "source": [
    "# !curl -o FremontBridge.csv https://data.seattle.gov/api/views/65db-xm6k/rows.csv?accessType=DOWNLOAD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:52:35.959546Z",
     "start_time": "2020-05-28T09:52:31.157270Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "counts = pd.read_csv('../data/Fremont_Bridge.csv', index_col='Date', parse_dates=True)\n",
    "weather = pd.read_csv('../data/BicycleWeather.csv', index_col='DATE', parse_dates=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Next we will compute the total daily bicycle traffic, and put this in its own dataframe:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:52:39.055553Z",
     "start_time": "2020-05-28T09:52:39.034915Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "daily = counts.resample('d').sum()\n",
    "daily['Total'] = daily.sum(axis=1)\n",
    "daily = daily[['Total']] # remove other columns\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We saw previously that the patterns of use generally vary from day to day; let's account for this in our data by adding binary columns that indicate the day of the week:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:52:40.132371Z",
     "start_time": "2020-05-28T09:52:40.122377Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "days = ['Mon', 'Tue', 'Wed', 'Thu', 'Fri', 'Sat', 'Sun']\n",
    "for i in range(7):\n",
    "    daily[days[i]] = (daily.index.dayofweek == i).astype(float)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Similarly, we might expect riders to behave differently on holidays; let's add an indicator of this as well:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:52:41.139824Z",
     "start_time": "2020-05-28T09:52:41.097242Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from pandas.tseries.holiday import USFederalHolidayCalendar\n",
    "cal = USFederalHolidayCalendar()\n",
    "holidays = cal.holidays('2012', '2016')\n",
    "daily = daily.join(pd.Series(1, index=holidays, name='holiday'))\n",
    "daily['holiday'].fillna(0, inplace=True)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We also might suspect that the hours of daylight would affect how many people ride; let's use the standard astronomical calculation to add this information:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:53:26.441097Z",
     "start_time": "2020-05-28T09:53:25.954629Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(8, 17)"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from datetime import datetime\n",
    "def hours_of_daylight(date, axis=23.44, latitude=47.61):\n",
    "    \"\"\"Compute the hours of daylight for the given date\"\"\"\n",
    "    days = (date - datetime(2000, 12, 21)).days\n",
    "    m = (1. - np.tan(np.radians(latitude))\n",
    "         * np.tan(np.radians(axis) * np.cos(days * 2 * np.pi / 365.25)))\n",
    "    return 24. * np.degrees(np.arccos(1 - np.clip(m, 0, 2))) / 180.\n",
    "\n",
    "daily['daylight_hrs'] = list(map(hours_of_daylight, daily.index))\n",
    "daily[['daylight_hrs']].plot()\n",
    "plt.ylim(8, 17)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "We can also add the average temperature and total precipitation to the data.\n",
    "In addition to the inches of precipitation, let's add a flag that indicates whether a day is dry (has zero precipitation):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:53:30.749580Z",
     "start_time": "2020-05-28T09:53:30.738215Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# temperatures are in 1/10 deg C; convert to C\n",
    "weather['TMIN'] /= 10\n",
    "weather['TMAX'] /= 10\n",
    "weather['Temp (C)'] = 0.5 * (weather['TMIN'] + weather['TMAX'])\n",
    "\n",
    "# precip is in 1/10 mm; convert to inches\n",
    "weather['PRCP'] /= 254\n",
    "weather['dry day'] = (weather['PRCP'] == 0).astype(int)\n",
    "\n",
    "daily = daily.join(weather[['PRCP', 'Temp (C)', 'dry day']])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Finally, let's add a counter that increases from day 1, and measures how many years have passed.\n",
    "This will let us measure any observed annual increase or decrease in daily crossings:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:53:31.910236Z",
     "start_time": "2020-05-28T09:53:31.904789Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "daily['annual'] = (daily.index - daily.index[0]).days / 365."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Now our data is in order, and we can take a look at it:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:53:32.995247Z",
     "start_time": "2020-05-28T09:53:32.977299Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Total</th>\n",
       "      <th>Mon</th>\n",
       "      <th>Tue</th>\n",
       "      <th>Wed</th>\n",
       "      <th>Thu</th>\n",
       "      <th>Fri</th>\n",
       "      <th>Sat</th>\n",
       "      <th>Sun</th>\n",
       "      <th>holiday</th>\n",
       "      <th>daylight_hrs</th>\n",
       "      <th>PRCP</th>\n",
       "      <th>Temp (C)</th>\n",
       "      <th>dry day</th>\n",
       "      <th>annual</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2012-10-03</th>\n",
       "      <td>3521.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.277359</td>\n",
       "      <td>0.0</td>\n",
       "      <td>13.35</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-10-04</th>\n",
       "      <td>3475.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.219142</td>\n",
       "      <td>0.0</td>\n",
       "      <td>13.60</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.002740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-10-05</th>\n",
       "      <td>3148.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.161038</td>\n",
       "      <td>0.0</td>\n",
       "      <td>15.30</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.005479</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-10-06</th>\n",
       "      <td>2006.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.103056</td>\n",
       "      <td>0.0</td>\n",
       "      <td>15.85</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.008219</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2012-10-07</th>\n",
       "      <td>2142.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>11.045208</td>\n",
       "      <td>0.0</td>\n",
       "      <td>15.85</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.010959</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Total  Mon  Tue  Wed  Thu  Fri  Sat  Sun  holiday  daylight_hrs  \\\n",
       "Date                                                                           \n",
       "2012-10-03  3521.0  0.0  0.0  1.0  0.0  0.0  0.0  0.0      0.0     11.277359   \n",
       "2012-10-04  3475.0  0.0  0.0  0.0  1.0  0.0  0.0  0.0      0.0     11.219142   \n",
       "2012-10-05  3148.0  0.0  0.0  0.0  0.0  1.0  0.0  0.0      0.0     11.161038   \n",
       "2012-10-06  2006.0  0.0  0.0  0.0  0.0  0.0  1.0  0.0      0.0     11.103056   \n",
       "2012-10-07  2142.0  0.0  0.0  0.0  0.0  0.0  0.0  1.0      0.0     11.045208   \n",
       "\n",
       "            PRCP  Temp (C)  dry day    annual  \n",
       "Date                                           \n",
       "2012-10-03   0.0     13.35      1.0  0.000000  \n",
       "2012-10-04   0.0     13.60      1.0  0.002740  \n",
       "2012-10-05   0.0     15.30      1.0  0.005479  \n",
       "2012-10-06   0.0     15.85      1.0  0.008219  \n",
       "2012-10-07   0.0     15.85      1.0  0.010959  "
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "daily.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "With this in place, we can choose the columns to use, and fit a linear regression model to our data.\n",
    "We will set ``fit_intercept = False``, because the daily flags essentially operate as their own day-specific intercepts:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:53:34.084872Z",
     "start_time": "2020-05-28T09:53:34.073512Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# Drop any rows with null values\n",
    "daily.dropna(axis=0, how='any', inplace=True)\n",
    "\n",
    "column_names = ['Mon', 'Tue', 'Wed', 'Thu', 'Fri', 'Sat', 'Sun', 'holiday',\n",
    "                'daylight_hrs', 'PRCP', 'dry day', 'Temp (C)', 'annual']\n",
    "X = daily[column_names]\n",
    "y = daily['Total']\n",
    "\n",
    "model = LinearRegression(fit_intercept=False)\n",
    "model.fit(X, y)\n",
    "daily['predicted'] = model.predict(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Finally, we can compare the total and predicted bicycle traffic visually:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:53:36.008945Z",
     "start_time": "2020-05-28T09:53:35.520348Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7d+/G2rVrcc899+Dhhx/GypUrcd999+HZZ5/F5s2bx/a2cxCEUvQl9HjrguDO+cciIRR5EYWSGBD/GYhy4peSIOHXb3bixsvnobWhCoBH9i8HcRCl1LzxK/f8cJ9TxflzXAitrQsqfm6mWW45Yfvr58BxLDb+0TLtNwDc+vHKrZsmE2XFPufOyR3/i7/4C3z2s5/FL37xC+zduxcf+chH0NjYiOrqaqxbtw47d+7E4cOHsWzZMixZsgShUAgbN27Ezp070dvbi2KxiJUrVwIANm3ahJ07d07um11gONeXxv4TQxrhKHmYu3GcvNrFwHJjRqIcgR0eLUIQCU6dr4wrVnG0cwS73unWrHzUU4Mfwh5MmYmB5BF8rsRLKBmYt+NdSew/MTQV3TKhLFuYTqexevVqfOMb34AgCNiyZQtuvvlmtLW1aWXa29tx+PBhDA0N2a4PDg7arre1tWFwcLCijnrZq04W2trqprxNNwykS6ip0e2va2qjrv2rr4sBLIumxmq0tU39d5uJmEljWV0dBesisjOiri6m9bu2JgqwLFpaak3WPiLDoqYmivq6GIqiTLkHR+W50thUg/qaCAaVuVNbG3P9DjU1UYgSQVNjNZpbagFKwXEzUyU4k8bSCeo6Vftp/f3vu04gHGLxJ//lMgDAy+/2mu5PFcoS/2uvvRbXXnut9vu2227Do48+ijvvvFO7RikFwzAghJiOpeWuV4K57uSVyxaRy5W034lEDo0x5+HLZkvI5XkkhrMIT0NikJmGmTaWmWwRvIfYTkU6zOLY6SG0NsSQyZaQLwqIJzIo5XXiHx/OIZcrIc0xpvkBQCs7kswjlyshmcrbvsOBk3HkigLyeR6CSJAYzuKdI31IZUq49eN2b9XpxkwbSxW8IGE0x6OtsUobh3g8A0qp6bcoEdNvALbfE4VxO3nt378fb76px6uglGLRokWIx+PatXg8jvb2dsyfP9/X9UQigfb29opfZi4jYuEUJQ+lF1uBjDfA1MOvhUs8VcAb7/ejezCra2Itj6oMkVONqoJXFfc4pWg8P5TBSLqoK4UpkMqUbOUCeOOtY4N44/1+0zcmlNpEbcIkRCQdK8oS/0wmg+9+97solUrIZrN4/vnn8U//9E948803MTIygkKhgN/+9rdYs2YNrrnmGnR0dKCrqwuSJOGll17CmjVrsGjRIkSjURw4IGeueeGFF7BmzZpJf7kLCZwl4cfxrqTrSYipwKknwNSj0nF573RcI+7WJyVJQmvmJFjBnnxdbUbdBETJvV11zkxHCskLAaqprXFjf/W9XpvDntfGTymFNNIDSsp7Yk8Eyop9PvnJT+LQoUO49dZbQQjB5s2bcf311+Puu+/Gli1bIAgCbrvtNlx99dUAgO985zu46667UCqVsHbtWqxfvx4A8Pjjj+OBBx5ANpvFFVdcgS1btkzum80BiBJBhLXLjlWJmh8FX6EkIl8U0dJQmY1wgLFjLHuyNpSWMWUKo6gr9oMdKSFRdbW5HQfOv2sgg/kt1YiGzfNGmzMzhzGdVXD6fukcb1uDXmNPckmI5/aBbVmK8PLrJ6GXZviyA/za176Gr33ta6ZrGzduxMaNG21lV69ejRdffNF2fcWKFXjuuefG2M0ATnOGYYC+RA4LWqpNOhSd8y9f72uH+lAoibj14xeDUgKGmZlKvgsJ43FssnH+Gntvr1OQCLIFQZsHuYKA907H0TwYw5prFprKqrNnrjhdTRasolbrKc/r1CfxcrA/mpV9eSilOHAyjosX1qO5fuKZs2ClzxY4LMrOgQzeOT6IrkGzokhdyH45fwAQE93gD7wAWrKLDwJMP1Qdjy00BFRZvX2s3zo6gN/tP6/NA5UwGSOKqmAMMv8AlUP9flZdXLdlbXqtSalYkP8RjuFIxzB64zn0xLN461hllpF+ERD/WQKnKaN5DvJmy5FyMn9KKYTOd0Hyuh25OCxHg6SFmWdJEUBXFLpx5n68d71QiagwgB0aw2UZh5MWXw3jfUGUkC/qMX/EUl7+BxfBmZ5R7D8p2/4bLcP6EjnseqsDRX78eoGA+M8WOKxJdaGyFmWwLn90WchCEUNnT6L/nd9pl4zH1dM9KfTEg8BwswHqZkApwbLEG2jOnnEoY/5tNR4AjJx/QPzHBBcLO9Zi0m7cXHcf7MNv9+khuEeTowBkxTxDJcdj2Hsn+jG/7xUUzx8bd5cD4j9L4LQkVeI+lCyYFq36T1cujmGRGC0gMZJGSCqgqjQMopqoMcDRjpFp8TgMUB6UAr3xrGFslXGjBCwV0FDoQW1xEC3Z09pEqISgBwZiYwMD59O21Z2JEIKWzClExCzCiVNgiIhYJASW8ChlM0iMFlESJFyUeB1tmZNoyHcjJMnXkpkSIqLMlPHDfTjXlx5Xn4PAL7MY6jyLpwoYGMljQYucpUlz53ddyfr1Jan9AJEgtV+iPDNp3Q2A8XPWfcM5nO0dxYeWNeGDS5u0ScAQXXzQmjkJBgSjVYshclUAJaguJZCPtAAM4+n/EYh9xgdr5FTjp37z6ABGB3qxoNiH+mIfAIAlAgrhD2DZ8F5kAWQB1HJJAEBtaQAoAbXFQew5XI9MnkcjkfUCZ4d4DJYSWNhajVhkbGQ84PxnCZyIRsGQmckYK8TNJtxQmfZPTuEciyUBAyN5FEo8FqQOoqaoc/77TgzhtUN9Y+57AB3jJa2q/FfV9zBUHj9W0ok/o4ypei+aOY956SOoLQ2iupTw7p/pBBlsBH7hJmo1fsPBkTzCkmLRo5BejoqI8knTM2zRzNGHCI9MXvYj4JRNnjCyqS7JpVDa/zxIzlyHHwSc/yyGk9UGYJQD+1+83QNpRIUSMJRATEghJqQgSh8GyzLoVeT/hFKbDDNAhRgnPdWtStQxllyr1TYGIQ8CoC1zAgDQ03QDCKWOqT+MU4ai0vQgcwO9iRyiIRatjVXaNfU7WU9VVdEQcgVjIhdl3BgWDCXyGIkF0zPWsWSgM3bqCY+qOpqUzJSR9BDyXUdACUXdlf4caAPOf5agEiaMAmCJqD0jEYKDpxOmk4IVjEJEGKqXeWlvJ/YdH5Ibp1SzKioJEo50DAcexGPAeMUqekpGgrde3YPhITlsitNGz2pEw0zCOSq4cqim68HwOmLf8UHseb9f+13iJS0/svW7RkJWEms+lzMgYAQzE2cdS4YShMU8QCkY5YTHEREMlSCUeHQOZFCSGJw9cRrnTtkV/m4IiP8FiEghgWXDe8AV5KNg/3AenQNpHO1QU/3ZV7VG/CVzurn+4RzaMiewbPgNSJJc5nhXEmd6RgOLoGmAevASMsOoGjmFSOKUe1mF8weRbNcJsQRyoBSgxMRkBPJ/f9hnMI4o5+TFWP9SoolyVDh99sXJd9CY79I4/2o+gWXDbyA+kkGRF9EV108PhFBfjFlA/Gc4SoKEoWS+omdiBXkysrxss69OBM0L2DS75GsqoaCiPddobWkQLBVx4mw/tr9+TgscJ3jELA/gjImip8XR8rH+1Q1dswhSwFJJ7oehL3WZDixPvAYq6Sc/+cBH0ZvIBac8Dxj1bdbv5K5cV9YkJQgRcyA9t023vtirb+jqs4zcdrGkr9sX3+jA7oO9ZfsdEP8ZjjePDmDvkQHfETrTOR5CUVEqqUohZTI52Xcbj58AIImWXLCGiTiUSAOUaHHeRYcIhZIoIDPY46uvcxFO4pmIkMHy+KuaGZ8XtLGk7jl7VbAqobA0yVDJRmCq8opC3yB/ppRieLSIfccHcbTTPUF8AB3WdWpftzrRB4ComAZHzGPpxiBwRDARfwAIUZnop0bNnvmjHjmdVQTEf4YjowyiVwhnI/7wbo8e5lcR05BiBg3582DV0XaYXeqkymYNpwxKDdwj0J4+huWJ1zS5s1OUyK59e3Dujd8il6rc+mAuwGldNxTkzTImjJZ9Xh1blthPaFYwmjLY3Gpb5oTM1YOittiPhnw3CCPnCGAFI/HXn0llgzDPfmDd3AmhqOJHEBbdw6aEJfPJ3stQw3pKgCKmZWn5/BBWBMR/hoPxILRuUC0BEiOjeHn/ecS630Fz7myZCSLXXyroyqewlDc9o01SLVaMfUPKjcocoihOTVjaWQeHYVRPXdRjOTJUQhU/rNmNcz7C/uomn07doKAUaMucRHPuHIgS0M+o86GgCCkKS14IRHxjARVLmD96GPPTR5QL5dexl4jNulFAEdM15Tsr7ltA/Gc41NANKqFtzHeVdeFnqHq0lJArCJoc1xoGQilt+L95ci1O7sP89Pu2J8RSAUtG3kYo02+7R5V+MuzcnlpDybxmm22EU7x8leiz1J2bb08fw/zR9wG+qD1VDuo8cGrz0JmEKbGIKCqbvGGzN86piYglMxdgpdshRe/GKpu1H9PZSrQrTrH/G3OdWB5/FVmH+WfE3F6hswCqjlbl/JtyHZqYwPUZheNjLTbgLCgopeBPvGarn3E5FTjJoZnMIEJSAeGM3fFLyx41x5XBe48M4PcH7OPkxfix1J3AVvPyiYpQ/9+VIzwYg8mvCsKEMJQs4FiHLsdn1FliqJ9SaggV4rvZOQ1VZFNf6EVIzIMTZWZK5NT82+U/ZCX+OaOjdnFSU74LAJDPeuuQAievGQ41ZohUgdhHUwqptttKHdHcAEBbQIx2xWNY1LQkTyrqIPahVAIDgJDKZZBzAU7rWtusPUU5qh2+crLyMXANhfOoK/aDaZpvuq4yBRKRdALgYBZqMvkPzD59QbaiomjJnkYLgEK4CYC84UaFtOcGr6KSjdbJMkhiw/LGL3hbCQac/wyHno/XP8en2exbCEQsfhwwcHOAs0igLJSY/1RwUAIqRIRIAfF3BkWMT8rxd6gehoEBI4+X4lAnF6WoLQ6YTmVOG64XWCo6EAhqmweaOMIk9jGGeqio2TmDIi+axHvUYkMbFdVQDRQLU++iMd9dts7xbrSMdlzznisB5z/DobnzV8D5qyZ+YamAqDCqKYDVRW/EWOaZKtJx5O6pmUMNYAahwPz0ETBUQrpqEfhQrcaJh6U8lid2gzAhdLV+DDWlONoyJxAxWoqIJSxIndAXuA8w1L7FMyAWIqNy/gaxj+FuwPk7473T5lhJhJrl+uo4sRWI68YLTXdUZsgC4j/Docv8bZmgbfFi1QWqxgKJCSksTL0HTkkB56T+Gxvxl8DCmQtlNM4/IP5u0Dh5TTEvfyvV1JOlIppy5yCycuyYan5YezaWGwDnwyTUCKchZomIWLpL/62F9zDK/AOi7wVCqUlpDtg5f93iaupPwuVO9QHxnyWwHt0ZUFhDcxGNmHgMOiEmajAWsQ9VOX4X4k+VMolUAbFoCLVV4YrbuFBhJKaqWI4BkdlFw1AYxQNGC6yxEGNOKsIqaV468iZqYmGoZwrNpNdIpALC74k9h/ttwRXdPtlY7PDHD28GLJD5zxIYlUAMGDBUAkMlcJIud9dpscsMpAClBGf7KuMcbX1RG3I4yqoETZIk7Hm/H7/bf95WZi7DTBx0zt9v9MyxxNsJlZyTfpg2IuqyoRMJrZmTNi9UtS+2E+kcglNUXbfNeVo4/zJzxTfxf+yxx3DvvfcCAI4fP45NmzZh3bp1uP/++zWHnr6+Ptx+++1Yv3497rzzTuRyMl+RTqfx13/917j55ptx++23Ix6Pj/V95hzU4bM6fnBEwPzRw1g68qZ2rRxhoAAkySrrrRy6NZH7wq9UMTlXYPzyOudvl8i7Pj8G2bGbjb7TLKDUbO1TSg6irtgvZwazYN/xIby0t7Pi/lzIIIq1jxXTw/l7wxfxf/PNN/H8889rv++55x5s3boVu3btAqUUzz77LADgoYcewubNm7Fz505ceeWV2LZtGwDgn//5n7Fq1Sr85je/wZ/8yZ/gkUcemYRXuUCh2VkrilSGAxggKmZs4QB8EfUJOMqHBcV+mNrlnWrtUmDqCUAeN9PGTZzEKg7WOC6YSBm8Y4hvw6Z98EwChzrkAHJOnH//cG7C+zTb4f4tpuEblbEZLUv8U6kUnnjiCXz5y18GAPT29qJYLGLlypUAgE2bNmHnzp0QBAH79u3DunXrTNcB4NVXX8XGjRsBAJ/5zGfw2muvQRDKxyYJoE8ZdU4JXA0YmJWAKvvGqGsAACAASURBVNyY7WHleEqVsL3j75PuEGSa7FTXJxCHoG9zEa++14sX3+jQfjvJ/GHX3buCTrK3lXZioxQYOq35HljDDhvhN+jgbIcgStj++jnPMhQzJwEOY0kSY0VZhe/WrVtx9913o79fduUfGhpCW1ubdr+trQ2Dg4NIJpOora1FKBQyXbc+EwqFUFtbi5GREcybN8/3i7S01PouO1Foa6ub8jatqK2NguFYVEVDYDgWkXwIYZFDdUhChMjfeh4dQGPDYjS31KCmJopImgNH7EMbi4XR3FyNSHhi9PzhEIu21howrBw9lEoiwmH537GqEGp42atxJnzHqe5DTY387pLyb7V9hqPoV75/dVUYbCyKSCaEMJXA+SCiJMohIkyenQYbYbGYPwMhXItGXlE6h0MIsdT2DdV3bGqqQSw6dbYj0zWfRtJF7Z3dUFcbw2g2gkh6+m1pavLekQA8e/gf//EfWLBgAVavXo1f/epXAGRlH2NgUyilYBhG+2uE9bfxGbbC2C/Dw9kpjSne1laHeDwzZe25IZMpolASIfIiSoKEhpIITpLAlIahHsSrEyeQOd8EDpcglytB4EVIDp6EhaKA4UQGvDAxcVoIYREfSoPh5GlEiajVPZrKI5eXI0VO93ecjrHM5cwOcGr7IyP69y/kS8hLJfC8AAaiLw66WBDATtD4OSJfRDg/gjAAo6CHMNT2DUtFAaJEMDCURk1saiy6pnNdJjMl27hakUpzyOdKE7bGxoNi0bsPnsR/x44diMfj+OM//mOMjo4in8+DYRiTwjaRSKC9vR3Nzc3IZDKQJAkcxyEej6O9vR0A0N7ejkQigfnz50MUReRyOTQ2Nk7A6134oBaZP6CICCx0giESQCga8t3uLuR0YhWxlAJHz8Vx8ZI2VMdCps1ZDDx8XaB/o4iYBauEw7DZero9PcnydepieWRVSh/vHNEsfZzyOlyI0PxoqASAAWXsDOxsUn94st8/+9nP8NJLL+GFF17AV77yFXzqU5/Co48+img0igMHDgAAXnjhBaxZswbhcBirVq3Cjh07AADbt2/HmjVyIuG1a9di+/btAOQNZdWqVQiHA9tvP9Byq2qTyk2qSEGzCTTnzsGNiFBMLPGQCEFHbwoHTg0pfTU4CEkCGnOdZeLVzD0YvaKb8p1oyxwHS8UK5MSTTF3cFPVG1Q6lOHlezyQ2VzK6qQzYRYnXsTi5z3QvxicR41PKd5ohO8BkePg+/vjjeOCBB5DNZnHFFVdgy5YtAIAHH3wQ9957L5566iksWLAA3//+9wEAX/3qV3HvvffilltuQV1dHR5//PGxNDsnES6NoD7bh+H6DwGQyb4boShrLU7phIdnDEsFzDu/D+drPoaBYgQR5Xo024emfFoxcbtsQtuc1XD4/gwlvjW+1kxOEw3GZbM2cv5FXnUII2CphBI/N055xqELSWZl6oLRQwCAbNu8MSp8/Z38JhK+if+mTZuwadMmAMCKFSvw3HPP2cosWrQIzzzzjO16Y2MjfvSjH42jm3MXramjYCQeI9JycIpzl+vsUtI2ukGM1EHqeHtC+xcTZG6n+8RxDNd+AMvUriiRQ6fDuWU60RvPuuRNkOF88vJv7jPZxB+u40XRl8ihsTaihReflz6Gaj6BfGnT5PZphsDJ0qq2OIBiuEH73dK/F+nwpZXXzTAVxWuaCEy/SjqAJyQmhBB4RKQ85o8eli9yDtI66sMBiBItteNEoSnfCRoJwbYjVRB6+ELCvhOyCCwqpCGyEUhczHR/LE5aRjBlXPbHC0YSXUfsneODCIdY/NGVCwAA1bwc1Cyft3u6XogQrcSfUrRlTpgucWIBDWLlXu1UC94+cSgXuiUI7zCDQSgFofKUMEZ2dLGhKi/PlxO3TiL0ynXl2NyQB1uxMPUulo68Zb8xXuI/6Zy/9wQRRAKpmENdoR+EkXlHsegdN/5Cgd3a0P6tKMrE1nKFdVVPvrdAQPxnMAihGqdny93pgHKWPJN2qqQU1DJX5xa/XwFciLffpT7ZxN9XoL/z76E1exJaCtBRezrPCxHWnBpOp1pBIGM6nVFrhF6/Xn/jQED8ZzAkQrXFHpa8vfVkzr/cpCOTQpTVCDXG6aoySYxT9vBZDokQvLz/PAaT5Tdkhkpmi6dxKtwnW+zj2bbyHkTJCS0qIi1SurA4f7H3GMSug9rveKqA7a+fQzpn9nJ22ohFQlDFj9iul4eF+PtiB8a3QQTEfwaDEKolgQgRb7mqHEa8nMyfAg62yROBqJg1xX/RxT4UhWQcueKFE84jXxSRKwg4ck5e5IlRmTg4JWxfMvI2lg3vMVyZoKB604CFqfcAAISVbbrU8aZEQjJTwptHBqbUEXOyIPWfhBTXQ3KMHN+PpcNvaGFSVDTlOyesTTux9yLs8r1yp4NyJ/2A+M8AUEohxTtBxZLtusrphQyhm90sQ8rFfWGkUpkNYuycRETMYFFyv94XZebVlBI49cp/Ys8bh7R7mTyPvoQ98fRsAdVONfLfnrj8LolR+wZtDYjmejrza+3jm/OfeLFBRJLfU2JlHx3t3SjBe6fjGEzmkSlcOJu8imi6CxwRbGIe05ocLyoQ+6gbhb/TgTtmFfG/UKMH0kwcYtd7kHqPm64TQgymkuWVuWVTJxrzwzrdHqOc0alK67WQpBPG3x/owTvHB8fU1kyAnjGt8mfcvv9Ey/wnU2YsMaqDpvIdDI5hMyWo2URCHTLO5jk/kfSoAs5fG9s5Qvz3HhnAm0cHprsbkwIyqhBCTvd6ppIICM5yfrchD/ccKNuW13QdLydhquvC3KcBQLNzd4td5QQ9Ouv4xDZ+48JP5FhaYXMmpOIFPd7qiIWlPBaP6H4yTpF1xwrreHmNn35vfGM8a+z8swUe2fyFdaQk+RRoKQ+SSWA0x6OejWgDwr+/C7RYmf102QVY5j7DMB5l3D0Qnd2WVNlI+XZnGzSrD8Z6nWJB6qAjd04dci5PLpw4yYkZCJtVGSEAJQiLs1eUZ8RIpgRJIlis/KaKKVtVMQ6UNbwYKyo39aSe67X8aM8a4q9SNqfoobMVwrFXAABFrgb9wzkMxJK4si4OprYVEO3KQxXu6SK8h5vCzc5fJQx+JhxrJ25jZPtO96TAiwRXXNQ8puenC2r0TSv/RQiVPZ4d4Jq3ZZJQjjCMq25rPmkqoSF9Gq2pLkBYCmhBPmYHSC4JJloDqfcouEWXY0ix4tKIv/IhOcJjsvzVbWI6L5m/Nrblwrl43541xD9EeAAsJEIR4i4M4q9CFSOEsoMQTvYitPQa7wcYFrBNQ38OXI5cuupa7mEJpJZx9EQc42Z8tEO2lpltxN8q9lG/qZeliybyd7k/8fyMf4kuw7CViaOsmz0hiJZSsnjEI+nLTAQtZiEcfxUIRQGx5KhX1AwpJlW2VYmp58RMllkj8w9LOUSEzAWZMFolGmHFnJPmvROsOynzKHHj+8tPFEaZBt4EyF3O6DUmfqbpbFPkEwvnr8LrLTr603IWqCnKbVyRPqLCnYfYTn4SrG+fLQh4/VAfBHFmx3aiSgwqKJZ2tGjPFaCtrEk0Y61E5q+Zevqo1Quzhvi3Zk5hUeoAhAswdrjCSEKNByYlOuV/uBJF+8To6B/VcqoaYZxE7tX5Nx1z3Hh8EO/6orsXKK+MqSgRdA6kyyain25o+ZRVqx8ioinX4R4OGcCxTvmUMxHT11cUmIoIemXE30r7GcAW2fNkdxLD6SL6h2eZA5ikn1yI5bhGJzFIYUViH58K3wtH5q+AiCJIsQQ2Nv2pAScKKkPhX5rlg5tXsqvBIvt1JNTKRPOiF7pGYGxHzojonn2pxEuIhjkcOpPA+aEsamNhtDZWjamdqYT6KauSZ4F8F0LpVrhrarSnxt0uw5SXQNjCBYBxDbLHMBWG37OJiCg0s09lfpwfylZS4zTC/c1f2/UKbmxJlTXTnQjYT2pepp7li/jBrOH8VUgDpyAc+R1Idiwu1DMTqkzRGgnYVbHrRKVtE9Pv0RCAllLTfTbpk3Pi9S1FXrafTmUVj9EJb2FiQSkQFnN6YhaFGDKSB+k3GCw4oSI+3Vdh/0u7ErFPU67D4WRGHf41S2DrsP4tmvKdkAg1KOsrPbZVMKoOm7VbfRNl6jnriD/NJiBIBFIZufhsQlGQiQjnEQfeCMZPiAYHYu0a1NPX4h+/V2GJl9A/nAMnlRAV0tp1NTmI+vozPUQAmx3E4uQ+VOcVUZb6/TzEAhpv7fJqlRBgb3k+Y/rjrz7/ZKAx32Ujgn6iWGYLAnriM/E0YOm7l1jTQ6znXPPEit6obU3PETt/FaJE0NM7ihCTwBXty6e7O+MGpUBeiXvjd/27TSqBq9ajfzpW5mXq6Q/jMbN9/9wweuJZLEvuB0sFxOtWoCnfBb74aVBSDUah/jNd5s+UZN2KbteuCMQ8lbmKWKSYdrzrR44vC258khQrQfcw8zcTFR9qRK/N2eXWK+/1yrbzbbVl659RMCyZig0TKnGtsKwrpyRIEx3zf/YRf8V6IJmaiVxE5ejoT4OoFhF+J5cfAqzJ8cvbezMMW9ZsWCP6FRIKIyFX/81SebNrzZ4GQyVEe/aBj5fAhm6Qy80wzp8SAkg8mLAlMQvM34R6xN1hKEFMSGHkzPvObfgYU1XWz3iMgS7bn0SFr6VNxiDzd7M5k6bRSo+KPMhID9i25XbmxYcoR5f5V/oOLOA3FpM6hxQ/GtbxOcbpkTFj1ol9REEmHCxmf2Lw4XQRvMkUzh/Rc+L9jAtQvSL/0cuKEnXmqv3I87Ui/kVEVljFWgInK3WLqWH0D+fBKZuCZCD+VBJB+em1GBG7D4I/9BvNs1UncFQ3FYS3+GP+6PumhDw2VCT2UVt3eGZMEgHWvT4F1HCSsHH+xvcus3FP1qmOFyQcPJNwNDuWeo9C7D4EmombrlNJhHD6TUtpJ7GP+o8KiX9F1Fn+vmqCHOf0p5bBHSf1n3XEX+Jle1yf4vEZjXjK4io+Ts6fMRVhTH8BgBclZ7lrJcpcjUPxRyi8oE70fEnAaK4EqaT4ORg+g3D6DfCHd/mqb7JAUopsX3FgUt39w3wG/KHfIJJV7nsQh6iY9szJ4Efurh2+tAuOpZT/W+vzPNaVLWK8yViiWRpthcp5mU/Wqe7k+RQ6+9PoGnSw01c3bd7y/SUHhzRHmb9W0Xi76Q5l/KmSh5s1tJWo/SBS1Uu1Ncd4TwDfmHXEn/BKYvBZEj+QEgli7zFQJRGGHL65A9Rp4hmoniiRsnb5nnAg/u5l/UwD//W5cZDW97GWEwpKyGAj5z8DrLoYVl6QEM1jFhbljZQVFe5/HFxtRcpBD78MbV2MwXzIbx/CBeuY6E866QOMGbAmy6HPK3wGE1ICJlrXnE/OWdvQJpPzV8qKbBQAkIvN025lqhYgWXMxNKMLX5s1ys5HX8T/ySefxIYNG3DLLbfgZz/7GQBg79692LhxI2666SY88cQTWtnjx49j06ZNWLduHe6//36Iokz0+vr6cPvtt2P9+vW48847kcuNLQiUeqybLeF9pKGzcnKIoXMAAJodhth1EGL3YXth1RwQwJleZ6ct+b6LMtc081WvXT+yZD9in0osDXxaLVlWarQwhMZ8F/JFAUc7R0ApxUi6iLO902zZxconFOMG7oTyhM3jfgXiNC/Oz2oRwof8KFgrYBTgRlPcqe+Bk7q4ZbIcnNWuv39uWNtsqMhD6DwA7VsUi/j1m50Y0ZKy+GFkDKi085UkTlJeQOBi6Gz9OFK1dmMWtS+6BNa7/+VmY9nevfPOO3jrrbfw4osv4pe//CWeeeYZnDhxAvfddx+2bduGHTt24MiRI9i9ezcA4J577sHWrVuxa9cuUErx7LPPAgAeeughbN68GTt37sSVV16Jbdu2lWvaEXpQLQa0mB13iNxJhxagTRko1VxMcI/YqRKRkuBmWuYy6CaRv7tccKj+ciRqL7OX9YBOb1T5sDv8my2aa6krDqAp14EzPUmcPp/CSLqEoVQBwnSH9OAUuwiN83cx25xkKyWdrHuJ3ORTCmPh5j175mPzt6qV7QXc/RgGR3SdzWTJ/I09H1aS6khD50AS3ZASXQCA0XQOgkhwpicFaeisHNPHVpHH3B035+/FXCnMGqXyGDr2w8noYuwoS/w//OEP49/+7d8QCoUwPDwMSZKQTqexbNkyLFmyBKFQCBs3bsTOnTvR29uLYrGIlStXAgA2bdqEnTt3QhAE7Nu3D+vWrTNdHwtUmSEnFcAfeRlS/8kx1TNlUPKdqqIDLXSDA3STMu8qnYa8vtBvTvWoin0cShdD9chULYQUrlWKVuAQNIGcP+uymFTZuDVh9nRBHTtKBJD0EMLpXudyZdz/64oe+Sh8iefKFyUK8bfbhJev17sP+j2n6an7MVi2CYt18WQRf1bI4KLE6+CkIsIhTm1d7Zz8iy9gefxV1I+ehth92JchgUlHUWHfbfF6fH7fskXUjWKc+Zx9mXqGw2H84Ac/wE9/+lOsX78eQ0NDaGtr0+63t7djcHDQdr2trQ2Dg4NIJpOora1FKBQyXa8E4XAIJBzSXdtDEqproggji7q2yQn10DYB9eaGwyjlo6hpbUCommCUHwZqogjXRREJmz9/LBZCdU0Uokhs94yI1sZQ4q33KYzDGYqGIUohhGJhiMRctqYmComLIkIawaWLiFRFwBdDYGJhUOrcLhMNg0IErYqAkUIgbAisy9wTuTBCkp0QVtWGsaz7qPZuTJhFmLG3VxtjwUejaGisxrBStqWlBiw7dhXVeMZyoCOCVEHEJfUR5E6+gyqmiEg4hHBEHq9oXkCkJKGqKgzeY9y8EI1FQG1jakaIY8CyLGKxMASJOo4BE40hXCqBiXCgfAg0GkakFAJhObDEmcCw0QiIEAINhcC4BB8ytiUR2OanxHLgSAidQ1nQBgE1NbLsuqmpGjU1UY2INjfXor5mfCGfncay+WgcyRCDVnYUzc01aG2sQiFfg8JoFGwoAiKyKGRGEQmH0CQNIVQTQYhjwbIMzpxPIhYJYfG8OoTqYqZ3C4U5fb6yDCjxP740GgZjWJPyNzRbKarRctnqCELFEGLREGpqooiwBJGk/Kz6LSPZMEKiCFTVIEJyYDkK4jHfIpGw6z2gAjv/r3zlK/jiF7+IL3/5y+js7DTJm9QY+4QQx+tOMfgrdRYSBBG8oH84qSQinyNArgfFhe5xY8aKtrY6xOPjr1dIZkByJfCjRTCFUQg5xVqJLZjeBwCKBQH5XAmCSGz3jAiXuQ8AkiBBEkQQXoJoKZvL8ZA4BqIgymVKShlWBFzqZRgJVBBBSyIYQQRhANaW1k6GSAiIZL/HDPaAzca1+DcC4eWMZRYU8kUUxRLOdI1ofR8cGkWIC8ly3OOvIHTxh8HWNHl+AxXjHcsDJ4YQLWRQPzQK5EooFgXwggjCsMjnSiiV5N/5fKnsuLiBKUllnyWEgyhJ4HlWad8+BkWWggoi2FIRRBBRgqSMF3XNAsbwIqgggtAQWNG5D17jrd6XqIihRBbd6fPa9WQyj1y2pHH88XgGpfzYib91LCVCcOjMMKrS8revThxHPLESVBAhpvKQciUQVsJgfBSEArwgokBCOHImjlgkhGXz65DOlpBGCc21EbCMeQxzOV77rTrZmcHATahGGfnbG7+R9RtSsGBAUCpKiAoiSqyAXK4EkaNauzmFZpR4EUQSURBZQBARJsRTJMrz3uG1y7JSZ8+exfHjcm7Zqqoq3HTTTXj77bcRj+tKnHg8jvb2dsyfP990PZFIoL29Hc3NzchkMpAUblAtPy6YTmNE+zvdNuG0lAPJJfULmks4Y5YZOhwheZHgRHcSBcH7OFdT5b2ja+0Z/jiBY8vbd6vQRFIVKYetlfgLC6CKEE6f1xOjqFYkJD0EWspDGjhdts+25imB0LEfJJOo7DnlXYmVMFojA0yI/qm8Ca3OONm/nxCqUcpyljte8nymTAk/8DC3McCv2Ie66MT44T6IPUe03/2JPLoHMyazaavBUTrHYzTHI5OX2Q6WkznpIi+a/AKc+mYk9k5mrN6+EVaxDweAwXDtpfpFTZRnHlPG0ZZdUQorY1yItTmU0VFOalqW+Pf09OCBBx4Az/PgeR6///3v8fnPfx4dHR3o6uqCJEl46aWXsGbNGixatAjRaBQHDsi5ZF944QWsWbMG4XAYq1atwo4dOwAA27dvx5o1a8o17R/KmEi9x8Ef3mW3550kUEptJpv8+791ViRRaiJ+ThMpo6SpHM06Bwirq47gA4saUR3zQfy9TD0t96jlune1qj3yWIi/mfN0k1k6EVEtOb2iQGdClXOPNJcEGT4PsetgRc9p+hrRykl5ODtVCj/mlpoS333ZjtRcjMH6KyFEGh0f9ap2PFA38gWjhzBv9IjpHgXAEgERMevLzp9kEuAP/QZS0q5byR593bTxaw5vRomDpQ2bRzKnfz9jathT51MYtaSKLTukHh/P6mtBwaCjbS3SVYtM14z16AyRx6bCRtDZ+nFkapd5dm00V/K8X1bss3btWhw+fBi33norOI7DTTfdhFtuuQXNzc246667UCqVsHbtWqxfvx4A8Pjjj+OBBx5ANpvFFVdcgS1btgAAHnzwQdx777146qmnsGDBAnz/+98v17QnGMY4Kop1zMgAOCpzDUxk8kMCk/g5iN2HEbnqJjDRmjKlqXkmeXIZbhyxLPf1I1jQnLycewJADuYpwZ91jhb216Nea9u265SYDZJcOGWnAMPxZB77T/di3bKivKTGQvz5PERCEXIQNXlBfZvB4SwWQ/9+hFKI41AImhth9cZcqtE4fy/dB8MiH21FiySLXrwV9GpjPkw9y4QJMY5ZNZ9AWMxhXvoYIH0aALAwdRBhKQdCLsXvD/SgsTaK6z/ozLmS9JDc90IaaFpkuidJBIPJPBaIEsIhztFM2ShyFAkFY92jDWM2mDRLCkazZoJpvW+FV7wdyli+umNBNy2+h7UP5FPEePdsXzL/u+66C3fddZfp2urVq/Hiiy/ayq5YsQLPPfec7fqiRYvwzDPPjLGbZUApJEJwtHME7VEeSyenFRtISrbeoKWcK/HPFUUUMyW0gYJkh/UbHiIC97jr1n+4wx6Lx9wCAE2BqnqsesHKofgxW7Nd9sn5s0RAdSmBfLRVu6ba+mcyWTRgjJw/oTjTk0J9HY/lFTynMhp9Q6NY3Ab9pKmYDVZH1WVkfR8PSm7tmy8rKnWDYF1LMrZ/qPV71DwhTjPm92zMdyMs5SCM9IPSaoQl2WelKEjIZvPIZXOuxJ8K8sndiYGLJwtIZkqQBkexfFEzGFDUFIdM7RPlhJbK8ejtSaHWIiYlHtE5K/dA9nOkMm+yRmg6ANZsoeQk9dHOBD687P1g1gV200DNP2Smi5HlelMVFVI7c7oT8hPdSVTxebSIIkjfCf2GJxflxAVQA3fog1j78PBV29GmpWdZtVx5XYJrPRZLBzfOvzV7CgDQ27RKu6adiVTRC1v51FVNR9OZCsWCasYuVbekXFY3LzUTmVXI6pVAxQqjCM769T6wqAGEAh3DklrYT4UAoCl5JTYC1pJfV8vd7IOHrNSjXn3v84kcEKrWro9meSwb3gsGBJRe5jw/Vc7dYYxVGX0ylcOp3iyuapPQnjlmKqPOkVxB/WtRsnoIw50MELxAPU5E+vpyj8earlqE+kIvxHAdIjAwfgyLQrgJmaqFhgrNa897RMqP16wL72AEoVR2hLJEjpwyxy+N+LsvcHXA97zXrcWtl697Un/HOrxs9yXWzN2oZbyIf0gxBVOTkFCP6UBVW3eNJamc8x9JVebVXRc1VKkuWK+EKWUgSdoWAioUQRX9gZTq89QTqREpdWsZuy07AIR4c9ykUMiqdPWAx4kqxLGIhFjD5u9Wr+FZpUyIKD4TrP4xBa7aPF/8hgswtVSusKKgtyzFoVRB2zTdcz8rdRMJZNRsEq5y5sP9vQilulEo2OXaRDEsCXOqQQO13Pcg/uLY55etLkOkTjcM116Kjta1tg2dYRkMNF6DXNR+OtLX9vj6N2uJPwOgN55DR39atvKh+seOj4wtdMTYegFf8UoYKqFQMnAVlTgw+VD0WYfSS+xTUxXGDSvawVXJTl4RXhapiFzMVlaFxEaU6vwEIHOelV6mgo71OCnIrV62FcAYMyj19n+iZ/evQCmFeOZtCCdedX2uJiYT0kiYc2xaCydgea4yc2aPTVXxMKa2k5/eYm/TKnQ332ioTi4rcLI4MhOdZyh7Pc43r3ZuywU+JIOOIGBQU9ItADM5nbi65uNW2pIGTkE4vRdkVHeOI8p7taePySdEB2KtMn9uU9WWgN6ICpkLzmODZ2zE3/4RGYYxr1H1lOnVqDZV5HqdQnj4seCbtcQfoMgpSVBkBY5+fM05cANSss85mNp4oA6qD+LPUslEHLw4f+tmYtP/O0UetA62zSxQx7zmGixqqwWtkWXqUky2l08zdueZfKQFhAkZSJOXLkHpi8uqqytW5thHDI5i2jdRF6fDNxfO7YPo4fFtNOXrHspgZDSvzyHePdyGmlu5JqYQYV+9ByojriqhcKhFzSNgWPQfXNKERa36oudDtZAMm7dq6slz1ehoXYtCuNF0T40bD1S6SSldKPOIarVCKdCePqpdJwamhxACKjhZpCjfoiifpIxlWM5MbAUHvwRVpk8dHA0B87yy97uybF0hzut0Zyb+jp7RLkoa5zExn+aFcB16mj6MVNUSt6KemLXE32gjTixcNGNR6JB8CuLZtyGedwimNq5OaC3I/1esFJzQUDhvJlgeskU7XbOKfZz64jx5KBcBH6rFcO0HtHucaupW3YSulo+CX3IDBhquBm2ym44NNlyFrpaP6t3m5BMARzw4JFfKUBm33pDQx4slEuoKfSASMXHwRpCRHki9x0BF3tHfwymhSKb3XNl+Oy9JxwAAIABJREFUeMmILSXNPysgqowXd1hVL//VdA+SXHU4qjzh0A5rCAHg0o9UtUw0pJDVWMGhDxXblijE38tksftd8Id2gFJq9o1xqQsAGM6sB7A6MAK6NY/buNEK0zF6wtNCyuxHQ1i7iba+n6vjRV2rdTLJFkLVcKYIFzTnbw4TK8cQkV+4WBLw2suvItnbLRdQuTpHLmM8UGX+SvWn3kBJkJAvivYyMJMG3YnFgYt3I/4qHEz9rItMs+RhWPQ2rUK6arF2L6QQf45lQNgwWJbDRz5yNW740Dw4wmhDHZYJhZdDE6NZo4xTKGn4YvWjp9CaPYWhoQTO9HhH+eTf3+WYA8Ap3DDbc1Br6VxfGiXeIX2elslJ/euz92MSyjrI/Jddi9CSqyBEGuQS6ukn7GDObBE1qPGTrrnULjtOVi9HR+saEIV79czFa7NBKKdulOuq4c0OdQ2FHkMHZDt+Ej8H4firOvPkeao0c9qSk9hHIe5WplC/P5E6wfJjzCmGDqJB75Ko/SAG66/Ux0vvnUetihLfRxcuaLGPSR5MzEKUVDqPhsw5JA+/Jt+XeBR5yXHnHV8nVLGP3peO/jS6h3T3c9M8dlhbYYfYHDaRkGq5oVrLOJo5WhVG7uaAqmfv4rZaXLywHh+6qAkNNRGEQywStZchXrfC4SkZhOUwWrUE8cYrXcuMRYFYDpwhgYj8fTwIlcupyunEoCqBeUHC4bMJHDhlP71pHuSgyBYEpFycZ8rlK/CEjQgAy+bVYXFbLZhQBNy8D2gEna9fBLZ5MaTWSx0qUutTCTpBW2MVWurtGwXDKkpkRlH8e4g8rO9STvcTFeQNuoo3c/TNubOGOmWoXL+udK9ApOgg9tGSt7jMAy/iX/GU9eE9pyrXS2FdrJqpWoB8tNUuTtUedWAKXU081bljyLbmQzc3a4m/US5OKVFE/vJHCCl22Wrci3wuj86BNLoT7nLdMcHDzV7rn5FrNt231uFwT2/I/DMUtRawu5IrGwQj2glVSBFisyyDqy9pRTSshgEGMlULkY3Ntz2j1s4yLEZqL0Ex4h5XR7NGcC0xFphrG0vET6dnRJVQqKc3ByWkca45ZkJzQ0VSLrvCNxzmbDbqAAA2gvDFN4AJR5RmHOafmoNAM/n16CYnt6FaMzkniTH/qxxxMZqYloU6LuqJ1tq80Y/OaulEHAi8qm9wke1PrNjHy+FO0UFGW9HfcA2yhtP3DSva0dZYZRsX7fTlLNtVqnUeU4kNI163AkN1l/vq+qwl/mbFEUW+JOqyNUnSrgMAzysBkkpjO+5RSXQ0AdN2Z0ptStrhVB57DvebxtDJKshphy/ylgltpQtOxN/KOSgiAVayb3huFgqePgGMeTMzepnG61agv+EaQ+GJn1bWL2eV35d4CSe7U2aLKmsdDsQ4mSlhJFPSxsbpG2hmphUaGFUk9nEgfOyy68G1LTd0hHH+6wAh2oSRmov1vA1OimTlL6nAZ4J4GBI4wcvCSxsPlYBrhL0Czt+R+Htz/hOTUab8GBg3zGKkyRSvZ1FbLT561QK9sHavvLWP294osRFkY/ORi/mLmzZriT8snP/ug716HHjLoKubwFjz/gpHfw/+4K/tNwzEnwx3m24dPB1HYrQAyci1ONTt6aqvl5L7UbcQbH0bmMYFrmU0KMrAfP1yW0mV87ciEvLoi/q9tf7qdWRj880nAbY8t1kp7LbaqjUJhdB5AMnBflBQDKe9TnfO1HtIceGvK/Q5LrpyYTfcavfjOa3DzvlzzYsRWrbSUMKq+Hfn0BmWwWj1UhA2rBR3KKtOX42Z8COu03VJfuDLekbhxBmGlRmtfMpSwPBlLYQ7mnewIFOJv9PGAGcmrFJUki9BZcxYZV3UGGJzqZso4WRHuGy03XTdqR7noG8+T1kGzFribwwNQAgFQwnCkryIqSUAl6TRrbFRI/dIobrMX+x813SHc/qyDnOO80P8lW6TcA3Cl30MDGcXBUQiZu6NBdDR9gkU6+3BLtzaNE64XNTMPbAa3fHhZexhuTJWWBcskUSIPUcBoQCS6EakZ59Sboz1Q/UslkD5Aogxd7BSaTQfd3zWVInxZwWvrzrRecrd1TFwECmqUJX5jInvZBxj4Kg6EBJrwFD95Ripu1Qr09XyR+huXq1XbLVZ90n83cJIA3K0TatTpnjuHUi5FOKpgqOOxsoEGMebUf7TxD6TSPz9rANWtXhSle8sg09etxifvG6RrSzhIuhoXaMZZow4MDHWDUF9DVWhXCnxn7XhHUymnpIE48pjLPb8qn23C8NrAy1mIRWcZPGWvAQeHr5hUkSDE1cCIF8SNS7by0nE0JC5Pac92zIxvPYU1mPCXrG8GeEQi4OnPgTUfcjwjGxfpSmSHRZ/f8NKNOU7EA7FwNm75AjnGOl2EGL2PyaJTkiMoNn9q8pwr5DBTtY++k35DycJyOz/NYqChPa1n1MfLNs/uQqrf4Z/eyc1q5q3Ca36BdxFVNqpzniL0TcDyjC47rI2RCMc3jwiO099cEkT3kqXUB9KAgrTTWyExEr8/Yp93In/SKYIiVAsrJHLjKQLYIYGIAq8doJra6wCKIVwbh+4+Ze5+sBoXaQwiH1cZP7jp/3gOA4SEeHM4Mgd0RlU/aTWYElko23JDMpvqOqJTzM+U+gaVTzVDQYtfkZn1nL+xmEXJWraDKxyRlU/4Jfx54+8jNF9djEPzSQgdr5nU+bSkl0J2JQ8iubcWU0UpWJwRI4/PpSUr3OORwQzbEohx0csxN9LFumxM1y6uBEXza+XGzXUoXfTvd5ipBH9jdcC2iT0Rf19wRamV7WhLsne3Jpfg1FCkLFy6h4bg/KXoyI6BtLoHzZ4iaucZJk+ZgsVhgM2luUiKESaTZZW9iFUiYi7LXhIYSqMAcrMUh8GS+fVYV5TNZYvqEc4xKKpLoqbP7IMDbWy+Mer2+oW7N+SyfsjCKKkWWcdOtGLnsGUjeOnpRzISA/Es2/p+hf1HrW/J1cYloMouih2vZkN7/eKhjksbK1BWDOS0MtTy+bMR2VRaDFcP9bmTNDDvJjno3pd4KodnnLHrOX8jWDO7MayYZ0A24m/Um6c7Qin9gAAuMWXy0pXZbCleKetrMrxRES9XyVB0jxKVUIRCXFoa6hCfNQ9tozKQep8pJP2zkr8VZm4vehYpF+ag5HG+XsVtvwtU9QPjWRgcdxjwgAtgZbMIjkjMRBO7UX0+j/2UTu0XrCGdihfUAjI2FhFY2yXcoleGIbFQMPVtjR/lkLGrkKPF69/aDWejS1ujvaoXvaaD7Timg/okVMZB2VuPtIKwnCoIWntXQCA0PF7ccj9geZ535TvlOtWdXTqRFXjSpXyoNQs8rTObwZAurcDXcle0JB7uBLvHrkjzLGor44gpaxj40LoaboBUSGjBZrL1V2EJGnTTMyd1kxFcXqs1oXKn9GqxbKyN+rip+OCWcz567Aq763RC9WvRCnFqfMpvPKecwJu31BmnChRJDMlbbqc6NZtmiWH3LRGjkYTTzAsWhpiiHjGCDH/w4/uwovzH5smVu9v2bbZykQDfmAlniVBRKEk2kJ2mImB/OPAiUFsf/2cp6w3q0R+ZA3cIn/0d+CPvOxb7GNFJQpfVYlnzlNsPfKZOT/NzcRQLhZRCKXxVRm9Ji+5sNNwDTZciXj9h0At83kCJCdaRRJfMp20VJGPNodNL2OV+Rs4f0P/03l+TLL9ck8wjGWcDOtB5KqQi7XrQfRYVnaidDiVqqiMEXMW+4BhZfNsJ5G0By4M4m/5qhFJn0gkPWT46gTHOkdsCRsqhlLfmYE8BpN5Z/NChyOnzYQTqEgyoido0R8aaLga55tvtMl/WcM0XnPNQnzyOt3GeGy0XwlhoRC0aETfrC5Z1GBuW3MwK9+QW2wTWzkLAe4ZTKNrMGNz6HKS+Z/s8godICOZUQiO8dSo1M2OMZJoJU5e6ndgDYopV7GPJnW0m4defUkLPrSsCW1NVYanGDBcGPG6D5pNcl37Yu/3aN1yAICgxA8iE0Q6KKWIpwoYzfGwE3ZgeLRo9umxrCsv+u6p4xnjM+qn4TwYnJ6mVfKaVAZGTbvqtP7DIfNaWTrPHl/L2jhjEfuo8GT4HHBBEP90zn1xCqfeAJuTZb/hnHvsnYpAzSFpHRNA+I0L7scJx2qCZyhbiDRD5KpsN3UJAUVzfcykaKpkklx1cQsuWdSgLYqikl9YT2Ail/n41Xrcca1+f2dZpZ9liL9lqqu/BUtsFxO3Z6EMfhzDWIPClVKYNvZKGUmb74XHO6rfzEsfY8/da58Q4RCHDy5tMut7FfVNNrYAEmf3EXFoyHapGGtHR+taXa48Qb4cRUHSle0WkddQKo/4aAEJg0jUygSY5feMqetOsZx89ccDGgPGus9xwoYhcroDVyTMgmMZXLak0VY2rJz4VWdDr1M9tWz+tvnIOP7TFRcE8Vfl6G5g1cxAkuApe6V8AfyR35VvkFLwR3+P2mwXAJhEP3oRfxPPmuezXGn9/86or41h+QIPBRMq4/wvWdSAqy5u0WbavBY5ts+y+WYOpaleJyrqwqhIjFmmsFsWMNUjVyX6TuaB6oKVpPLUmzOIDAdG8ugazBjk52MVdvj4EqrYxzA4ZRW+mtjHfx+8nbP0caupCpv6ctmSRoBhNALkx0JLRTlmgzr8y3SfGDl/r5hS5t9Smd3aXYdm768tmq16UlN+17d4J1Pf+NHluPyiZtt1lfNX56YvVZrG+ZutviqNznpBEP9yoA4ywwMn40ikzEpWsfsQaDGDcqAiD1pIg1PEAbmigKTFLpfxKyqoYMDc3LoBgy0xxyIa5nQbY4e1Miapj1JRQ00Mt378YtRXm2XHxgXOWhaIr/or7BXjQeytVzhWJf6Vcf7lEmCXQ3NDlWN/nMBotuCs4Zrl5GDh/L0MANy+pqeM2XBi+y/XL8Zn/ugiXLxQFuktX1CHZfPq/O/WpjbLEP8yRJoa02OWz6iuFy1z0lO5bOvcc3Jg08Ry2jFFCZ/ChXD52ptw0UfXuT7jdeKrr5ZFQqquxjXHAXQDAtWYQ5U4qLWbxtYPv1G+yMzBmO0L1PjehkvnhzLY836/uZxfe27FtNM4D4csG0ml4kbPN3MlAk7X5CFV/QicjrFjid+uviyrOhF5VKHL/O3Tq7YqjIYawynB4V9+oJ7gJEJwfigry/8VGMVw/PFXEWLl3/GUdzJuYOzyfSfUVkWwYql7DCQjHIm/vZD8l1bG8Rnv+xl7BjLBZlkGV13cjM9+dDkYhsGVF7egsc6H2MipwnHAtCzLWU0Zi3rE7Qd0psDaP8fYRuolJWYWienjGm5Z7JhT2g+9+uDSJtywol2T9XsRf83gw3KSHatdxawi/pxfLy0FtuMkVThGN+7BYWI5cSWUlxVUmYI7ofBtaVCJfNyjjGZYopQJh+S/TkqmMdF+1RRSE+l4yK89HHwXtNRgQYvdHrny8McK8ZeoTexnNHOkuSQijEwEig7hmm3wIP6VCn0qeSfWISSGjfO3Rmq1jLm5sHlbVX8uaLHG7re3Z90s1L6FQywWt8nOaHr8MX+byXjA5QzOkh7rirE05ubhq6IqqibnsXL+Tj1W1lPbhxC+/FNa+BQv+FnaLMtgUVut1peQV4gVqMRf/kUsTMCkKHx/+MMf4pZbbsEtt9yC7373uwCAvXv3YuPGjbjpppvwxBNPaGWPHz+OTZs2Yd26dbj//vshKiFX+/r6cPvtt2P9+vW48847kctVnmqRq9RAXYu/rofkbc8cw/LEbjCU2F3pHScWRWK0iN6Eob+SgGx+grOC+YCXTbAukzRz/kva7SnexnSCstj5e1XhKwSEVlbdTCrjQ7zEPlYbd9YjvLUVIeo+rrxQoQKxIpFe+YBpdrGPdsdW1rpUQhyLm25YimsvbbWVdWjJ45aqaFCZAT/VeX8HL69sAGCM+ZW9dHY+umJEu2YR5UfmL4PlwmCrG7Tv4MnkVbDMmuqiuO6yNlxzSYtHfUpUAEu9TpI4P02XHbq9e/diz549eP7557F9+3YcPXoUL730Eu677z5s27YNO3bswJEjR7B7924AwD333IOtW7di165doJTi2WefBf7/9s40yI7qvPv/0+vdZ+bO3DubRqN1tC/IwuwSYRMgj7GI/QZDolAUZTsopAo7VikONoGKU4qtID7YUJWESqps84GwCSihuOwUqdhyYSB5WRxeIduSQNtoJM16Z+7a/X7ofb3dd+6s9/y+zNzu06dP9zn9nOc85znPAfD444/j3nvvxZEjR7B+/Xo8/fTTAYpnJVAcHBN6tWgNRgaiRSVmS8/lt9B78ZcWDxCvSdqLI5MYmzBphJVy1QZrxVdSVr06yAbusKchQP91S7DOZZKpFs2/oq4H9NsnwFmiEDcKWSZtwtd1Vy/ToXyxguLls4gWLumxn/wwNtlxEjaMtN/uXI60QVZ62yI/alQbYWinYxGuyhqR6qqq9kwlwqHC8BhTXUDNcLZnqfb0oVZC1yM2gwohQHtLzBkO3UUs6v5VjBH+vGr+IRv14vaksU+0D5rN3/hd29iqaovLZDLYt28fBEEAz/NYvnw5Tp48id7eXvT09IDjOPT39+PIkSM4c+YM8vk8Nm9WIhHefffdOHLkCEqlEt5++23s2LHDcjwsrO+QSMH8wvV2ov41ywlWKoBAwnu/vWQctH3chXdehjRszAvo2VVKoYQ/71PuILHvda3YpYc3EtlOyhJYhqkyPxCcCy2bcDHRB1a1bfIcg7amqD4h6FYU1/1oPbWW2iyQbgLZXDMnz48iPfQROkY/QDJ/zpHWjuSyOUjNaHNNAUZCorqpT8nH1dDYIc1q65Xdtge03CtYfQeyQAqKtkxkCZ+0XodSvPqq0mrNLZwi5U3YbAghaEmKaIpH7CfccldO6XNemubvl3+48ti5acsibN9sBIErc4q5VFbDtWv7cHS1xfUirultUe9d/eZVwzusXGnsFnTy5Em88cYb+OM//mNkMoZrUzabxcDAAC5cuGA5nslkMDAwgKGhISQSCXAcZzkehhU9LbhwccR1mz0zhBgVwjAEsbiISKEMYYIDz7MQbJriqAxkMspky0hcQIUYtrxYXIRQGoSgfZgVGacvjGN5ugKOYyEEVAQTcQHjHmsR4gkRMVJGNJqHlyeiLPIgEodUKopMJglZlvUyxdXJ02hRRGWcQyQqIhaXEUlFEctY3TG1azKZpG+HBAArl7Ti7OC4/m6EVDPykQQymQRiakhaThX8aTWNVpZkEijyHCIiD7lkbWKxmAiGIXpZBIGFDAJZ4EFIeFMay7EQeOuLi0R5xNSy6Pdx2THNDZ5nQ0/We5EQZcRYEYgLEPKXIDOMIzaNRkdHE+KXxsCa3k3GVn+JZAQFnkMiJiKTSSKaiOCDtrUoJdoRhwCBZ/VrLo6XEB9UTJVXbepCS7J6qIOxizGM8Rx4kXfcW0OudOECz6EQb0Y8LiIVYSAMWt8tKwhgikZ71+rYC55n4eeIFYkY9SlfnPCsS4YhYIh9lbQ38ZgAEILIJEExb+TJCjzYorUtMgwBK8loaY4jk0liKBXBBM8hGjHeVTxunQdobo5hZLKsf7dB0fJZvkQxAb134jJKZQkytwwj0RRWLFqKeOky2pqjuGlrD4ZGC7gwWgDPMbhuSw+u29KDX/zkHdddAs0Eju1z/PhxfPWrX8XevXvBsixOnjypn9OiXUqSZOlxtOOOaJgIr33KkoR8oYKiy4bNZhhCjCieDMFEroD8ZAnFUhmyJOm7e2lMTBQxOKh4ihTHJiDnFfe+WFxUriWj+j1/f0YJefg/vzmDpFRy5OVFsch6ljuXK4InBZRK3s8msRUwpTLGxiaNsqppc6o7Yr6ch1wqY7JYwUSuhMLIBHKDVrdV7ZpLl8aqmtDWLEphVVdSv9/4eB6FUgWXL+eQUzWOgnrvippGK8t4pIBiqQymUHY808REAQwh+nECGcVSBTKpgFSpW1dkGcWyVSHIT5b0hl0slSHwXNV245dfrYwKnYjEZQwyE+goDQCEBTyiXOYnisjlCkjGBL2sg7b6y+VKkEpl5HJ5DA6OYbJQxgDJQigy+IMr2sGxRL9mZGQCuVwBy7ubUM6XMFhlLYxyzaTynRQrjntrDOVk/D6xRVnpmyugI0Ic75YBC8l0jCHwf/9V3vnkZAkTvBE0zSsvhiihq4Oa5yZUU65drlSIBNb+TKpcGR8vYHBwDOO5IoqlMqTJgv6uNixpwZnBcXx6QfEGzI3nkcsVMCYwnu/TDe070q7ZsqIVA5cn8Lszo8iX4xgbU/LlCTB0OYfh8QJyuQI4lsHFi8q9i8VyVRkbqIt89913cf/99+Mb3/gGdu3ahY6ODgwOGhETBwcHkc1mHccvXryIbDaLdDqNsbExVFTXKy19WMI6xNj323YT1pbJE8sychnnL0+gVHT6erNSKZR26JeUqHvTMqx3P2xf2eeaj2oDLzQtBtPWC7bLuQ/vYHINxiKdgTpehhCL7ZbVFyFVvdRUqOr2Zb0sNZp93FZXT8WKUB+bsvpMHA+ue63JhuxvS79+Qyeu2+DcQlPD690TKJ4rvDk+lGYSCvE8Rl34pylxMTQno7hhYxeWupj9HBlM0c/fkrbqOftK8ACeMPa2Z98q0pyrwzZm5NuRjuEzqwy5FtpBRSUqcpaQKamYgJWLjNXBmuIm6ZPuxFrGgFT94s6dO4c9e/bgwIED2LlzJwBg06ZNOHHiBE6dOoVKpYLXX38d27ZtQ3d3N0RRxLvvvgsAOHToELZt2wae57F161YcPnwYAPDKK69g27ZtIYuKgE8X7oWTcl7folELDwwoC3yGxws4PzjiuIaViu4hHTzu7bfZtdSyBGzHSpRbnJuumDJQ//i4uWmT1YwAfskWEJetHscj7biYXFWT6921GzqxfmmrVcDYMEJI+Ag5r3M1GkjLrlpe7QI86JW1eEz5xXljGAZtzVFEBJ/BuIfN360omrALZcLSZb9fJ6X8lQG0NkVc0zpMPFW9faoVTHb915FKlp0dvx4wL3h9uc2h6Gu7bJvl+PVbYR1UNHZ8drGyqt6DaERpI0s6lJX8RuC4cO2+qtnn2WefRaFQwP79+/Vj99xzD/bv34+HH34YhUIB27dvx+233w4AOHDgAB599FGMj49j3bp12L17NwDgsccew759+/DMM8+gs7MTTz75ZLiCLt6M4sTvgNGPfNOFlSFdg0dR/L8JsG1L9GPnLk1gUp1bKOedHiKMXHZtg0ro5XAVIPNRcIuWgx182zsNTF+cB5rwd2xw7Za2BkGbiPJYsciq5Qmbd1p+b9/cDRkyTh37WLuTy821f2zuinXc9zes6DdvKBP0AzLPLfnlq/5TPb8AwqkSUT72ckqZBPTztTfWg4WX/r7jNZugcW1L9kNV6tZaRgKHN5PH/0HQvsgwmj8hwKfpqwAoXoHKfTUt2+qS61eeWncOrAbPEnzhhmX6b32EEfLlVBX+jz76KB599FHXc6+++qrj2OrVq/HCCy84jnd3d+NHP/pRuNKZYJraIZNToa6xOfu456utlrt4Uj82kivok0p+G4I7IMR2M6Uhu092KeeMUaTvWFu9wt2W2dkaBzmraf4zt27PvqpRaezE3yvJkQkx/6kPob0+TCbCMGvzvNJqGeoCovoLIQE6bfAxnMjciA2JVktZ/dZ91GLF8huhaAH9VmhmCb9mq3aq1ZQNs7dPVQWqBo8ewN9c6fZ9KsESXfJjrcLf7wXoMrlODgTGLa331DoZydGJ+jOvNnMJohxaHllW/cDr15aq3JyxTOiFGgkE0BLcNLzPX7cUIMAxVfhre8HOJm6bjHgnNlzn6loXITAL8uAfqrf0186EWeEbRPO3CxPebyFfLZp/ALMPzzEWrdO9jo0OXbl9CJMLIc65LdnzR6D8AP/36+l+bD0KQAYjxNVfSjn8TFYFdVHg4LD3Rk31oFY///kl/AMLE2NF7/HTw5bww3ZqifnteWu3VuTlvql1DC5L6t3Sav9pfJq+CjIYbFIb9VjrBhSKx9EqOAXBjOOjFNkPhdkTVvMcq4aWIpcPNmojJkEeNFploO8thCkriHui1kY0DY/nGHzu2iWuE4t+G4j43MHyJ9AVvgvCAKWJhxFODABvz5+wX6uWnrWVwRKY0LR4Uobsqoedbb4CrFREj+qubmTn/WylOnmN2bHfsdaJ5XkV26fW+Dd+MV3G8yX8v0+GLI2q1p7Ufm8j/G11KejfsTltemU2aonNLolxXEr21dV2XivE5T8vDOEfZAFfOD69ENC9rpbq9m0j2nyGkuaza9o9r2lriiIVEwJp/m7aPMd6LeQzlyQYtcy/+Ap/vTMJp/k7jlXL3xer5i9wLBZlEuhsM8c4sgYrNOfa255EtiWGAp/ChNhmCkfiXzbA8C50C+VcT/QV3BYlt3rNzyvNv1bhH0j7kYEa2qoVm/Ym+2j+dvVY9vv49aBf3v7LjK1RziphCqF7sFRvrr52djM12oXDXeOjodps/n724ZjIoa0p4usRZi9noPZciweI5jIYynToa/RX/oSYh/JaDFaRZDAMqX1DHdP8SCJq2wfY7L5pu0FyxRVIiQngA8Xxw+7y7FccLepmTZFQfbC/IUIIrl7XYdmwKQizryaGIJjZx01zCGIqmLr5x1k+79drjAq8rnWm9StikNFKc6K+jdCLmjaoCWL2maauraZcfTVeLUmQ9qr9DbA3cgg7vj3yYyD0GeQQOqFPsYNMirpc5DhUrkg4fnoYl217ZoTR0rTVrumUc6UzMQt/G2z7CjDNxtoLw4PHbVWBwpreFrSnY3qAQW6avH7MdKRjemTQoMwzzV/942P7DaJBuSGbNP+acbiMVR9KGB4bbuXWVN3qttgg97p+Y2eg3aymjN5XBXihYbyTAtZP2I48jOIvg1G8rvwu8nAyVFcIAAAgAElEQVTDCbDmzRfd5l89abhRggqjhkAOo/n7dsja6CiM2celN9GC943mipZRRLBBoFJChmMdeysQIQq5OKmbHrXRXBDvQE2gu5n1V6n3+fm7p5W0AYL2haJOfcm80vzNJgLvNPV4M7Xl4Rje+go29UM2nLU90T0WfL7kIDKUYxnLxutzgSATvppAmC79KZSGqifx22vXmlgPAuaSv3EkiNlH+RtE86/J20cPRFcnsw9jFqrBiLhor9od7BFcg42stDpwPhO/6gZwSz8DiYuak/qifWcxdaGV3/vVAq5Fxbn1zWnMK80/0PROjcK/Pqv6rfdmfASbrCr1fpq/5hFkTJx5F9I+ETWbBBmFGImr7wymuNBKNddt9TIof/xcczVPEL02qnpnyYGeX+raCJbNW9Kea94MGQSb7GUIoc3zqrYpBgxoB8DY3yLMhK/rgFWrf9b6u8YMtceVJNkyqgsyspRltb5cTC9EjIMV4yDkhPXevqt2if63qzUOsdt7Mnf14masXNRUd82/XubP+SX8zQuCqk6khkPG1O0+rq6enmXSNH+Pa7UkstHI/WL7zIBZMTDhNOkAawJ8J86dhA/ta+qkvV1L1HPBOzY9Rr+fO2+sGVy7NSxynm92pjPdMog2n05FsKUv47tzlx1ZUEIGlyLu93fHR7DVsObEdXJYfVxJtq7Z8RUD2qUWzd/L60+r0+CT7oCMVFwAG3EJBWFKy4XcfbBeBFljMs/MPgGESq2ujnXQ/O1ao9+OVppGJhmJXXMEAJlR+2jW+2NizB3jLCOraw3yMe8gZRrG5hg+mnSItQA1oZtlfJLYf5vaWW970nVfAybQqCb4M4WN17O4vXrobjNSrA2nWz6LQry7emIV/5XptXyLbpq/7bsK0QFr6ycYH+1bd7rQR4B+5lW9B1YvmsEV9drfIDpVEKeAqRVnpqk+8el1rtpQKYAVtWoK+8v0630126a+eZiPf/N4rBtD8aWQ0sscafTSzQWpryFEcaJtOyYTXVWTMmwQ00AIMxKAiUI5cLhtc75+tmnDkuVsg1GRs2h4hlywjwSDF8mvDPXczcpOiYsFWnOg45dU1+LDrDJ2Ef6my2WY3kOA9tCRjiHTFEVzyrlvdJB726l5DVAd0Np0rYu67Mwr4R8ovINHoqnWWRD7ov0efo1T24rN39VT1fwJg+FYL4iP5j+XZD8AtUABOkw1lLVjP2UTsr51pJJfRY266NWhj00Ucep89QVeXa1xtCREk4tcFdOT218ATHoRuN4tRnm148Ra7imbFbX2ME2yv7Zs/SZ8tboNkLPWAVcTbCELybCsEn3U59vRniGUAuUXWGmaKJUV4R+PepuaDBbYIi8C+8fklsj9XLUFQmZtyjWHQHZn9+GpW6NqSiUwOjKGtg7F3uve6IM3rFpc+6YLI+Jh9fJXEhkAJ6v07KpZxj4/4FOn9k3c3eA4Bu3xGC5NVPe4sgtws5LBL7vSJTKlydRgMlcu62pCqSzpq4/DeMJMu+ZfQ77OaS6j0ychNH9jSsVN87ebU/XEgctHONF7Osc+qpOVsMr+zPyHtry7Cb8/OxpoAjlIhzuvhL++atHXzugh/ANND3kj27occxhg77J4V1JizbXYsKoIJhX3TCuHKHKYBUDTDXH8400l1oZzTZuQbU6Aveyxx67N1KJPgCPIhJ/PaMn+n58gts+pOHz4nQ9rzPkY1wgcAyGEHd5MbfF6gmPYvsMrHQCwclEzCAGOX1BjKmnvPpBrqrp2x8386bhcqXlCqodNNOqg+oJLTQGTZbnqgimi7WUsBDAn1YkNy1p94/xbCaD8TK04M0wQk79XJbtcZI3jHvDm5p+2a7TeViYMiCwpEQq9chPjYHhjktDP7KP/8ltVGmIB0LSj11N1ISeDQV5o8ZW7sof5pNpoTsk/iHYYYk6BVO8oZFm5qzY56Gv0CSNoXUP31pHqAyAXjNQOW3RN4cW95768U/hlR6wTBT73DLIpuwbT2guej4Ckqm9gPxssuAlfP+8ZUyL3wwEOliUZF4cnXeWJYw9i1zTa18NaUrlVhCOKo4/ZJ4jFWNcK6xiltFa0cvqVRBcUWp362Xo96937Gm1eQPadxLUL/eA2f/+AZsqTG3bmEJ2LD7w6qRzGgycMNbUcX4VE86IKpvkDcO0wHKNZbQTo4yThyJcQ8H3XgV91g2cZtG8yaHmZpo655WhhYsGZfVwcLVzSeE34ugzLYTSWUwNjSER5jKmbOrN2uxpDqqrVhpcHA0jQ/bwdebkccyufMRnsVMm2rspC4I08tMvngOx3CEo3lnY2QZJlfBLA00bXUWwNwP+7Cz7vEKS8zi44wIgCNrOPz62DkGmOYtOKNizKzIGw3Sp+5dc8ucIoJK6LHZ0SXfunen76t8OASSn76/IrroY0ftmRn9nsY+f6DZ3Il6YnRPNsMa+Ev/FB+6TQKjKATd5sNpBlWZ9N97u35WJbI6kwIoBxsJBQAdCUiEBkYmhpS2BkaKhKWbw1f03RK5vi8iyybeBh315vNvH7JNnsMlQu/F51jSS6Vu/n5SE7tG3riMj1GnuH4VPOQJvIEyOtXCVfrVFpa5z8RZTz7A0bu1yzJ4RgaWfKN7epYGzNGOYq78Sa8A+jkGh1LfIsCqqwdWr+WkRVf4VOzVE5bqpbprkTTHOns7w+cyptze47e81n5pXZR++h/ZJ4CBH3Bm09WPHxEHFoJC4Z5qPqZIzq4iaDQTopGr7sfrjkNyEoS8fXr2hHa1MEaZ/QsIYnSPVbTTd+woNbvAni1l0uF1WfmOV5W5pA5j+/NNa0YYR0EC8dRn8mTQC5CCuXm7Y2RVyjT84cwaW/6yY06kNp58II/6jIo6s1jm7T6MZ7MX/1cuqlC9Cx62afOfANTZUgpqt5pfkHmZgLZfaxHbIHjnJL7Lcv6UR8McaaE2iXzoM1RQsMtmzcmeZSYiWGY71YnYjjho3+Gh8zlzT/MKqjqdPyvErNLyryGIPZHOaN3dyTigkYVU16Rr5W11G7R5e1CLbOJMAzEocwmZv2YY0pua4zTlESRvM3m0xTccGySM/p6ml01tqZjnQMIs/i9OC4rbdQfwQIshhmjmKuE2jSevqLUT+CxIyZygSM3wuzxBWylYGAgOdYyAAKfAotCQERgUNzMgLbRVXztx207Nblf73yd9o8QaaJzrTiKheP+Y1qlIeL8CyWdqR0Dc3vtcr6hwwk44LrsF0TzqI6oij7SCn7Vpp+ZiptspllTT0bYGm2RoiCufcJhv2CWtZehWXb+x3HQwl/7d76gj7TOYfN32nSa9YX69lKLwdRFWz3nmffUK0Ebnnj4+P43Oc+h9OnlRjVR48eRX9/P2677TYcPHhQT/fRRx/h7rvvxo4dO/DXf/3XKJcVn9+zZ8/ivvvuw+23344/+7M/Qy6Xq6G4dgHs9kTBV/jaD/n2+FqMEJeM+nqasawzpQuIWITDko4kUurOOrXuMeBZULfizaVFXiHSplMR3H7VYvR0JD3TaJPjMiEQBTZgB29SFGSPaV+1XuJRHq2pCLp8JlLtC6z86vRs8xZcSK4x5mFM5/hV14NbtN5UvLkj/PX2H1L6L169DsmWFsdxXt3vVrSb61xvrs6TuCh47n7+7tjPkECavwqvKCCsXKqedo5TN83/vffew5e//GWcPHkSAJDP5/Gtb30LTz/9NA4fPowPP/wQ//mf/wkA+OY3v4nvfOc7+Pd//3fIsoznn38eAPD444/j3nvvxZEjR7B+/Xo8/fTToR+I+AhgI1EYk0PwtHbN3yxOCIHuTgwAjD6LrCVgIHDKB9DdlnD11giz1Z17+ZS/c0HzN7/Ws81bcK7JHpwYIFHDjBUROJN93IkWN8e8uEu5j88ksVl4eJWT5fUCZ5qjiIp+y+at9/LbcD2TbUMu0m60U63DAAGTzIDtWBnoGeY7PM9icXsSi7LeHbuGXfM3v26HUub7/dt/Gt4+VcvAx5CI8licDhI+YW4TxHQVSOI8//zzeOyxx5DNKq5S77//Pnp7e9HT0wOO49Df348jR47gzJkzyOfz2Lx5MwDg7rvvxpEjR1AqlfD2229jx44dluOh0SJAuoZmVSeZAvj5E5sQCYIh/IPbfI1VMwRLOpPo62lGMsY79hC15Ot27xDlmwOyH+lUBC1JEeuWpFHgU6oXlBV+zY0QNu/Uf/uZUVhVIGhm4CChG2S7BumWPafueapuYuIfoVLv9dXyen86W1dnLOEBtCox+6UbxZtDmr+u+NenQyKEQUzkDPNXgHuDU0ylTMwZVrrCCFrG1r9+ZQgTfZPh0LvhCrRuvrF62jlOkA15Ak34fve737X8vnDhAjKZjP47m81iYGDAcTyTyWBgYABDQ0NIJBLg1GGgdjwMra0JjI2kMMpziAgsmhIiWIZgcGgSACARBowsIZ1OYOICZ50NAhCNCtA8OTUvTUFgfRuQYNoIg48IKBU5ZScsQsAIvOrQCcTiinBLxxIoyhNIJkTESiLEVBSFCRFCUxzFstV7I52xakNycQwDto03FnWkMDRWQFsmWXXoXJCBeFxEIhlBJlNd05puvtihrF7+9ccXwZUrEMa1uncvmyTJ+K3t+Rd3JHFpJA+hKYahUQ7xtixixQGIfBEcw0EQWE97sizyEMCB8ByAImIxwVKfAJBqSYKMF8DwDCRWBCtEHGk0xAgPUuYgixwIOCSSEeR56zNp13a028I7F8dwjufARXgjrcChUpHRmmlCc2puuBEOTZYRj4toao7W1IYm+jaAcDyEkf+BXOGQao4hUhbBxoz32tfbgkpFwu9Oj1iulQkBkRk0pZPouvqLKEzmcfLEaUuaMssDlQIiEQGkXAAjcpDKSr7aNyiIPBiTP348LoAHQSydQMTjmc4kIqjwHJIJEZ1XXBP6uecil7uvQ0rwV5Jq8vaRJOuuSrKseL94Hdf+mgk73L10aRzDY0UUS2VwDNCuTuCdKSlzCqmWZuTHxpDLFVAslR1+/uUSi6KaliFEMY8QoqQlDGTZ+qIEnrPkIxUrKJfKIATq8TJkNb+JXAEAMIkicrkCRjAJIhWQH8lByhWQFwqQ1DQalUFr1Mnh4Um9fBoblrTgwtAkRocnqr6f4aEJ5HIFjAosBgerR7ScKXK5ArhyQX82r7LJsux4fo4A7c0RyHEecpyH2NyOYqUFFz49h7b8MUCWUXTbRBVAHhWQUhklqQSZAyYninr+Wp2OT8pgcwWAKQGShHyp5CiDTqGMYqkMGSWQUhmTEyXHM3k949BQDsVSGZVCST9XKlVQrki4dDmHUsHjnjPMkNaGRiZra0OpFQCAQuFtoFTG6JjS7omU199Nuaj8tb9nbW/k8bECLo1WUJx01kVZ4sAxQKGo1AVTKEOyfYPFkoSy6bqJXB48yigOT4IV3J9Jkxlj4/k59e1MhdGCotD4UdOYs6OjA4ODg/rvwcFBZLNZx/GLFy8im80inU5jbGwMlUrFkj4sxGdnoO7OVizrSoFIdmGg+RybD1lNOH4mB4eN32f4qEXbk/TFWOo1Afz83TpDkWfRkw22mnPa475MhVq9nVRYhkE6FQEhBGx2Gcrq8F/ycSORtLDPcgVNCQEW7yytKkXt3QZpB1azWpg5Gm3Owm1OYS7Z/DVlqV5FYkKYtLRwHxxvC4lhwpjHcZ5ju9eC77vOcY40K3tKkGRb4LI0CjUJ/02bNuHEiRM4deoUKpUKXn/9dWzbtg3d3d0QRRHvvvsuAODQoUPYtm0beJ7H1q1bcfjwYQDAK6+8gm3btoW+L2G9Byps2xLlH946hNYaDGtu0fYVncE2CrCkdfs+4uqmzpoMYZu7wHasBLdoQ+Dsa0V7gjkp/KeK/m6s3ih+zyqpNs+WGKcsmDK935HkUiWbjhXgeq8A29ar/A4QByiIt4+dRGsGPWs2oPdKo83PHZFvok7rEYpQOmdWm5tzqSd7p5dtiaFT3V8B8PokvW39XOcqMKmswxWbJDMQt+4CE/VbJ2Odz2kUajL7iKKI/fv34+GHH0ahUMD27dtx++23AwAOHDiARx99FOPj41i3bh12794NAHjsscewb98+PPPMM+js7MSTTz4Z/sY+Hxzb1gsm3QP5+G/UtFCj+Sl/GbNWpy4PD7ZuQM3HrvkTYGlHChVTw165qBlRkUPL8FnIYwAYRnHrq+HZ3CaFfS+fQxO+tVJmI5jg00jlz9rOaPVjHVH5CX99wxe5DBDrFOZYYikuCj1YTTiwmSUof/KektZ38aBV+IeJWEkIg/SaK13zm0ua/+L2BC4MT2LlIueWlGEYEbLI5C+CE52rlPl1NwPlIpjTr8EUrQQMQ5CKCoE8uJxrbkzYvqNAow/dJXcefzw1EEr4/8d//If+/zXXXINXX33VkWb16tV44YUXHMe7u7vxox/9qIYiGhCGQYURMZbsAXDJ9byzRRB8kr4aySUtwH+/oRzRK7v6cF/rPfQZAdNHLwpWcw7DECxuT6I0rA+gAz6ZtQyrtn4WXFM4s5jdD31uEew9fJq+GoxUdhH+KroHbfX8KkQR/kXOaTbbvLINH564bIqOGcAjxNau/Fw9wzCX6ovnWFyzrvq+y9UYF7PIp5NY05SFfBaAaT5N08CJoVVZ0ZV7lzomWqevJfUzDWk3DGByNC5uKOaOn1kACAE+ab0GuWSvbxozMoAKGwER46ZE1hWCQfZuLZaVliEKITRyt/YrxkFiTs3KXIbI4vWhhb8myKptQjHTbFjeii19meoJVZLqwjgLeqUG+TqVtGU2igvJtbiYVtyOicl1sLM1jlu39jg24/az45tDCqiJHWnKTMQ3hLQ1P/XWgVLPP8psFFwkCjAM2O61jvNZ+4prh3++S3RPfcSn/E3GnG3F4VgSoJOeS0ERZ5K5JSmqEFEngyaLEuA5h2qO16LZfaz+/459AQIMvbtaYygxIhKJCEaHquiyPkvKhQ23uV4SZGs2P5IxAVeuziLbMjfcBjWWdzVhcnwUg9WT4o6re0GkMj76xK7VOUdzdrpa47g0mke+JOsLe3KRLATCoeW6u5E/exn4+KT7jTVLTgCzj/7bRah8mr4KALDZMxfnEyxEeROP8MjlS2BYDuKWuwAAAsdaFJNUXADPMTg1oG5nqZ9R//Ox+bc2RSDEEhASIoYu2pNYFYWpLp5cyMwr4a9tXCzJ1SP0OQ67zPfqk0IBtLWowKI1HUMuwOKJMJ2KBscFyLcK3XMoznstiDyLslvMdLuktNSfciyVEJGKC/jo0xGLOl2uyMpKXt9t/FSzRADNP50SIRVlpJuiuOBM5Hm9S4bKvReg9N+2uQuForUel3UFDUWtjbBcTDqm0VciyqPo8rpjER4jk6bcQnia2d29FzrzSvhzLINNK9rQmooAH7mnsWj1polay4QvU13zb0mJELkozl3SfOyDT/RxS7agcuF3IHEj3gnXuxlywTuekWMLvAVEkO0c9bRqXdjnU8wYMZR4TOS1SJ1KR6BF5tTSaELHVwYEcN/U4gvxHIu2VBxskDDdPoyk1yI3lsPihSf7IfKs66JEIviEqQ4gpKMRAcjnfE1lna0JpEUJJ86PKtn6uIfbb72QquKmLYuQL/pvPjOvhD8AfTOLgmcKqweP7DKB5JjwdWl4XZkEJieK6sReBZDUBUJEe2U+JgIxDq5no+UYm1nqmR4I1kjnLSH6NYZh0JNNQBTMTdPd5t/TnsSxU5eMJLI6EVupAAS4cnVWHw35dkCqxuenJRqx3hVT4lSD9eXjXRip5Bek5u+GsOlOh+Jk+SZt/7g5YYgCBykPu8evNU+GUYL/wTv0uuMaWwymhUAqLqA56f/sC84g1tIUQUtCRFebNsGr2fyNNM6Nmp0vSWsQWlwSqah0N5LqrRAkXkkoFq7iH3INA0E8woNjzILBrpq5ddrOuR0LQTz+XDT/bHMMbamIEStFNsUImQJ9PcoEdFiX3vkK4UUjkF6wKxxH9EWU8KkD9diSjiQyzdGANn9NGWws5p3mXw2GMGhPx5Cv2F3znEZ/2fbbDVbVyPOtq9AUl1AsKkNXfooTtE6UMkx14ncuUsvmLkwqC7ZrDcBykC78Tj2pTuLJFUQETo0Mqsz4sekeVC6eNNWlbYLWt3f1XriVTimLjgaKNu1wipp/RzqGL9ywbEp5LCjsqr+bQqYJcm2Kxkf4iwKrxuEKUU8NJv3nr/AnxNgk1X4cRiRIP28fRxhZF7ItUUCqIJttAZdqg3juDAAgadLY2EXrQmo1LhCCFd3NdVtaP7cI/lCEMODX3QwixkDU3aEk20u57caNqHxKwHX0AR/9HgDA9m4Cu2gtyMDLejrLt+wr+wN4hmjnfCYFb/7MooVkOZhRAsh+04hdecluo2/CRyBjxHGNH3NpF7yZZN4Kf+GKzwEAukZfNC3WAQyTgPJLF/AE6G1PYnyyhJxjNaxNSzQJG17g0Z0xJviakxHwXU0QIiJQVkxBXEff1B+IED0GzEIj7CpW+1J8tmstIMtgWnuU8ywPZskWyJIRwIsQBuBEMAyDCpyLfXzLEESb18w+Wuwol/zc/M4p3tjHZn50t8Uxpr1zbf7NRfnjlm6FNHwW5dMfAuVSMPNcg67wnbc2BsJwIAyHVFywLmzSzAZqHCDN55shBFGRU+yAtgkeu5tlR0vMyC6iuk+WjClmgZuO17YwBT9gaFYRoTZdg3ACuN4r9JGA6YwjrfdcTBB3HyNNU1y0mvYcHcPCra+ZwjypS+Ktyl/BOlenwTCM8d1WVOHvEuuLcIIS5yuMec7dn2DBM281/2owvGKGYWSXjTq04GzqIc4kzLta4/r2iwDAda9F6fivQOLaCtFp+ugXpr0HAMCwBMu6mqZlnmR5V5NluM55mm4CaP6mNJ2tigLApBdBunwaRG1PC7eWZh7zNBzX1QchmdSVLftITeQZw4QjlQCwAMtjaUfKPTxLCOG/EOJi1cICFP6q2UfdpYmowt8sINrTMZweYdAUF3BpAihXFK00X3TGVSfxNMQtnzcdmC41YSGLFTI9oyUCm8kPEMwhgWVr2niER5NL+Ai2cxWk8UtgEmnHOW7xJmDxJrSfPQbmUgTppoieH2UKMCwY0zfJc7wxyjbBMgQrF9kUL+06lvNZD+IczXmhf9ENJv0XoPBXICyPloSIoXHFXFMxxX6PRQWsWNSEsYrScEqSjCjPIF90E+k2y6S29V+5CGHDbZAd+wfUWN4FrPnr1P0ZnfllWqIYvkwAAgi8dS7Ia28EJtEK8Yp+SBPDLrcgICwPhmXRZolH0wD1NZ0wLBjTt8O57KDW2560jMrtLtqE8XGyME/2VSvKAvTzD8KCEP5MyiUImurymUzFcZawaE4IRmRO9cONiorwb22KYmJwGBJxaUz2tmPaL4CIcSoCwjADHRzDMFi5qBmZ9jZkTXM3wfB2HXQr+/KupsbotKcBJt4CacTYypVxMQnagxSKAoccACbRAiAPkmoDdDdgG/p6jAAbt9v+NgrzXviLW3dZD5i+RX7ltWiOJHCHGtFTn7JVP1ieZbB6cQuYZAQTWuSxKi1AcwckvM9SdYoH9RWUhBCQeAvYzBLjIMuDEGfUyNqFtNVl2JShw+RECQ637ErIEyNID/0Ugtme70O6KYpUVwpcew/4ReshTY5Wv1GoFb40ts+CgWlqdz9hbxCE8QvW4DjCr7vZMP9QqlNDoLugCGtutPzml1+F8pnfuIbNrorPoiFnTCeq8U8FwvIgyTYjCq1f22AYQJJACINETPAJ7WK6pLkD0vD5QJ2KEe6lsVjQwt8b26QtwwIEIKgovr6M2c7obJT+W8JRHMjBJ9+mChGi4JdunVIeFZMtWat/JplBBeoiolKeyv564yekGR6QCqbFO9XFNLfss/o6nGqI6txQra7I85UFN271X8avwDR3Kmm1XYU4bcs/NcAXF0Fq8y1gO1dNUykbDE2AmjZUmZPIEuIRHqmOxY5TTLwF4tZdpo3AqfSvK357KbC2BXYBdHTCsCBCsDmf5mQEPdkkujPx6okXEAu4q/NuIExrD4TmTlTOHwdwXtEsVIrt68EvWwou1Qqum5p26gFhefCrbqjNFFPvskSTnueYWDOWXXsLSKodxf8+VC2n+has0fHR/Llln0Xl3P8Dm10OcvIsmLYl6jX1q4N4hAuy4+OCYgELfz+IYrPXGg/L6Z9yqWmxdctHSl1gdI159uDX/kFVbVAbFXrB9WxAheXBNHeCX3ENwDVGVM5px0uQcyKYeAuYFdcAAFpu+D8YHBybnjI0mNF/AQr/ELP7JrSon3TXt4VLPcxOhI+A61X3BW6e+mbnFBUXzZ9fvc23s9ZNvAt5L4xpZEZF3WuvvYY777wTt912G37yk59M781CLtjIbrkRkQ23YXHW2yxAoVCmCTeFLNEKIgTYk9oR86nWezeW6j9jmv/AwAAOHjyIl156CYIg4J577sFVV12FFStWzFQRvJFlCOkurHKu7qdQKDPAVHZGW9C74E0jM6b5Hz16FFdffTWam5sRi8WwY8cOHDlypP43arBJGwqlUdFDME/ZVmuL/94gzJjmf+HCBWQyGf13NpvF+++/H/j61lb3uCx2pCSD4bMiEitWQ8hYTTiX48quTGn1+OREHJOjIqJNEUQzTnNPxuXYdGIvH6V+hK1LWhczQy3vWavL8lgZo3ERXDyO1BTqqVCOIXdRhNgURbyB6nvGhL8kSZaJVlkOtrmyxqVL45CkgF3zmjuVvXxsXgHl5uWonDuGinq8PJJHJVdAYSiH8bg1bSaTnD6vAg9KbBNIrGnG77vQqaUuCzk1ICCti2lFWnI95ImRwPVjrkspN4ZSrgCGlVGYQj1VhidQzhVQGJnExAKqb4YhvkrzjAn/jo4OvPPOO/rvwcFBZLMuAdmmEa5zFTjTwi3dVijXJzLnVOH7rpvtIlBUhA23QS4XZ7sYC9DvrNYAAAoQSURBVB4mmgJqXDFPYs1gu9cqm7fUAbqT1zRx7bXX4le/+hUuX76MyclJ/PSnP8W2bdtm6vbuaJNMDRbQiVIdIsbBxFtmuxgUHwgh4DpXgfDiVHNS/zaW8J8xzb+9vR2PPPIIdu/ejVKphC9+8YvYuHHjTN3eHXWiSJao8KdQKI3FjC7y6u/vR39//0ze0h+q+VMoFI3GUvwXXmC3UBAtYBQV/hQKpbFoaOGvbcwyVyZ8KRQKZaZoaOGvm32o5k+hNC4NGt6hsYU/q0ZkpJEZKZQGpjHDAizAqJ7BIfEWcL1XgGnpmu2iUCiU2SZkMMj5TmMLf0Ksm39TKJTGozEV/wY3+1AoFEqDQoU/hUKhNCBU+FMolIaGqJvBELaxHD8a2uZPoVAopKkD3OKNYFp7Z7soMwoV/hQKpaEhhIDNLp/tYsw41OxDoVAoDQgV/hQKhdKAUOFPoVAoDQgV/hQKhdKAUOFPoVAoDQgV/hQKhdKAUOFPoVAoDci88fNnmJmPvjQb96RMD7QuFw60LoNR7T0RWW6wOKYUCoVCoWYfCoVCaUSo8KdQKJQGhAp/CoVCaUCo8KdQKJQGhAp/CoVCaUCo8KdQKJQGhAp/CoVCaUCo8G8gXnrpJezbt8/z/L59+/DSSy/NYIkotULrcuEwW3VJhT+FQqE0IA0v/Kv1uguRP/mTP8Fbb70FADh9+jRuuummWS5RfaB1SetyPjPTddnwwp9CoVAakXkT2G26+fWvf42DBw8in89jdHQUf/VXf4VbbrkF+/btQyKRwG9+8xsMDAxgz549+MM//MPZLi7FB1qXCwdal9MHFf4qP/7xj/G3f/u3WL58OX71q1/h7/7u73DLLbcAAM6fP4/nnnsOH3/8MXbv3j2vGtk777yDnp4etLe3Q5ZlsCwLANDi+ZXL5dks3rRA63LhQOty+qBmH5Xvf//7OH78OH74wx/iX/7lX5DL5fRz1113HQgh6Ovrw/Dw8CyWMjwvvvgifvaznwEAjh07hp6eHrS0tOC3v/0tAOjnFhK0LhcOtC6nj4YU/u+88w4GBgYAQO917733Xrz//vtYv349vva1r1nSi6IIACBk/sUR/8pXvoJXXnkFd9xxB44fP44vf/nLePDBB/Hcc89h165dyOfzs13EKUHrktYlrcvaaEizz4svvoj169fjvvvu03vdI0eO4LnnnoMgCDhw4AAqlcpsF7MuLF26FP/2b/9mObZx40YcPnxY//3nf/7nAID9+/fPaNnqAa1LWpfzkblQlw0p/L/yla9g7969+PGPf4yOjg489dRTGBoaws6dO8FxHK6++mrk83lMTEzMdlEpVaB1uXCgdTmz0J28KBQKpQFpSJs/hUKhNDpU+FMoFEoDQoU/hUKhNCANJfx/8IMfYOfOndi5cye+973vAQCOHj2K/v5+3HbbbTh48KDjmr1791oi6r3zzju4++670d/fj6997WsYGRmZsfJTDOpRlxr/+7//i/Xr1097mSnu1KMuX375ZVx//fW46667cNddd7leQ7EhNwi//OUv5T/6oz+SC4WCXCwW5d27d8uvvfaavH37dvmTTz6RS6WS/MADD8hvvvmmLMuyfP78efmrX/2qvHHjRvnFF1/U87nlllvk48ePy7Isy9///vflf/iHf5iV52lk6lWXsizLExMT8j333CP39fXNxqM0PPWqyyeeeEJ+7bXXZusx5iUNo/lnMhns27cPgiCA53ksX74cJ0+eRG9vL3p6esBxHPr7+3HkyBEAwGuvvYabb74Zd9xxhyWfw4cPY8WKFSiVShgYGEAqlZqNx2lo6lWXgOJD/ad/+qcz/QgUlXrV5QcffICXX34Z/f39+Mu//Es6Ig9Awwj/lStXYvPmzQCAkydP4o033gAhBJlMRk+TzWb1FYYPPvggvvSlLzny4Xkex44dw/bt2/HWW29h586dM/MAFJ161eXPf/5z5PN53H777TNTcIqDetVlJpPBQw89hFdffRWdnZ144oknZuYB5jENI/w1jh8/jgceeAB79+5FT0+PZWm4LMuBloqvWrUKR48exUMPPYRHHnlkOotL8WEqdTk4OIhnnnkG3/72t2eiqJQqTPW7/OEPf4jPfOYzIITgwQcfxH/9139Nd5HnPQ0l/N99913cf//9+MY3voFdu3aho6MDg4OD+vnBwUFks1nP6wuFgiXg0uc//3kcO3ZsWstMcWeqdfnmm29ieHgY9913H+666y4AwF133YXx8fFpLzvFylTrcmxsDP/6r/+q/5ZNUTIp3jSM8D937hz27NmDAwcO6KaaTZs24cSJEzh16hQqlQpef/11bNu2zTMPjuPw+OOP48MPPwQAvPHGG9iyZcuMlJ9iUI+6/NKXvoSf/exnOHToEA4dOgQAOHToEBKJxIw8A0WhHnUZi8Xwz//8z3jvvfcAKGGgb7311hkp/3ymYWL7PPvssygUCpYgSffccw/279+Phx9+GIVCAdu3b/e1/7Isi4MHD+I73/kOKpUK2tvb8d3vfncmik8xUY+6pMwN6vVdPvXUU/ibv/kb5PN5LFmyRHcZpXhDY/tQKBRKA9IwZh8KhUKhGFDhT6FQKA0IFf4UCoXSgFDhT6FQKA0IFf4UCoXSgDSMqyeFEpTTp0/j1ltvRV9fHwBAkiTE43Hs3r0bd955p++1P/jBD7B69WrccsstM1FUCqVmqPCnUFyIRCL64i8AOHPmDO6//36wLIsdO3Z4XvfWW29hxYoVM1FECmVKUOFPoQSgu7sbf/EXf4Fnn30WfX19eOKJJ5DL5TA4OIjVq1fjqaeewgsvvIAPP/wQ3/ve98CyLLZv344DBw7g7bffRqVSwdq1a/Hoo4/SVcSUOQG1+VMoAVm9ejU+/vhjPP/88/jCF76A559/Hj/96U9x+vRpvPnmm7jvvvuwfv167N27F7feeiv+8R//ESzL4qWXXsKrr76KbDaLAwcOzPZjUCgAqOZPoQSGEIJIJIJvfvOb+OUvf4l/+qd/wsmTJ3HhwgVMTEw40r/55psYGxvD0aNHAQClUgmtra0zXWwKxRUq/CmUgHzwwQfo6+vD17/+dVQqFdxxxx248cYbce7cObhFSZEkCd/61rewfft2AEAul0OhUJjpYlMorlCzD4USgBMnTuDpp5/GAw88gF/84hfYs2eP7vnz3nvvoVKpAFCCjJXLZQDA9ddfj5/85CcoFouQJAnf/va38eSTT87aM1AoZqjmT6G4kM/n9Tj/DMNAFEV8/etfx4033ohHHnkEe/bsQSwWQyKRwJVXXolPPvkEAHDTTTfhySefRKlUwkMPPYS///u/x65du1CpVLBmzRrs27dvNh+LQtGhUT0pFAqlAaFmHwqFQmlAqPCnUCiUBoQKfwqFQmlAqPCnUCiUBoQKfwqFQmlAqPCnUCiUBoQKfwqFQmlA/j9e3OPkOXhBPQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "daily[['Total', 'predicted']].plot(alpha=0.5);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "It is evident that we have missed some key features, especially during the summer time.\n",
    "\n",
    "- Either our features are not complete\n",
    "    - i.e., people decide whether to ride to work based on more than just these\n",
    "- or there are some nonlinear relationships that we have failed to take into account \n",
    "    - e.g., perhaps people ride less at both high and low temperatures\n",
    "\n",
    "Nevertheless, our rough approximation is enough to give us some insights, and we can take a look at the coefficients of the linear model to estimate how much each feature contributes to the daily bicycle count:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:53:37.022122Z",
     "start_time": "2020-05-28T09:53:37.016768Z"
    },
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Mon              504.882756\n",
       "Tue              610.233936\n",
       "Wed              592.673642\n",
       "Thu              482.358115\n",
       "Fri              177.980345\n",
       "Sat            -1103.301710\n",
       "Sun            -1133.567246\n",
       "holiday        -1187.401381\n",
       "daylight_hrs     128.851511\n",
       "PRCP            -664.834882\n",
       "dry day          547.698592\n",
       "Temp (C)          65.162791\n",
       "annual            26.942713\n",
       "dtype: float64"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "params = pd.Series(model.coef_, index=X.columns)\n",
    "params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "These numbers are difficult to interpret without some measure of their uncertainty.\n",
    "We can compute these uncertainties quickly using bootstrap resamplings of the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:53:39.894650Z",
     "start_time": "2020-05-28T09:53:38.322073Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "from sklearn.utils import resample\n",
    "np.random.seed(1)\n",
    "err = np.std([model.fit(*resample(X, y)).coef_\n",
    "              for i in range(1000)], 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "With these errors estimated, let's again look at the results:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2020-05-28T09:53:41.278481Z",
     "start_time": "2020-05-28T09:53:41.272296Z"
    },
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              effect  error\n",
      "Mon            505.0   86.0\n",
      "Tue            610.0   83.0\n",
      "Wed            593.0   83.0\n",
      "Thu            482.0   85.0\n",
      "Fri            178.0   81.0\n",
      "Sat          -1103.0   80.0\n",
      "Sun          -1134.0   83.0\n",
      "holiday      -1187.0  163.0\n",
      "daylight_hrs   129.0    9.0\n",
      "PRCP          -665.0   62.0\n",
      "dry day        548.0   33.0\n",
      "Temp (C)        65.0    4.0\n",
      "annual          27.0   18.0\n"
     ]
    }
   ],
   "source": [
    "print(pd.DataFrame({'effect': params.round(0),\n",
    "                    'error': err.round(0)}))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- We first see that there is a relatively stable trend in the weekly baseline: \n",
    "    - there are many more riders on weekdays than on weekends and holidays.\n",
    "- We see that for each additional hour of daylight, 129 ± 9 more people choose to ride; \n",
    "- a temperature increase of one degree Celsius encourages 65 ± 4 people to grab their bicycle; \n",
    "- a dry day means an average of 548 ± 33 more riders, and each inch of precipitation means 665 ± 62 more people leave their bike at home.\n",
    "\n",
    "Once all these effects are accounted for, we see a modest increase of 27 ± 18 new daily riders each year.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "- Our model is almost certainly missing some relevant information. \n",
    "    - For example, nonlinear effects \n",
    "        - such as effects of precipitation *and* cold temperature \n",
    "    - nonlinear trends within each variable \n",
    "        - such as disinclination to ride at very cold and very hot temperatures\n",
    "- Additionally, we have thrown away some of the finer-grained information\n",
    "    - such as the difference between a rainy morning and a rainy afternoon, \n",
    "- and we have ignored correlations between days\n",
    "    - such as the possible effect of a rainy Tuesday on Wednesday's numbers, \n",
    "    - or the effect of an unexpected sunny day after a streak of rainy days.\n",
    "    \n",
    "These are all potentially interesting effects, and you now have the tools to begin exploring them if you wish!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![image.png](img/chengjun2.png)\n",
    "\n",
    "<!--NAVIGATION-->\n",
    "< [In Depth: Naive Bayes Classification](06.05-Naive-Bayes.ipynb) | [Contents](Index.ipynb) | [In-Depth: Support Vector Machines](06.07-Support-Vector-Machines.ipynb) >"
   ]
  }
 ],
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