notebooks/ML/Linear Regression/Polynomial Regression .ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2576f3a3",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import math\n",
    "from mpl_toolkits.mplot3d import Axes3D\n",
    "from random import random\n",
    "#from mpl_toolkits.mplot3d import axes3d\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.linear_model import Lasso\n",
    "from sklearn.linear_model import  Ridge\n",
    "from sklearn.preprocessing import PolynomialFeatures"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f81f9769",
   "metadata": {},
   "source": [
    "https://www.analyticsvidhya.com/blog/2020/11/lasso-regression-causes-sparsity-while-ridge-regression-doesnt-unfolding-the-math/"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c32eff5c",
   "metadata": {},
   "source": [
    "<h2>Polynomial Regression </h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f82d1ba1",
   "metadata": {},
   "source": [
    "In statistics , polynomial regression is a form of regression analysis in which the relationship between the independent variable $x$ and the dependent variable $y$ is modelled as an $n^{th}$ degree polynomial in $x$.In Machine learning the polynomial regression is just the extended Linear Regression.This extension we achieve by the tranform the dataset as will shown below. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "id": "540553ed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plt.rcParams[\"figure.figsize\"] = (5,5)\n",
    "np.random.seed(0)\n",
    "x = 2 - np.linspace(-10,10,num=20) *4    #np.linspace(-10,10,num=10)  \n",
    "y = x - 2 * (x ** 2) + 0.5 * (x ** 3)  +100*np.random.normal(-50, 50, size=x.size)  \n",
    "x = x[:, np.newaxis]\n",
    "y = y[:, np.newaxis]\n",
    "plt.scatter(x,y, s=10)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "81071906",
   "metadata": {},
   "outputs": [],
   "source": [
    "model =  LinearRegression()\n",
    "z = model.fit(x,y)\n",
    "y_pred = model.predict(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "2bf6d784",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x31a919970>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, y_pred)  #L = 0.0028\n",
    "plt.scatter(x,y, s=10,color='r')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05c42a31",
   "metadata": {},
   "source": [
    "We can see that the straight line is unable to capture the patterns in the data. This is an example of <mark>under-fitting</mark> or <mark>High-Bias</mark>.  Computing the RMSE and R²-score of the linear line gives :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "d15a3b60",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7767230510045652"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(x,y)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "987afe81",
   "metadata": {},
   "source": [
    "\n",
    "Using the straight line model we achieve $R^2 = 77$% accuracy.To reach a more accurately result we can improve the model by increasing the complexity using higher order equation.We can add powers of of the original features as new features.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ffc84c7b",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "256ee90c",
   "metadata": {},
   "source": [
    "We can add new features to the dataset, which are just the  $𝑛_{𝑡ℎ}$  degree polynomial in existing ones.\n",
    "$$X = \\begin{bmatrix} \n",
    " x_1 \\\\\n",
    "\\vdots   \\\\\n",
    " x_n \\\\\n",
    "\\end{bmatrix} -- >  \n",
    "X_{polyData} = T(X) = \\begin{bmatrix} \n",
    "1 &x_1 & x_1^2 & \\dots & x_1^p \\\\\n",
    "\\vdots & \\ddots &  \\ddots & \\vdots & \\vdots \\\\\n",
    "1& x_n & x_n^2  & \\dots & x_n^p \\\\\n",
    "\\end{bmatrix} $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1eab986",
   "metadata": {},
   "source": [
    "The new Dataset 𝑇(𝑋) can be trained in Multiple Linear regression and the weights we achieve will correspond to in $w_p $ in $Y = \\omega_0  + \\omega_1 x^1 + ... + \\omega_p x^p$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e1dd314",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "42ff4a75",
   "metadata": {},
   "outputs": [],
   "source": [
    "polynomial_features= PolynomialFeatures(degree=2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "65f1809b",
   "metadata": {},
   "source": [
    "Example of tranformation of dataset "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "94093237",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1.],\n",
       "       [1., 2., 4.],\n",
       "       [1., 3., 9.]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "polynomial_features.fit_transform(np.array([[1],[2],[3]]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b8ef75c",
   "metadata": {},
   "source": [
    " $$X = \\begin{bmatrix} \n",
    " 1 \\\\\n",
    " 2   \\\\\n",
    " 3 \\\\\n",
    "\\end{bmatrix} -- >  \n",
    "X_{polyData} = T(X) = \\begin{bmatrix} \n",
    "1 & 1 & 1   \\\\\n",
    "2 & 2 &  4 \\\\\n",
    "1& 3 & 9 \\\\\n",
    "\\end{bmatrix} $$ T(X) 2 degree"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9fff0dae",
   "metadata": {},
   "source": [
    "Let's returned back to out dataset "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3b92a24e",
   "metadata": {},
   "source": [
    "We see that if we using linear eqaution the result is underfitting,Let's compare the 1,2,3 degree polynomial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "3e224c28",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "scaler = StandardScaler()\n",
    "#X = scaler.fit_transform(X)\n",
    "def polynomial_tranform(X,degree):\n",
    "    '''\n",
    "    applying standard scaler and transform data into polynomial     \n",
    "    '''\n",
    "    x_data = PolynomialFeatures(degree=degree).fit_transform(X)   \n",
    "    return StandardScaler().fit_transform(x_data)\n",
    "\n",
    "plt.rcParams[\"figure.figsize\"] = (10,10)\n",
    "for degree in 1,2,3:\n",
    "    x_poly = polynomial_tranform(x,degree)\n",
    "    model = LinearRegression().fit(x_poly,y)\n",
    "    y_pred = model.predict(x_poly)\n",
    "    plt.plot(x, y_pred)\n",
    "    plt.plot(x, y_pred,label=\"$degree = {}$,accuracy={:.2f}\".format(i,model.score(x_poly,y)))  #L = 0.0028\n",
    "    plt.scatter(x,y, s=10,color='r',label=\"data set\")\n",
    "    plt.title('graf 1')\n",
    "    plt.legend()\n",
    "plt.show()   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "b2e85d66",
   "metadata": {},
   "outputs": [],
   "source": [
    "def poly_regression(degree,x):\n",
    "    polynomial_features= PolynomialFeatures(degree=degree)\n",
    "    x_poly = scaler.fit_transform(x)\n",
    "    x_poly = polynomial_features.fit_transform(x_poly)\n",
    "    model =  LinearRegression()\n",
    "   \n",
    "    y_pred,model.predict(x_poly)\n",
    "    return model,y_pred,model.score(x_poly,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "6bb73a19",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    },
    {
     "ename": "NotFittedError",
     "evalue": "This LinearRegression instance is not fitted yet. Call 'fit' with appropriate arguments before using this estimator.",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mNotFittedError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-26-7fb0255a93de>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      4\u001b[0m     \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfigsize\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m50\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m50\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      5\u001b[0m     \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 6\u001b[1;33m     \u001b[0mlinear_model\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0my_pred\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mscore\u001b[0m \u001b[1;33m=\u001b[0m  \u001b[0mpoly_regression\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      7\u001b[0m     \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my_pred\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      8\u001b[0m     \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my_pred\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mlabel\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m\"$n^{}$,score={:.2f}\"\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mscor\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m  \u001b[1;31m#L = 0.0028\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-25-52fccfdbcbfc>\u001b[0m in \u001b[0;36mpoly_regression\u001b[1;34m(degree, x)\u001b[0m\n\u001b[0;32m      5\u001b[0m     \u001b[0mmodel\u001b[0m \u001b[1;33m=\u001b[0m  \u001b[0mLinearRegression\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      6\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 7\u001b[1;33m     \u001b[0my_pred\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mmodel\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpredict\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx_poly\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      8\u001b[0m     \u001b[1;32mreturn\u001b[0m \u001b[0mmodel\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0my_pred\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mmodel\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mscore\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx_poly\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_base.py\u001b[0m in \u001b[0;36mpredict\u001b[1;34m(self, X)\u001b[0m\n\u001b[0;32m    236\u001b[0m             \u001b[0mReturns\u001b[0m \u001b[0mpredicted\u001b[0m \u001b[0mvalues\u001b[0m\u001b[1;33m.\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    237\u001b[0m         \"\"\"\n\u001b[1;32m--> 238\u001b[1;33m         \u001b[1;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m_decision_function\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    239\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    240\u001b[0m     \u001b[0m_preprocess_data\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mstaticmethod\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0m_preprocess_data\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_base.py\u001b[0m in \u001b[0;36m_decision_function\u001b[1;34m(self, X)\u001b[0m\n\u001b[0;32m    216\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    217\u001b[0m     \u001b[1;32mdef\u001b[0m \u001b[0m_decision_function\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mX\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m--> 218\u001b[1;33m         \u001b[0mcheck_is_fitted\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mself\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m    219\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m    220\u001b[0m         \u001b[0mX\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mcheck_array\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mX\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0maccept_sparse\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m'csr'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'csc'\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;34m'coo'\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py\u001b[0m in \u001b[0;36minner_f\u001b[1;34m(*args, **kwargs)\u001b[0m\n\u001b[0;32m     61\u001b[0m             \u001b[0mextra_args\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m-\u001b[0m \u001b[0mlen\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mall_args\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     62\u001b[0m             \u001b[1;32mif\u001b[0m \u001b[0mextra_args\u001b[0m \u001b[1;33m<=\u001b[0m \u001b[1;36m0\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 63\u001b[1;33m                 \u001b[1;32mreturn\u001b[0m \u001b[0mf\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m*\u001b[0m\u001b[0margs\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     64\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     65\u001b[0m             \u001b[1;31m# extra_args > 0\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32mD:\\ProgramData\\Anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py\u001b[0m in \u001b[0;36mcheck_is_fitted\u001b[1;34m(estimator, attributes, msg, all_or_any)\u001b[0m\n\u001b[0;32m   1039\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1040\u001b[0m     \u001b[1;32mif\u001b[0m \u001b[1;32mnot\u001b[0m \u001b[0mattrs\u001b[0m\u001b[1;33m:\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m-> 1041\u001b[1;33m         \u001b[1;32mraise\u001b[0m \u001b[0mNotFittedError\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmsg\u001b[0m \u001b[1;33m%\u001b[0m \u001b[1;33m{\u001b[0m\u001b[1;34m'name'\u001b[0m\u001b[1;33m:\u001b[0m \u001b[0mtype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mestimator\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0m__name__\u001b[0m\u001b[1;33m}\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m   1042\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m   1043\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mNotFittedError\u001b[0m: This LinearRegression instance is not fitted yet. Call 'fit' with appropriate arguments before using this estimator."
     ]
    }
   ],
   "source": [
    "#fig, axs = plt.subplots(size, size,figsize=(25,25)) \n",
    "plt.rcParams[\"figure.figsize\"] = (10,10)\n",
    "for i in 1,2,3:\n",
    "    plt.figsize=(50,50)\n",
    "    print(i)\n",
    "    linear_model,y_pred,score =  poly_regression(i,x)\n",
    "    plt.plot(x, y_pred)\n",
    "    plt.plot(x, y_pred,label=\"$n^{}$,score={:.2f}\".format(i,scor))  #L = 0.0028\n",
    "    plt.scatter(x,y, s=10,color='r',label=\"data set\")\n",
    "    #plt.legend()\n",
    "plt.show()    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bed3bfc6",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "531092e8",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams[\"figure.figsize\"] = (10,10)\n",
    "for i in 1,3,25:\n",
    "    plt.figsize=(50,50)\n",
    "    y_pred,scor = poly_regression(i,x)\n",
    "    plt.plot(x, y_pred,label=\"$degree={}$,score={:.2f}\".format(i,scor))  #L = 0.0028\n",
    "    plt.scatter(x,y, s=10,color='r',label=\"data set\")\n",
    "    plt.legend()\n",
    "plt.show()    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "339dfad5",
   "metadata": {},
   "source": [
    "For degree=25 the model fits training data too much well 100% accuracy that is the very bad sign.In general this means the biases or  noise is captured too, that is called <mark>over-fitting</mark> or <mark>Low-Bias and high -variance</mark> .This is also mean that the model will fail for new unseen data."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff678259",
   "metadata": {},
   "source": [
    "<h2>Bias and Variance</h2>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3465654b",
   "metadata": {},
   "source": [
    "Bias refers to the error due to the model’s simplistic assumptions in fitting the data. A high bias means that the model is unable to capture the patterns in the data and this results in under-fitting.<br> <br>\n",
    "Variance refers to the error due to the complex model trying to fit the data. High variance means the model passes through most of the data points and it results in over-fitting the data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "dd7c3fe7",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams[\"figure.figsize\"] = (3,3)\n",
    "y_pred,scor = poly_regression(1)\n",
    "plt.plot(x, y_pred,label=\"$degree={}$,score={:.2f}\".format(i,scor))\n",
    "plt.scatter(x,y, s=10,color='r',label=\"data set\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "37ef2ba5",
   "metadata": {},
   "source": [
    "In case when degree=1 it called has high Bias and low variance or Underfit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f9085407",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams[\"figure.figsize\"] = (3,3)\n",
    "y_pred,scor = poly_regression(3)\n",
    "plt.plot(x, y_pred,label=\"$degree={}$,score={:.2f}\".format(i,scor))\n",
    "plt.scatter(x,y, s=10,color='r',label=\"data set\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b60dfcf2",
   "metadata": {},
   "source": [
    "In case when degree=3 that is correct fit,that has low bais and low variance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "06d4b986",
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "poly_regression() missing 1 required positional argument: 'x'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-17-d9e7d64aa5fe>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mrcParams\u001b[0m\u001b[1;33m[\u001b[0m\u001b[1;34m\"figure.figsize\"\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m(\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m,\u001b[0m\u001b[1;36m3\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mlinear_model\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mpoly_regression\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0my_pred\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mlabel\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m\"$degree={}$,score={:.2f}\"\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mi\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mscor\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[0mplt\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mscatter\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mx\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0my\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0ms\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m10\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mcolor\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m'r'\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mlabel\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;34m\"data set\"\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mTypeError\u001b[0m: poly_regression() missing 1 required positional argument: 'x'"
     ]
    }
   ],
   "source": [
    "plt.rcParams[\"figure.figsize\"] = (3,3)\n",
    "linear_model = poly_regression(1)\n",
    "plt.plot(x, y_pred,label=\"$degree={}$,score={:.2f}\".format(i,scor))\n",
    "plt.scatter(x,y, s=10,color='r',label=\"data set\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c521c6b3",
   "metadata": {},
   "source": [
    "In case when degree=25 that is overfit,that has low bais and high variance."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9daedec8",
   "metadata": {},
   "source": [
    "<h2> Some notes PCA </h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "id": "ec2d4bd7",
   "metadata": {},
   "outputs": [],
   "source": [
    "polynomial_features= PolynomialFeatures(degree=3)\n",
    "x_poly =  polynomial_features.fit_transform(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "id": "84a047e9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(20, 1)"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(1)\n",
    "x_tranform= pca.fit_transform(x_poly)\n",
    "x_tranform.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "id": "a240fb3a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 42.        ],\n",
       "       [ 37.78947368],\n",
       "       [ 33.57894737],\n",
       "       [ 29.36842105],\n",
       "       [ 25.15789474],\n",
       "       [ 20.94736842],\n",
       "       [ 16.73684211],\n",
       "       [ 12.52631579],\n",
       "       [  8.31578947],\n",
       "       [  4.10526316],\n",
       "       [ -0.10526316],\n",
       "       [ -4.31578947],\n",
       "       [ -8.52631579],\n",
       "       [-12.73684211],\n",
       "       [-16.94736842],\n",
       "       [-21.15789474],\n",
       "       [-25.36842105],\n",
       "       [-29.57894737],\n",
       "       [-33.78947368],\n",
       "       [-38.        ]])"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_poly\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "id": "17d41ea6",
   "metadata": {},
   "outputs": [],
   "source": [
    "model = LinearRegression().fit(x_poly,y)\n",
    "y_pred_1 = model.predict(x_poly)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "id": "08bf8eff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x313de7700>"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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PPc5u6UBiucMSgEynPaGS9grHGGPCgEZAViXfP8lam2ytTW7evLl/LkpERERqjRnL0okIDWFEYiHsWOTrVavlI6f8MRu0uTEm1nkfDVwCbABmA2Od3cYCHzrvZwNjnBme7fBNJFjs3CrNM8YMcsaj3XbUMWXnGgXMc8a1iYiIiABQ4vEye0UmF3drQczGmYCBXqPdLqvKwvxwjtbAZGdGZwgw3Vr7sTFmITDdGHMnsB24AcBau9YYMx1YB5QC91trPc657gXeBKKBz5wXwGvAW8aYVHw9arX75rOIiIj43Tcpe9l/qJjr+8XD3Heh/fnQKP7kBwa4Koc1a+0qoF8l7fuBi49zzOPA45W0LwGOGe9mrS3ECXsiIiIilZm5LJ2m9SO4oN5myN4GFz7idkl+oRUMREREpNbLzi/mq/V7GNE3nrDV0yC8PnS9yu2y/EJhTURERGq9j1ZmUuzxMqpPU1g7C7pfA5EN3C7LLxTWREREpNZ7f1kGXVs1pFvu91CUU+ufrVaewpqIiIjUaql7DrJyRzbX90/ArJwKMfGQdJ7bZfmNwpqIiIjUajOXpRMaYhjZOQxSv4TeoyEk9OQH1hIKayIiIlJrebyWD5ZnMLRTM5pv/RisB3rXnVugoLAmIiIitdjCzfvZmVPoLC/1LsT1gxZd3S7LrxTWREREpNaasSydhlFhXNp0P+xaBX1ucrskv1NYExERkVrpYFEpn6/ZxVW944hcOx1CwqDn9W6X5XcKayIiIlIrfbp6JwUlHkb1awWrpkOny6B+M7fL8juFNREREamVZi5Lp12z+vT3rIKDu+rUs9XKU1gTERGRWmdHVj6LtmRxXb94zMp3IaoRdB7udlnVQmFNREREap0PlmcAcG33GFj/sW+sWliky1VVD4U1ERERqVWstcxcls6g9k1I2DUXSgvq5CzQMgprIiIiUqss3XaAtP35XN8/AVZOhSbtIeEst8uqNgprIiIiUqu8tmArDaPCuLJNKaR95+tVM8btsqqNwpqIiIjUGlv3HeLztbu4dVBb6m1439fYe7S7RVUzhTURERGpNSbN30J4aAi3n9PWdwu07RBonOR2WdVKYU1ERERqhT15hcxYls71/RNokbsW9qfW2WerlaewJiIiIrXCm9+nUeLxMm5oe9+i7WFR0H2E22VVO4U1ERERCXgHi0p5a9E2hvdoRbvYMFgzA7pe6XsYbh2nsCYiIiIB790ft5NXWMo953eAlE+h4ECdfrZaeQprIiIiEtCKS728tmArg9o3oU9CI/jhP75JBe0vdLu0GqGwJiIiIgHtwxUZ7Mot9PWqpS2AjKVwzi8hNMzt0mqEwpqIiIgELK/XMmn+Frq2asj5nZvD989B/ebQ92dul1ZjFNZEREQkYH2dsodNew5yz/kdMLvXQOqXcPbdEB7tdmk1RmFNREREAtZL324mPjaaK3u3hu//BREN4KxfuF1WjVJYExERkYC0dFsWP6Ud4M5z2xGeuwPWzIQBt0N0Y7dLq1EKayIiIhKQXvp2C7H1whkzMBEW/hdMCAy6z+2yapzCmoiIiASc1D0HmbtuN7cNaku9khxYNsW3YHujeLdLq3EKayIiIhJwJs3fTGRYCGPPSYLFk6C0AIb82u2yXKGwJiIiIgFld24hHyzPYHRyIk0jSmHxy9DlCmjexe3SXKGwJiIiIgHl9QVb8Xgtd53XHpa95Vtaashv3C7LNQprIiIiEjByC0v434/buaJXa9rEhsPC5yFxELQ52+3SXKOwJiIiIgHjf4u2c7DIWbB9zUzI2QHn/sbtslylsCYiIiIBoajUw+vfb+Xcjs3oGRfjewhu867QaZjbpblKYU1EREQCwgfLMtibV+TrVds0F/as9c0ADQnuuBLcVy8iIiIBoWzB9h5xMQzp2NS3YHtMPPQc5XZprlNYExEREdd9sW43W/Yd8i3Ynr4Etn0Pg++HsAi3S3OdwpqIiIi4ylrLS99uJrFJNJf3bOXrVYuKhf5j3S4tICisiYiIiKsWb81ixY5sxp3XnrCsVNjwCQy8CyIbuF1aQFBYExEREVe9PH8LTepHMGpAIvzwLwiLhIF3u11WwFBYExEREdek7Mpj3oY93H5OEtGFu2HlNOh3CzRo7nZpAUNhTURERFzz8vzNRIeHcuugtrDoBbAeGPyA22UFFIU1ERERcUVGdgGzV2Ry41mJNA7JhyVvQo9roUk7t0sLKAprIiIi4orXF2zFAr84rx0seQ2K83wPwZUKFNZERESkxuXkl/Du4u1c3bs1CQ1CYNFL0OEiaN3H7dICjsKaiIiI1Li3FqWRX+zh7vM7wMp34NAeGPIbt8sKSGFuFyAiIiLBpbDEw5s/pHF+5+Z0a1kf3vsPxPWDdkNPeuys5RlMnJNCZnYBcbHRjB/WhZH94mugavcorImIiEiNen9pOvsOFvsWbF8/G7K2wA2TwZgTHjdreQYTZq6moMQD+CYoTJi5GqBOBzbdBhUREZEa4/FaXvluC30SGjGoXWNY8Bw06QDdrj7psRPnpBwOamUKSjxMnJNSTdUGBoU1ERERqTGfr9nFtv35vgXb076DnSvgnF9CSOhJj83MLjit9rpCYU1ERERqRNmC7e2a1eeyHs6C7fVbQJ+bTun4uNjo02qvKxTWREREpEYs3Lyf1Rk53HVee0J3r4LN82DQvRAedUrHjx/Whejwij1w0eGhjB/WpTrKDRiaYCAiIiI14qX5W2jWIJLr+sfDh3+BiIaQfMcpH182iUCzQU+TMSYRmAK0ArzAJGvtv4wxTYBpQBKQBoy21h5wjpkA3Al4gF9Za+c47QOAN4Fo4FPg19Zaa4yJdL5jALAfuNFam1bV2kVERKRmrM3MYf7GvYwf1oWovO2w9gMYfD9Ex57WeUb2i6/z4exo/rgNWgr81lrbDRgE3G+M6Q48DHxlre0EfOV8xtk2BugBDAdeMMaU9Wm+CIwDOjmv4U77ncABa21H4FngaT/ULSIiIjVk0vwt1I8I5Zaz28LC58GEwqD73C6rVqhyWLPW7rTWLnPe5wHrgXhgBDDZ2W0yMNJ5PwKYaq0tstZuBVKBgcaY1kCMtXahtdbi60krf0zZud4HLjbmJA9jERERkYCwIyufj1ft5Oaz29DImw3L34Y+N0JMnNul1Qp+nWBgjEkC+gE/Ai2ttTvBF+iAFs5u8cCOcoelO23xzvuj2yscY60tBXKApv6sXURERKrHawu2EmLgjnPbweKXobQIztGC7afKb2HNGNMAmAH8xlqbe6JdK2mzJ2g/0TFH1zDOGLPEGLNk7969JytZREREqlnWoWKm/rSdEX3jaR3lgcWvQNcroXlnt0urNfwS1owx4fiC2v+stTOd5t3OrU2cn3uc9nQgsdzhCUCm055QSXuFY4wxYUAjIOvoOqy1k6y1ydba5ObNm/vj0kRERKQKpixMo7DEy7ih7WHZZCjM1oLtp6nKYc0ZO/YasN5a+0y5TbOBsc77scCH5drHGGMijTHt8E0kWOzcKs0zxgxyznnbUceUnWsUMM8Z1yYiIiIBKr+4lMk/pHFx1xZ0bhoJC/8LbYdA4llul1ar+OM5a0OAW4HVxpgVTtsjwFPAdGPMncB24AYAa+1aY8x0YB2+maT3W2vLFvq6lyOP7vjMeYEvDL5ljEnF16M2xg91i4iISDV6b0k6B/JLuOeCDrDmfcjNgKuec7usWsfU1Q6q5ORku2TJErfLEBERCUqlHi8X/PMbWjSMZMY9gzAvnuN7XMe934Me6HAMY8xSa21yZdu03JSIiIj43Serd5J+oMC3YPumL2DvBhjyawW1M6CwJiIiIn5lreXlb7fQoXl9LunWEhY8B40Soed1bpdWKymsiYiIiF99t2kf63bmcvfQDoSk/wg7FsHgByA03O3SaiWFNREREfGrl+dvpmVMJCP6xfl61aKbQP9b3S6r1lJYExEREb9ZnZ7D96n7uWNIOyKzNsLGz2DgOIio73ZptZbCmoiIiPjNS/M30zAyjJvObgPf/xvCon1hTc6YwpqIiIj4xbb9h/hs9U5+NqgtMUW7YfV06H8b1Ndy3lWhsCYiIiJ+8cp3WwgLCeGOIUmw8AWwFgbf73ZZtZ7CmoiIiFRZZnYB7y1J57r+8bQIy4elb0LP66FxW7dLq/UU1kRERKTKHv9kPQD3X9gRfnoNSg75HoIrVeaPtUFFREQkAM1ansHEOSlkZhcQFxvN+GFdGNkv3u/f833qPj5ZvZOHLu1MYkMDP74EHS+FVj39/l3BSGFNRESkDpq1PIMJM1dTUOIBICO7gAkzVwP4NbCVeLw8NnstbZrUY9zQ9rDiDcjfB+f+xm/fEex0G1RERKQOmjgn5XBQK1NQ4mHinBS/fs+b36eRuucgj13dnagQCz/8B+KToe0Qv35PMFNYExERqYMyswtOq/1M7Mkt5LkvN3JR1xbkFZby56eegANpPLLnImatyPTb9wQ7hTUREZE6KC42+rTaz8STn22gxGMZ3L4pE2auYnTRDDZ7WzM1rzcTZq5m1vIMv31XMFNYExERqYPGD+tCdHhohbbo8FDGD+vil/Mv3prFB8szGDe0PW/+kMYwz3x6hqTxkudqvIRUyy3XYKWwJiIiUgeN7BfPk9f1Ij42GgPEx0bz5HW9/DK5oNTj5c8friE+Npr7L+xIXvY+Hg1/mxXeDrzvGXp4P3/ecg1mmg0qIiJSR43sF18tj+r434/b2bArjxd/1p/oiFD+XP8DmpTmcXvJH7Dl+oH8ecs1mKlnTURERE7ZvoNF/L8vUji3YzOG92wFmSu43vM579rLWGvbHd7Pn7dcg53CmoiIiJyyiZ+nkF/s4S/XdMdYC5/8FlO/GY2v+mu13HIV3QYVERGRU7R8+wGmLdnBuKHt6diioW/9z4wlcO3LXNmnG1cO7OZ2iXWSetZERETkpDxey58/XEuLhpH86uJOcGg/fPkX38Nve9/odnl1msKaiIiInNT0JTtYnZHDo1d2o0FkGHz5GBTlwZX/D4xxu7w6TWFNRERETig7v5j/+3wDA5OacE2fONj+Iyx/CwbdBy1067O6KayJiIjICf2/LzaSW1jKX0f0wHg98MlvISYezv+D26UFBU0wEBERkeNak5HD/37cxm2Dk+jWOgYWvQi7V8PoKRDZwO3ygoJ61kRERKRSXq/lzx+uoXG9CB68tDPk7YJ5j0OHi6HbNW6XFzQU1kRERKRSHyzPYNn2bP5weVcaRYfDF38ETxFcMVGTCmqQwpqIiIgcI7ewhCc/20DfxFhG9U+ALd/C6vfg3AehaQe3ywsqGrMmIiIix3hu7ib2Hyri9duTCfGWwKe/g9i2vrAmNUphTURERCpI2ZXH5IVp3DSwDb0TYuG7Z2DfRrj5PQjX4uw1TbdBRURE5DBrLY/NXkPDqDDGX9YFsrfD/InQ9SrofJnb5QUlhTURERE57ONVO1m0JYvfXdaFxvUj4PMJvg3Dn3S3sCCmsCYiIiIAHCoq5fFP1tMzPoabBraBjXNgw8cwdDzEtnG7vKClMWsiIiICwH/mpbIrt5D//qw/oZ5C+HQ8NOsMgx9wu7SgprAmIiIibN57kNcWbGHUgAQGtG0MXz8B2dtg7EcQFuF2eUFNt0FFRESCnLWWv8xeS1RYKH8Y3hX2b4YFz0LPUdBuqNvlBT2FNRERkSD3xbrdfLdpHw9e2pnmDSJ8tz9DI2HY426XJiisiYiIBLWCYg9/+2gdXVo25LbBbWH9bNj8FVz0KDRs5XZ5gsasiYiIBLUXv91MRnYBU8cNIqw0Hz57GFr2grPucrs0cahnTUREJEht35/PS99u5po+cQxq3xS+fRryMuGqZyBU/TmBQmFNREQkSP3t43WEhRgeuaIb7FkPi16AfrdC4kC3S5NyFNZERESC0Ncb9vDl+t386uJOtIqJhE9+C5EN4ZK/ul2aHEV9nCIiIkGmsMTDXz5aS/vm9bljSDtYNQ22fQ9XPQf1m7pdnhxFYU1ERCTIvLZgK9v25zPljoFElOTCF3+E+AHQf6zbpUklFNZERESCSEZ2Af+Zt4nhPVoxtHNz+OR3kL8ffvY+hGh0VCDSn4qIiEgQefyTdQD88apukLkClrwGZ/0C4vq6Wpccn8KaiIhIkFiwaR+frt7F/Rd0JKFRFHzyENRrBhc+6nZpcgK6DSoiIhIEiku9PDZ7DW2a1OOuoe1h2WTIWArXToLoWLfLkxNQWBMREalBs5ZnMHFOCpnZBcTFRjN+WBdG9ouv9u+d/EMam/ce4rWxyUQVH4Av/wJtz4Xeo6v9u6VqFNZERERqyKzlGUyYuZqCEg/gG+w/YeZqgGoNbHtyC3nuy41c1LUFF3drCR/eD8UH4cp/gjHV9r3iHxqzJiIiUkMmzkk5HNTKFJR4mDgnpVq/94lP11Pisfz5qu6w/UdY/jYMug9adKvW7xX/UFgTERGpIZnZBafV7g8/btnPrBWZ3H1+e5IaR/omFcTEw/l/qLbvFP9SWBMREakhcbHRp9VeVXmFJUz4YDVxjaK474KO8NMrsHsNDH8SIhtUy3eK//klrBljXjfG7DHGrCnX1sQYM9cYs8n52bjctgnGmFRjTIoxZli59gHGmNXOtn8b47uRboyJNMZMc9p/NMYk+aNuERGRmjR+WBeiw0MrtEWHhzJ+WBe/f5fXa/nt9JVs25/PMzf2JbpwD8x7HDpcDN2u8fv3SfXxV8/am8Dwo9oeBr6y1nYCvnI+Y4zpDowBejjHvGCMKfub+yIwDujkvMrOeSdwwFrbEXgWeNpPdYuIiNSYkf3iefK6XsTHRmOA+NhonryuV7VMLnjhm1S+WLebR67oxqD2TX1LSnmK4YqJmlRQy/hlNqi1dn4lvV0jgAuc95OBb4A/OO1TrbVFwFZjTCow0BiTBsRYaxcCGGOmACOBz5xj/uKc633geWOMsdZaf9QvIiJSU0b2i6/2R3V8nbKH/zd3IyP6xnHHkCTY8i2sed83Tq1ph2r9bvG/6hyz1tJauxPA+dnCaY8HdpTbL91pi3feH91e4RhrbSmQAzSttspFRERqqW37D/Hrd5fTtVUMT13XG+MpgU9/B42T4NwH3S5PzoAbEwwq63u1J2g/0TEVT2zMOGPMEmPMkr1791ahRBERkdonv7iUu99aijGGl28ZQHREKPzwb9i3ES6fCOHVM5FBqld1hrXdxpjWAM7PPU57OpBYbr8EINNpT6ikvcIxxpgwoBGQdfQXWmsnWWuTrbXJzZs39+OliIiIBDZrLQ/PWE3K7jz+fVM/2jStB1u+ga+fgO4joPNlbpcoZ6g6w9psYKzzfizwYbn2Mc4Mz3b4JhIsdm6V5hljBjmzQG876piyc40C5mm8moiIyBGvLdjK7JWZ/O6yLpzfuTns3wzTx0LzLjDiv26XJ1XglwkGxph38U0maGaMSQceA54Cphtj7gS2AzcAWGvXGmOmA+uAUuB+a23Z45zvxTezNBrfxILPnPbXgLecyQhZ+GaTioiICLBw836e/GwDw3q05L4LOkBBNrxzI5gQuOldiGzodolSBaaudlAlJyfbJUuWuF2GiIhItcrMLuDq/ywgtl44s+4fQsNwA++Mhq3fwm2zIWmI2yXKKTDGLLXWJle2TQu5i4iI1FKFJR7ufXspRaVeXr41mYZR4fD5I7D5K7j63wpqdYTCmoiISC1kreWxD9eyMj2Hl28dQMcWDWDZFFj0Xzj7Xhgw9uQnkVpBa4OKiIjUQu8s3s60JTt44MKODOvRCrb9AB8/BB0ugsv+4XZ54kcKayIiIrXMsu0H+MvstZzfuTkPXtoZDmyDabdA47Yw6g0I1Y2zukRhTUREpBbZk1fIvW8vpXWjaP41pi+hJQfh3ZvAWwo3TYPoWLdLFD9T9BYREaklSjxeHvjfcnIKSph570Bio8Jg2ljYuwFueR+adXS7RKkG6lkTERGpJR7/ZD2L07J4+vredI+LgXl/h5RPYfhTvrFqUicprImIiNQCM5el8+YPadx5bjtG9I2HVdNhwTMw4Ocw8C63y5NqpLAmIiIS4NZk5DBh5moGtW/ChMu7QvoS+PABSDoPrpgIxrhdolQjhTUREZEAduBQMfe8vZQm9SN4/ub+hB3cCVNvhpjWMHoKhIa7XaJUM4U1ERGRAOXxWn41dTl7cot48ZYBNIvwwNSboDgfbpoK9Zq4XaLUAM0GFRERCVAT56Tw3aZ9PH19L/omNIL3boedq+DmadCim9vlSQ1Rz5qIiEgA+mz1Tl76djM3n92GG89qA9/+H6ybBZf+DToPc7s8qUEKayIiIgFm0+48fvfeSvq1ieWxq7vD2lnwzRPQ52Y455dulyc1TGFNREQkgOQWljDuraVER4Tx4s8GELl3DXxwDyQMhKuf08zPIKSwJiIiEiC8XstD01awIyufF37Wn1YhOb6lpOo1hTH/g7BIt0sUF2iCgYiISID4z7xUvly/h79c3Z2BCfVg8lVQcADumAMNWrhdnrhEYU1ERCQAzNuwm+e+2sh1/eIZO7gtzLoX0n+C0W9B695ulycu0m1QERERl6XtO8Svp66gW6sYnriuF+aHf8GqqXDhH6H7NW6XJy5TWBMREXHRoaJS7n5rKaEhhpdvHUDU5jnw5V+h5/Uw9HdulycBQGFNRETEJdZafj9jFZv25PGfm/qRWLIVZt4FcX1hxH8181MAhTURERHXvPLdFj5ZtZPxw7pyXpyBd8dARAMY8w6ER7tdngQITTAQERFxwQ+p+3jqsw1c3rMV95ybAFNGQt5u+PlnEBPndnkSQBTWREREatiOrHweeHc5HZo3YOKo3phPHoTtP8B1r0LCALfLkwCj26AiIiI1aOPuPEa/vJASj5eXbx1AgxWvwvK34LzfQu8b3C5PApDCmoiISA1ZkpbFqBd/wOO1TBs3mPY5i2DOI9DlSt9jOkQqobAmIiJSA+au283PXv2RZg0imXHvOXQP3wXv3QEtusN1kyBEv5KlcvqbISIiUs2mLt7O3W8toWvrGN67ZzCJUYXw7o0QGg43vQuRDdwuUQKYJhiIiIhUE2stz89L5f/N3cj5nZvz4i39qXdwO7wzBrJ3wNiPILaN22VKgFNYExERqQYer+WvH61lysJtXNcvnqdH9SZ8+/cw/VawFm6dCW0Hu12m1AIKayIiIn5WWOLhoekr+HT1Lu4e2p4/DO9KyPLJ8MlvoUl7uGkqNO3gdplSSyisiYiI+FFuYQnjpixh0ZYs/nhlN35xThv44hFY9AJ0uBhGvQ7RsW6XKbWIwpqIiIif7MktZOwbP7Fpdx7P3diXkd0a+CYSpH4JZ98Ll/0DQvWrV06P/saIiIj4wZa9B7nt9cVkHSrm9dvPYmizPHj1WsjaDFc9B8k/d7tEqaUU1kRERKpo5Y5sfv7mTxhg6rhB9C5dA6/c4tt46wfQbqir9UntpuesiYiIVMG3G/dy0yuLqB8Zyvv3nkPv3R/ClBFQvzn84isFNaky9ayJiIicoQ+WpzP+vVV0btmQN2/vT4uF/9BEAvE7hTUREZEz8Mr8LTz+6XoGt2/KpNGdaPjRWEidC2ffA5c9rokE4jf6myQiInIavF7Lk5+t55XvtnJl79Y8c0kMkW9f7kwkeBaS73C7RKljFNZEREROUXGpl9+/v5JZKzIZO7gtj/U6QMgb14P1aiKBVBuFNRERkVNwqKiUe95eyneb9jF+WBfui/ke8/ZD0Lgd3DxNKxJItVFYExEROYn9B4u4482fWJOZy8TrenBD1iT46L/Q4SIY9YYmEki1UlgTkYAwa3kGE+ekkJldQFxsNOOHdWFkv3i3yxJhR1Y+t72+mMzsAl69sQsXrhkPm76AgXfDsCc0kUCqnf6GiYjrZi3PYMLM1RSUeADIyC5gwszVAAps4qq1mTnc/sZPFJd6eX9Ma3p9ezPsT9VEAqlReiiuiLhu4pyUw0GtTEGJh4lzUlyqSAQWbt7PmJcXERZi+PgaQ69ProW8Xb6JBApqUoMU1kTEdZnZBafVLlLdPl29k7GvL6ZVoyg+G5pG4kc3Qb2mcNc8zfiUGqfboCLiurjYaDIqCWZxsdEuVCOBxI2xjFMWpvHY7LWclRjDlDafEDX3RU0kEFepZ01EXDd+WBeiw0MrtEWHhzJ+WBeXKpJAUDaWMSO7AMuRsYyzlmdUy/d5vJZ/zknhzx+u5crODXi34b+IWvKibyLBze8pqIlr1LMmIq4r6ynRbFAp70RjGf39d2Pljmz+9OEaVqXncF+fUMZn/R6zbxNc+Qycdadfv0vkdCmsiUhAGNkvXuFMKqiJsYzZ+cX835wU3l28neYNInn7klKGLH0AU7YiQfvz/fZdImdKYU1ERAJSdY5l9Hot7y3dwVOfbSC3sJRfndWA+0NnEvHD21qRQAKOwpqIiASk8cO6VHj+HvhnLOPazBz+NGsNy7Znc2GbUP7Z+luarn0TvB4YcDtc9CeNT5OAorAmIiIByd9jGXMKSnh27kamLEwjPtrDJ31+pHvaFMyePOgzBi54GBon+fEKRPxDYU1ERAKWP8YyWmv5YHkGT3y6gYOH8vhv+2UMO/AOISn7oOtVcNEfoUU3P1Us4n8KayIiUmel7MrjTx+uYenWvTzYbAnjIt8jIiMT2l8AF/8Z4ge4XaLISdWqsGaMGQ78CwgFXrXWPuVySSIiEoAOFpXy3NyNvPnDFq6LXMKrTT8g5mAaxCfD9S9plqfUKrUmrBljQoH/ApcC6cBPxpjZ1tp17lYmIiKBwlrLx6t28o+P19ItfzHfxnxAfOEmqN8drn4XulwOxrhdpshpqTVhDRgIpFprtwAYY6YCIwCFNRERIXXPQR6bvYaizd/zev336RG+DqKT4IpXoOf1EBJ60nOIBKLaFNbigR3lPqcDZ7tUi4iIBIj84lL+My+VH777it+Fv8d5kcuxUa3g/Geg360QFuF2iSJVUpvCWmX91rbCDsaMA8YBtGnTpiZqEhERl1hrmbN2N2/OnsstBW/zh/BFeKNi4dy/YgaOg4h6bpco4he1KaylA4nlPicAmeV3sNZOAiYBJCcnVwhyIiJSd6TtO8S/P/iagdte4X9h8yEyCs75PSHnPABRjdwuT8SvalNY+wnoZIxpB2QAY4Cb3S1JRERqUmGJhzfmLiFq0bM8ZeYSGm4wA+8m5LzfQoPmbpcnUi1qTViz1pYaYx4A5uB7dMfr1tq1LpclIiI15JuVqaR99BS3lnxEvZBiinqOIeKSRyA28eQHi9RitSasAVhrPwU+dbsOERGpOTt272fR1Ke4JOsdLjAH2Zd0BQ2u/hvRzTq5XZpIjahVYU1ERILDob3bWP/dB3g3fkHXgmXcYArY3nQIDa59nGaJ/dwuT6RGKayJiIj7SovwpC0kc+lHhG3+ktbFaSQDe0xTtrUaRtzQn9OmxwVuVyniCoU1ETmhWcszmDgnhczsAuJioxk/rEuVF9YWAeBAGqR+Sd6az4jc8T0R3gJa2DCWm24sb30/bc++hu69B9IiJMTtSkVcpbAmIsc1a3kGE2aupqDEA0BGdgETZq4GUGCT01dSAGnfQ+qXlG78grADmwE44G3OfHsuB+KG0nXwFQzt2Y7IMK02IFJGYU1EjmvinJTDQa1MQYmHiXNSFNbk5KyF/Zsh9UtInYtNW4ApLaTYRPCDpxvfeG5jd4tzGXzWQK7qE0+T+lppQKQyCmsiclyZ2QWn1S5C0UFI+84X0DbNhextAOyJSGROyYV8WdKb7Q37cWX/9tzaP54OzRu4XLBI4FNYE5HjiouNJqOSYBYXG+1CNRKQrIW9G46Es+0LwVOMN6weWxoOYFbYZXx4qDsHbDxX9mrNvf3jGZjUhJCQylYQFJHKKKyJyHGNH9alwpg1gOjwUMYP6+JiVeIKrwcO7YXcDMjdCXk7YddqSP0KctMBKG3alfUJY5h2oAvT9yTgyY9gaKdm/L5/Apd2b0lUuMahiZwJhTUROa6ycWmnNBvUWig+CEV55V65R30+Xlu59pICCI2AsEgIizr2Z2hE5e0Vfp5om/MzNBLCoyGyIUQ08LWZIO3tKc73ha/cTOdnWSDLPBLM8naBrTh+kcgYPElDWdthHFP2dmTWFkOp19IjLoY/XJXANX3iaN4w0p1rEqlDFNZE5PjysxjZcD0jh6yEQ/t9gWpTHqw5TtjCnvycYU5AKntFxUDjpCOfw6LAWwqlhVBadOzP4kOQv7/ybaWFp1ZDZULCfKGtLLxFNij3s+Hpfw4NgP+8er2+f1aHQ9dRP3Mzfe8Lc449NjIGGraGmNbQ7Hzfz5g4vA1as5smrDtYn6+2e/lo9W7yCktpFRPFnefFcV2/BLq0aljz1ypShwXAf01EJCAU5UHmCshcDpnLIGPZ4cHhwJEgc/gVAw1b+X5WaC+3vbL20PDquwZrTxD0CqG0uGJbSb5vQHxxnvPz4LGf83Yd6TEsPug7/6kIi4KIBhwimsyCUPI9IYSHhtAqth5N6kcCBkyIrzfPhDifndfh9yGn8N5UPJfXAwf3+EJY3i7wFFesy4RA/RYQEwdNO0DSub4g1jDOCWTxvpAW2YDCEg8bd+exLjOXdTtzWbcxl/U7czlUnAVkUS8ilOE9WnFd/wQGd2hKqMahiVQLhTWRYFRS6BtvVD6Y7dvI4V6pRm0gvh8k3wHx/aF1H4hq5GrJp8QYXxgMDfcFQ3+z1undKxfeDoe8Yz9vzdzN6i0ZRNsCwijFlML+LOgSFk6LhhFgvb5zgu+91wvYcu0nem8rb8dAgxaQOKhi+IqJ8/1s0LLSXr99B4tYl5nL+rW5rNu5iXWZuWzeexCvU16DyDC6tW7IqAEJdI+LoVvrGDq3bKhxaCI1QGFNpK7zlMCe9b5QlrncF8z2rDvSQ1S/hS+Q9bze9zOuH9Rv5m7NgcoYCI/yvU7hn9EtT80jo/jY2bTxedF8f/9F1VHhSXm8lrS9Bw/3lq3fmcu6zFz25BUd3ieuURTd42K4vGcrusfF0L11IxIaR2sGp4hLFNZE6hKvF/anHukty1wOu1Y5Y7nw9Y7F9YNzfuUEs/6+HpdgHVhfzdx+Tl1+cSkbdpW7jZmZS8quvMOze8NCDB1bNODcTs3o3jrGCWYxxNbTw2lFAonCmkhtZS1kb68YzHaudAb6A+H1oHVfSL7zSI9Zk/YKZjWoup5TZ63lYFEp2fkl5BSUkFtQQnaB7/2+vCI27M5jfWYuW/cfOnyXNSYqjG6tYxgzMPFwMOvYooGWdRKpBRTWRGqbwhxY8Q4sfgWyfGsrEhoBLXtCrxuO9Jg17wIh+kXsppM9p66wxHM4cGXnF5PjBK6yV9m2HCeM5Zbb5vEef9ZrYpNoureO4Zq+cYeDWXxsNEZBXaRWMtae4TT3AJecnGyXLFnidhki/rN7Hfz0CqycBiWHIGEg9B4N8QOgZQ/fc8JqMWsth4o95BWWUOqxeK3Fa31jrLzWHv7p9YLH+Wydnx5rsc6+Hmvxeo9zrLV4vDjbnX0th8/jtUe2eS3O9x1nv3Lfc+Tcx+63bf8h1mbmUlDiISI0hCb1I/BYS05BCcWl3uP+8wgxEBMdTmx0OI2iw33v60XQKDqM2OgIGjntjer5fsaW/YyOIDpCIV2ktjHGLLXWJle2TT1rIoHMUwopn8LiSb71FkMjfb1nA3/hu60ZoApLPBzILyY7v4QD+cXk5JdwIL+E7AJfW3Z+se/z4X1KyCkopsQT2P/zGGIgxBhCQgwhBkKNIcQY3yTUEFNhW4gp+wwtYiKpHxFWIVSVhayygFV+W0x0OA0jwzSgX0QAhTWRwHRoHyybDD+97lvKp1EiXPIX6Hcb1G9ao6V4vJbtWfnsyS0ku+DYgHXgUPkQ5gtnRSfoMYoMC6FxvQhi6/nCSYfmDWhcP5xG0RE0rhdOw6hwwkINocYQGnIkCIUag3HaQkOOhKGykBRaFpJCKj82pGw/J0CVP/aYEBZSLoSZIyFMRMQNCmsigSRjma8Xbc0M38NM250Plz8NXS6vkfFnJR4vm3YfZE1mDmszcljrzCLML/Ycs294qCG2XgSx0eE0rhdBYpN69E7w3aqLrefrLWpcz9eDVBbOGteLCIjncs1annFqS2iJiAQAhTURt5UWwdpZvpCWsQTC60P/2+Csu6BF12r72sISD+t35rImM5d1mTmsyfA91qHY4+sVqx8RSve4GEYnJ9I9Loa4RtGHe8Ma14ugXkRorRywPmt5RoVB/xnZBUyYuRpAgU1EApLCmohbcjJg6Ruw9E04tBeadoTL/w/6jPH7agG5hSWsy8xlbWYuazNyWJOZw+a9hw7PKIytF07PuEb8fEgSPeIb0TMuhqSm9evkrb+Jc1IqzM4EKCjxMHFOisKaiAQkhTWRmmQtbPvB14u2/iPfMkGdh8PAu6D9hRASUuWv2H+wiLWZuc6tzFzWZuaQtj//8PaWMZH0iGvE8B6t6BHfiB5B9lgHtx9UKyJyuhTWRGpC8SFY/Z7v2Wi710BULAy+z/fA2ibtzuiU1lp25RayJiOXNc74srWZOezMKTy8T2KTaHrGNeIG51Zmj7gYWjSM8tNF1U7V9aBaEZHqorAmUp2ytsBPr8Hyt3wPs23ZC67+t+/xGxH1zuiUGdkFzFyazoxl6Yd7zIyBDs0bcHa7JvSIa0SP+Bh6tG5Eo3rh/ryaOuFkD6qVk9MEDZGapbAm4m9eL2ye57vVuekL3yzObtfAwHHQZtAZLfdUUOzh87U7eX9pOj9s3o+1MLh9U24/J4leCY3o1jqGehH61/lUlIUKhY0zowkaIjVPKxiI+NOGT+CLP/mWgarfApJ/DgNu9y2WfpqstSzddoD3l6bz8aqdHCwqJbFJNKP6J3Jd/3gSm5xZz5zUTTXV2zXkqXmV3kaOj43m+4cv8vv3iQQLrWAgUt2KDsKcCbBsCrToAde9Ct1HQFjEaZ8qM7uAmcvSeX+p7zZnvYhQrujVmhsGJHBWUpM6OUNTqqYme7s0QUOk5imsiVRV+lKY+QvI2grnPggXPHLaIa2g2MMX63bx/tJ0FqTuw1oY1L4JD1zUict7tqJ+ZMV/VTVmSMqryceRaIKGSM1TWBM5U55SWPAMfPMUxMTx3ZA3eXhJDJlfzj2lAGWtZdl25zbnyp3kFZWS0DiaX13UiVEDEo57m1NjhuRoNdnbpQkaIjVPYU3kTBxIg5njYMeP0OsGPkn8Lb/7aBsFJb5fjicKUDtzCpi5LIMZS9PZsu8Q0eG+25yjBiRwdruT3+bUQ13laDXZ26UJGiI1T2FN5HRYCyvfhU9/75vVed2r0PsGnnhq3gkDVGGJhzlrK97mHNiuCfdc0IErerWmQeSp/6uoMUNytJru7RrZL75OhjMNL5BApbAmcqrys+DjB2HdLGg7BK59CWLbAMcPShnZBTzywWo+WplJXmEp8bHR/PKiTlzfP562TeufURkaMyRHU29X1Wl4gQQyhTWRU7HlW/jgHji0By5+DIb82vf8NMfxAhTAzGXpXNGzNaOSExjUrmmVZ3NqzJBUpq72dtUUDS+QQKawJnIipUXw1d9g4fPQtBPc9BXE9T1mt/HDuvDwjFUUlnoPt4UYGJ2cyKNXdqNhlP9WElAvioj/aXiBBDKFNZHj2bMeZvzCt5Zn8p1w2T8qXSLKWovXWsJCQ8AJay0bRjLhim7VFqDUiyLiXxpeIIFMYU1cEdADeb1e31JRc/8MkQ3hpmnQZXilu6buOcgfZ61m0ZYs+reJ5fFre9GtdUwNFywiVaXhBRLIFNakxgX0QN68XTDrPtj8FXQaBiOehwYtjtmtsMTDf79O5aVvN1MvIownr+vFjcmJWl1ApJbS8AIJZAprUuMCdiDv+o9h9i+hpACufAaS76h00fVvN+7lT7PWsD0rn+v6xfPIld1o1iDShYJFxJ80vEAClcKa1LiAG8hbfl3P1n18z05r3vmY3XbnFvK3j9fxyaqdtG9en3fuOptzOjRzoWAREQkmCmtS4wJqIG+FdT0fggsmHLOup8dreXvRNv45J4Uij5ffXtqZcee3JzIs9DgnFRER8R+FNalxATGQ96h1Pbn9E0gacsxuq9NzeOSD1azOyOG8Ts34+4ieJDU7s4fZioiInAmFNalxrg/kzdoKH9ztrOs5Gq6YCNGxFXbJLSzhmS82MmVhGk0bRPL8zf24sldrTCVj2ERERKqTwpq4wpWBvBXW9QyB61+DXqOO2sXyyeqd/O2jdew9WMTYwUk8dFlnYvz4UFsREZHTobAmwSE/Cz7+Daz7ENqe66zrmVhhl237D/GnD9cyf+NeesbH8OrYZHonxLpSroiISBmFNan79m6Et0bCwT1wyV/gnF9VWNezqNTDpG+38PzXqYSHhvCXq7tz6+AkQvXMNBERCQAKa1K3HUiDKSPAWwK/mAtx/SpsXrh5P3+ctZrNew9xZe/W/Pmq7rSMiXKnVhERkUoorEndlbvTF9RK8n2zPVv1PLxp38Einvh0PTOXZdCmST3e/PlZXNDl2JUKRERE3KawJnXToX2+oHZoH9w2+3BQ83ot05bs4KnPNpBfXMoDF3bkgYs6EhWuZ6aJiEhgUliTuqcgG966FrK3wS0zmLW3FRPfnkdGdgERoSEUe7yc3a4Jj1/bk44tGrpdrYiIyAkprEndUnwI3hkNe9bDTe8y60A7Hp6xisJSr2+zx0t4qGHMWYkKaiIiUiuEuF2AiN+UFMLUmyH9Jxj1GnS6lKc/33A4qB3ezWP55xcbXSpSRETk9KhnTeoGTwm8/3PY8g2MfBG6jyAnv4SdOYWV7u7aovEiIiKnST1rUvt5PfDBPZDyKVzxT+h7M7tzCxn98sLjHuLKovEiIiJnoEphzRhzgzFmrTHGa4xJPmrbBGNMqjEmxRgzrFz7AGPMamfbv42z2KIxJtIYM81p/9EYk1TumLHGmE3Oa2xVapY6xlrfygRr3oeLH4OBd5G27xDXv/gD6Qfyue+CDkQfNdOzxheNFxERqYKq9qytAa4D5pdvNMZ0B8YAPYDhwAvGmLLfmC8C44BOzmu4034ncMBa2xF4FnjaOVcT4DHgbGAg8JgxpnEV65a6wFqY8ygsmwLn/RbOe4g1GTmMeukH8os9vDtuEL8f3pUnr+tFfGw0BoiPjebJ63rV/LqkIiIiZ6hKY9astesBnM6x8kYAU621RcBWY0wqMNAYkwbEWGsXOsdNAUYCnznH/MU5/n3geafXbRgw11qb5RwzF1/Ae7cqtUsd8M2TsOi/cPY9cNGfWLRlP3dNXkLDqDDe+sXZdGjeAHBp0XgRERE/qa4xa/HAjnKf0522eOf90e0VjrHWlgI5QNMTnEuC2ff/hm+fhr63wLAnmbt+D7e9vpiWjaJ4/95zDgc1ERGR2u6kPWvGmC+BVpVsetRa++HxDqukzZ6g/UyPqfilxozDd4uVNm3aHKc0qfWWvA5z/wQ9roVr/s17yzJ4eOZqesY34s3bz6Jx/Qi3KxQREfGbk4Y1a+0lZ3DedCCx3OcEINNpT6ikvfwx6caYMKARkOW0X3DUMd8cp9ZJwCSA5OTkSgOd1HIrp8HHD0GnYXDtJCYtSOOJTzdwXqdmvHTLAOpH6mk0IiJSt1TXbdDZwBhnhmc7fBMJFltrdwJ5xphBzni024APyx1TNtNzFDDPWmuBOcBlxpjGzsSCy5w2CTbrP4JZ90LSudgb3uSpuVt44tMNXNm7Na+OTVZQExGROqlKv92MMdcC/wGaA58YY1ZYa4dZa9caY6YD64BS4H5rrcc57F7gTSAa38SCz5z214C3nMkIWfhmk2KtzTLG/B34ydnvb2WTDSSIpH4F798B8f0pvfEdHp2dyrQlO7hlUBv+ek1PQkMqu1suIiJS+xlf51Xdk5ycbJcsWeJ2GeIP236At66Dph0p/NmH/PrDrcxZu5tfXdyJBy/pVNlsZBERkVrFGLPUWptc2TbdN5LAlrEM/jcaGiVwcPR07pq6iYVb9vPY1d35+ZB2blcnIiJS7RTWJHDtXgdvXwf1GpM16j1ue2czG3bm8dyNffXcNBERCRoKaxKY9m+Gt0ZCaCQ7R0zj5v9tY2dOAa/clsyFXVu4XZ2IiEiNUViTwJOTDlNGgLeUtKvfY8y7O8kvLuXtO88mOamJ29WJiIjUKIU1CSwH9/iCWmEO64e9w5jp+4kMC2H6PYPp2irG7epERERqnMKaBI78LJgyEnIzWX7Bm9z8wSFaxETy9p1nk9ikntvViYiIuKK6HoorcnqK8uB/o2D/Jn4Y+B9Gf+qhXbP6vH/POQpqIiIS1NSzJu4rKYB3xkDmCub1fYY750VzVlJjXh2bTExUuNvViYiIuEphTdxVWgzTbsVu+57Pu/ydexc255JuLXn+5n5EhYe6XZ2IiIjrdBtU3OMphZm/gNS5fJT4e+5d2Z5RAxJ46Zb+CmoiIiIO9ayJez55CNZ9yMzm9/PQpj6MG9qeCZd31fJRIiIi5SisiTvWzoJlk/k4ZgwP7RjCw5d35Z7zO7hdlYiISMBRWJOad3AP9uMH2RLeiYf2XsHT1/fixrPauF2ViIhIQNKYNalZ1sJHv8ZTeJC7D97F/41OVlATERE5AYU1qVkr34WUT3mq+AbOH3KeFmQXERE5Cd0GlZqTk47n09+z3HZldcLNvH15V7crEhERCXgKa1IzvF5KP7iPkuISHg//JS/fkkx4qDp2RURETka/LaVGeH96jbC0b3mi9GYeueUKWjSMcrskERGRWkE9a1L99m/GM+ePLPD0ot2wX3JWUhO3KxIREak11LMm1cvrIWfqXRR4Qpjb6U/8/Nx2blckIiJSqyisSbXKmfcsjfYu5cV6d/PwjRdrdQIREZHTpLAm1aY4czX1FjzJl3YgN/z8t9SP1F13ERGR06XfnlI9PCXse+sOImw9Qq5+jvYtGrpdkYiISK2knjWpFmun/om4go3M7/wIFyX3cLscERGRWkthTfxu88r5dNn4Mt9FX8w1Y+52uxwREZFaTWFN/ConN4/QWfeSZWLpfueLhOnBtyIiIlWi36TiN16vZeGrvyHJppNz2bM0bdbS7ZJERERqPYU18ZsZH7zHZTkzSEm8gU7njHS7HBERkTpBYU384rs1Wxm46lEORLSi8y3Pul2OiIhInaFHd0iV7cjKZ+f74xli9lJy48eYSD2mQ0RExF/UsyZVUlji4ZU3JjGaueT1G0dkx3PdLklERKROUViTKnly5kLuzf0Xh2I60OiKv7ldjoiISJ2j26ByxqYu3k7vNU/SMjSHkBtnQHiU2yWJiIjUOepZkzOyckc2381+g+tDF8DQ30J8f7dLEhERqZPUsyanLetQMY+8PY+3w16ltEUvws7/vdsliYiI1FnqWZPT4vFafv3uMn5V8CKNQgoJu34ShIa7XZaIiEidpbAmp+W5LzfSdMuHDAtZTMhFj0LL7m6XJCIiUqfpNqicsi/X7ea9eT/ydb0pEH82nPNLt0sSERGp8xTW5JSk7TvEg9OX82bDN4jCCyNfhJBQt8sSERGp8xTW5KQKij3c8/ZSRpuvGFCyDK74JzTt4HZZIiIiQUFj1uSErLU88sFqCnan8kjo29D+Aki+0+2yREREgoZ61uSE3l60jQ+X7+C7FlMILQqDEf+FEGV8ERGRmqKwJse1bPsB/vbxOp5ovYD4A8t949QaJbhdloiISFBRF4lUat/BIu57exmDGu7jxtw3oMsV0Ocmt8sSEREJOgprcoxSj5dfvrOcvPx8JjV8BRNRH67+FxjjdmkiIiJBR2FNjjHxixQWbtnP9B4Lid67Cq56Fhq0cLssERGRoKSwJhXMXbebl7/dwvjeBfTY9DL0ugF6jHS7LBERkaClsCaH5ReX8ucP19C7VTT3HpgI9ZrB5f/ndlkiIiJBTbNB5bAXvt7MzpxCZnb6lpA1G+Dm96BeE7fLEhERCWrqWRMAtu0/xKT5W3iwywFar5kE/cdC58vcLktERCToKawJAP/4ZD1hoXBv0WsQEwfDHne7JBEREUFhTYBvN+5l7rrd/LP3LiJ2LYPz/wCRDd0uS0RERFBYC3rFpV7++tFa2jeNZvi+16FxEvS92e2yRERExKGwFuQm/5DGlr2H+HffdEJ2rYILJkBouNtliYiIiENhLYjtySvkX19t4uIuTem58QVo1tn3XDUREREJGFUKa8aYicaYDcaYVcaYD4wxseW2TTDGpBpjUowxw8q1DzDGrHa2/dsY3xpGxphIY8w0p/1HY0xSuWPGGmM2Oa+xValZjnj6sxSKSj082XkT7F3v61ULCXW7LBERESmnqj1rc4Ge1trewEZgAoAxpjswBugBDAdeMMaUpYAXgXFAJ+c13Gm/Ezhgre0IPAs87ZyrCfAYcDYwEHjMGNO4inUHvWXbDzBjWTq/GNKGFkufhZY9oftIt8sSERGRo1QprFlrv7DWljofFwEJzvsRwFRrbZG1diuQCgw0xrQGYqy1C621FpgCjCx3zGTn/fvAxU6v2zBgrrU2y1p7AF9ALAt4cga8XstfZq+lRcNIft18KWRthgsfgRDdFRcREQk0/vztfAfwmfM+HthRblu60xbvvD+6vcIxTgDMAZqe4Fxyht5fms6q9BweHd6BqO//CXH9oMsVbpclIiIilTjpclPGmC+BVpVsetRa+6Gzz6NAKfC/ssMq2d+eoP1Mjzm61nH4brHSpk2bynYJejkFJTz9+QYGtG3MNd55kL0drnwWTGX/mEVERMRtJw1r1tpLTrTdGfB/FXCxc2sTfL1fieV2SwAynfaEStrLH5NujAkDGgFZTvsFRx3zzXFqnQRMAkhOTq400AW7f325iaz8YqZc0Rvz/p2QeDZ0vBiAWcszmDgnhczsAuJioxk/rAsj+6kTU0RExE1VnQ06HPgDcI21Nr/cptnAGGeGZzt8EwkWW2t3AnnGmEHOeLTbgA/LHVM203MUMM8Jf3OAy4wxjZ2JBZc5bXKaNu3OY/LCNMac1YYeO2dCXiZc+CgYw6zlGUyYuZqM7AIskJFdwISZq5m1PMPtskVERIJaVcesPQ80BOYaY1YYY14CsNauBaYD64DPgfuttR7nmHuBV/FNOtjMkXFurwFNjTGpwEPAw865soC/Az85r785bXIarLX85aO11I8IZfxFifDdM5B0HrQ/H4CJc1IoKPFUOKagxMPEOSlulCsiIiKOk94GPRHnMRvH2/Y4cMxq4NbaJUDPStoLgUqfyGqtfR14/cwrlTlrd/N96n7+ek0PmqydDIf2wI1vHd6emV1Q6XHHaxcREZGaoWc1BIHCEg//+GQdXVo25Gd9G8OC56DjJdBm0OF94mKjKz32eO0iIiJSMxTWgsDL324h/UABf7mmB2E/TYKCLN9z1coZP6wL0eEVVy+IDg9l/LAuNVmqiIiIHKVKt0El8KUfyOeFb1K5sndrBseFwPT/QJcrIX5Ahf3KZn1qNqiIiEhgUVir4578dAPGwCNXdIOF/w+Kco7pVSszsl+8wpmIiEiA0W3QOuyH1H18snon913QkfjwfFj0IvS4FlodM79DREREApTCWh1V6vHyl4/WktA4mnFD28P3z0FJPlwwwe3SRERE5DQorNVRby/axsbdB/nTVd2JKtwHi1+BXqOhuSYMiIiI1CYKa3XQ/oNFPDN3I+d1asZl3VvCgmfAUwzn/97t0kREROQ0KazVQf/8IoX8Yg+PXd0dk5sBS16HvjdD0w5ulyYiIiKnSWGtjlmdnsPUn3Yw9pwkOrZoCPP/CdaqV01ERKSWUlirQ6y1PDZ7DU3rR/DrSzpB1lZY/hYMGAuxbdwuT0RERM6AwlodMmtFBsu2Z/P74V2JiQqH+RMhJAzO+53bpYmIiMgZUlirIw4WlfLkpxvok9CIUf0TYF8qrHwXku+EmNZulyciIiJnSCsY1BH/mbeJPXlFvHzrAEJCDHzzJIRFwbkPul2aiIiIVIF61uqALXsP8vqCrdwwIIF+bRrD7nWwZgacfTc0aO52eSIiIlIFCmt1wN8/XkdUWCi/H97V1/DNExDZEM75lbuFiYiISJUprNVy8zbs5uuUvfz6kk40bxgJmStg/Ucw6D6o18Tt8kRERKSKFNZqsaJSD3/7aB0dmtfntsFJvsavn4CoWBh8n5uliYiIiJ8orNViry3YStr+fB67ugcRYSGw4yfYNAeG/AqiGrldnoiIiPiBwlottSunkOfnpXJZ95YM7exMIvj6H1CvGQy8293iRERExG8U1mqppz5bT6nX8scru/sa0hbAlm98j+qIbOBqbSIiIuI/Cmu10E9pWcxakcndQ9vTpmk939qf8x6HBq3grDvdLk9ERET8SGGtlvF4LY99uJa4RlHce0EHX+OWr2H7DzD0dxAe7W6BIiIi4lcKa7XM1J+2s25nLo9c2Y16EWFOr9o/ICYB+t/mdnkiIiLiZ1puqhaYtTyDiXNSyMguIMRAh+b1ubKXs97nxjmQsRSu/jeERbpbqIiIiPidetYC3KzlGUyYuZqM7AIAvBbSDxTw4YpM8Hrh68ehcRL0vdndQkVERKRaKKwFuIlzUigo8VRoKyr1MnFOCmz4CHatggsmQGi4SxWKiIhIdVJYC3CZTo/a0XZlH4Kvn4RmnaHXDTVclYiIiNQUhbUAFxdb+ezOWxsuhb3rfb1qIaE1XJWIiIjUFIW1ADd+WBdCTMW2BuHwu4iZ0LIndB/pSl0iIiJSMxTWAlzbpvXwWmgUFY4B4mOjmTJgCw0ObYMLH4EQ/RGKiIjUZXp0R4CbNH8LMVFhfD/hIhpEhkFpMTz/a4jrB12ucLs8ERERqWbqlglgafsO8fnaXdwyqK0vqAEsfwuyt8OFj4IxJz6BiIiI1HoKawHs1QVbCA8J4fZzknwNJYUw/5+QeDZ0vMTV2kRERKRm6DZogNp/sIj3lqRzbb94WsRE+RqXvgF5mXDtS+pVExERCRLqWQtQUxZuo6jUy11D2/kaig/Bd89A0nnQ/nx3ixMREZEao561AFRQ7GHKwjQu6daCji0a+hoXvwKH9sCNb7lbnIiIiNQo9awFoPeX7uBAfgnjhnbwNRTlwff/8o1TazPI3eJERESkRimsBRiP1/LKd1vpmxjLWUmNfY0rp0JBFpz/sLvFiYiISI1TWAswn6/ZxfasfO4e2h5jDFgLS96A1n0g8Sy3yxMREZEaprAWQKy1TJq/maSm9bisRytfY/oS2LMWBvzc3eJERETEFQprAeTHrVmsTM/hF+e1J7RsQdClb0BEA+g1yt3iRERExBUKawFk0vwtNK0fwagBCb6GgmxYM9MX1CIbulqbiIiIuENhLUBs2p3HvA17uG1wElHhob7GVdOhtEC3QEVERIKYwlqAmDR/C1HhIdw6uK2vwVrfLdC4fhDX19XaRERExD0KawFgd24hs1ZkMDo5kSb1I3yNOxbDnnUw4HZXaxMRERF3KawFgDe+T8Pjtfzi3PZHGpe+CRENoacmFoiIiAQzhTWX5RWW8L9F27i8Z2vaNK3nayw4AGtnQu8bILKBuwWKiIiIqxTWXDZ18Q7yikoZN7Rcr9rKaVBaqIkFIiIiorDmphKPl9e/38qg9k3okxjrazw8saA/tO7tan0iIiLiPoU1F320MpOdOYXcXbZgO8COH2HvBkhWr5qIiIgorLnGt7TUFjq3bMAFXZof2bDkDWdiwfXuFSciIiIBQ2HNJfM37WPDrjzuOs9ZsB0gPwvWfgC9R0NEfXcLFBERkYCgsOaSSfM30zImkhF94480rpoGniLdAhUREZHDqhTWjDF/N8asMsasMMZ8YYyJK7dtgjEm1RiTYowZVq59gDFmtbPt38bpVjLGRBpjpjntPxpjksodM9YYs8l5ja1KzYFgTUYO36fu5+dD2hER5vwRWOu7BRqfDK16uVugiIiIBIyq9qxNtNb2ttb2BT4G/gxgjOkOjAF6AMOBF4wxzoKXvAiMAzo5r+FO+53AAWttR+BZ4GnnXE2Ax4CzgYHAY8aYxlWs21WT5m+hQWQYN5/d5kjj9oWwL0W9aiIiIlJBlcKatTa33Mf6gHXejwCmWmuLrLVbgVRgoDGmNRBjrV1orbXAFGBkuWMmO+/fBy52et2GAXOttVnW2gPAXI4EvFpnR1Y+n6zeyU0DE4mJCj+yYembEBkDPa51rTYREREJPGFVPYEx5nHgNiAHuNBpjgcWldst3Wkrcd4f3V52zA4Aa22pMSYHaFq+vZJjap3XFmzFAD8f0u5IY34WrJ0F/W/TxAIRERGp4KQ9a8aYL40xayp5jQCw1j5qrU0E/gc8UHZYJaeyJ2g/02OOrnWcMWaJMWbJ3r17T3RZrsjOL2baTzu4pm8ccbHRRzasfFcTC0RERKRSJ+1Zs9Zecornegf4BN/4snQgsdy2BCDTaU+opJ1yx6QbY8KARkCW037BUcd8c5xaJwGTAJKTkysNdG56e9E2Cko8FZeWKptYkHAWtOzhXnEiIiISkKo6G7RTuY/XABuc97OBMc4Mz3b4JhIsttbuBPKMMYOc8Wi3AR+WO6ZspucoYJ4zrm0OcJkxprEzseAyp61WKSzx8OYP2zi/c3O6too5smHbD7B/k9YBFRERkUpVdczaU8aYLoAX2AbcA2CtXWuMmQ6sA0qB+621HueYe4E3gWjgM+cF8BrwljEmFV+P2hjnXFnGmL8DPzn7/c1am1XFumvcB8sz2HewiLvL96qBbx3QyEaaWCAiIiKVqlJYs9Yed00ka+3jwOOVtC8BelbSXgjccJxzvQ68fuaVusvrtbzy3RZ6xscwuEPTIxsO7Yd1H8KA2yGinmv1iYiISODSCgY14Mv1u9my9xDjhnY4srQUOBMLinULVERERI5LYa0GTJq/hYTG0VzRs9WRRmt9z1ZLPBtadnetNhEREQlsCmvVbOm2LJZsO8Cd57YjLLTcP+60BZpYICIiIielsFbNXv52C42iwxmdnFhxw9I3IKoR9BjpSl0iIiJSOyisVaMtew8yd/1ubhvclvqR5eZyHNoH6z+CPjdBePTxTyAiIiJBT2GtGr3y3VbCQ0O4bXBSxQ0r3nEmFtzuRlkiIiJSiyisVZO9eUXMWJbO9f0TaN4w8siGwxMLBkGLbq7VJyIiIrWDwlo1mbIwjRKPl7vOa1dxQ9p3kLVZ64CKiIjIKVFYqwb5xaW8tWgbl3ZrSfvmDSpuXPIGRMVC9xGu1CYiIiK1i8JaNZj+0w6y80u4+/yjlpY6uNc3saDvzZpYICIiIqdEYc3PSj1eXl2wlQFtGzOgbZOKG1e+A94STSwQERGRU6aw5mefrtlF+oECxh29YLvX65tY0OYcaN7FldpERESk9lFY8yNrLZPmb6Z9s/pc2q1lxY1p8yFriyYWiIiIyGlRWPOjhZv3syYjl7uGtickxFTcuOQNiG4M3a5xpzgRERGplRTW/Ojl+Vto1iCSa/vFV9xwcA9s+Bj63AzhUe4UJyIiIrWSwpqfbNiVy7cb93L7OW2JCg+tuHHF/8BbqokFIiIictoU1vxk0vwt1IsI5ZZBbStuKJtY0PZcaN7ZldpERESk9lJY84OdOQXMXpHJ6OREYutFVNy49Vs4kKZeNRERETkjCmt+8Mb3aVjgznPbHbtx6RsQ3QS6a2KBiIiInD6FtSrKLSzhnR+3c0Wv1iQ2qVdxY95u2PCJb8WCsMjKTyAiIiJyAgprVfTuj9s5WFTK3Uc/BBc0sUBERESqTGGtCopLvbz+/VaGdGxKz/hGFTd6vbBsMiSdB806uVOgiIiI1HoKa1Xw4YoMducWMW5oh2M3bvlaEwtERESkyhTWzpC1lle+20LXVg0Z2qnZsTssfQPqNYVuV9d8cSIiIlJnhLldQG1VUOLh7HZNGdiuCcYctbRU3i5I+QwG3auJBSIiIlIlCmtnqF5EGH8f2bPyjcvfdiYWaNF2ERERqRrdBvW3sokF7YZC00rGsomIiIicBoU1f9syD7K3a2KBiIiI+IXCmr8teQPqNYOumlggIiIiVaew5k+5O30TC/r9DMIiTr6/iIiIyEkorPnT8rfBeqD/WLcrERERkTpCYc1fvB5YNgXana+JBSIiIuI3Cmv+snke5GyHZD2uQ0RERPxHYc1flrwB9ZtDlyvdrkRERETqEIU1f8jNhI2fQ19NLBARERH/Uljzh7KJBQM0sUBERET8S2GtqrweWDoZ2l8ITdq7XY2IiIjUMQprVZX6FeSma8UCERERqRYKa1W19A2o3wK6amKBiIiI+J/CWlXkZPgmFvS7BULD3a5GRERE6iCFtapY/hZYL/S/ze1KREREpI5SWDtTZSsWdLgImrRzuxoRERGpo8LcLqDW8pbCOb+EFt3crkRERETqMIW1MxUWCYPudbsKERERqeN0G1REREQkgCmsiYiIiAQwhTURERGRAKawJiIiIhLAFNZEREREApjCmoiIiEgAU1gTERERCWAKayIiIiIBTGFNREREJIBpBYMzNGt5BhPnpJCZXUBcbDTjh3VhZL94t8sSERGROsYvPWvGmN8ZY6wxplm5tgnGmFRjTIoxZli59gHGmNXOtn8bY4zTHmmMmea0/2iMSSp3zFhjzCbnNdYfNVfFrOUZTJi5mozsAiyQkV3AhJmrmbU8w+3SREREpI6pclgzxiQClwLby7V1B8YAPYDhwAvGmFBn84vAOKCT8xrutN8JHLDWdgSeBZ52ztUEeAw4GxgIPGaMaVzVuqti4pwUCko8FdoKSjxMnJPiUkUiIiJSV/mjZ+1Z4PeALdc2AphqrS2y1m4FUoGBxpjWQIy1dqG11gJTgJHljpnsvH8fuNjpdRsGzLXWZllrDwBzORLwXJGZXXBa7SIiIiJnqkphzRhzDZBhrV151KZ4YEe5z+lOW7zz/uj2CsdYa0uBHKDpCc7lmrjY6NNqFxERETlTJw1rxpgvjTFrKnmNAB4F/lzZYZW02RO0n+kxR9c6zhizxBizZO/evZXt4hfjh3UhOjy0Qlt0eCjjh3Wptu8UERGR4HTS2aDW2ksqazfG9ALaASudOQIJwDJjzEB8vV+J5XZPADKd9oRK2il3TLoxJgxoBGQ57Rccdcw3x6l1EjAJIDk5udJA5w9lsz41G1RERESq2xk/usNauxpoUfbZGJMGJFtr9xljZgPvGGOeAeLwTSRYbK31GGPyjDGDgB+B24D/OKeYDYwFFgKjgHnWWmuMmQM8UW5SwWXAhDOt219G9otXOBMREZFqVy3PWbPWrjXGTAfWAaXA/dbasumT9wJvAtHAZ84L4DXgLWNMKr4etTHOubKMMX8HfnL2+5u1Nqs66hYREREJNMY3KbPuSU5OtkuWLHG7DBEREZGTMsYstdYmV7ZNy02JiIiIBDCFNREREZEAprAmIiIiEsAU1kREREQCmMKaiIiISABTWBMREREJYAprIiIiIgFMYU1EREQkgCmsiYiIiAQwhTURERGRAKawJiIiIhLAFNZEREREApjCmoiIiEgAU1gTERERCWAKayIiIiIBTGFNREREJIAprImIiIgEMIU1ERERkQBmrLVu11AtjDF7gW2neVgzYF81lFNbBPP169qDVzBffzBfOwT39evaA09ba23zyjbU2bB2JowxS6y1yW7X4ZZgvn5de3BeOwT39QfztUNwX7+uvXZdu26DioiIiAQwhTURERGRAKawVtEktwtwWTBfv649eAXz9QfztUNwX7+uvRbRmDURERGRAKaeNREREZEAprBWjjHmd8YYa4xpVq5tgjEm1RiTYowZ5mZ91cEY83djzCpjzApjzBfGmLhy2+r6tU80xmxwrv8DY0xsuW11+toBjDE3GGPWGmO8xpjko7YFw/UPd64v1RjzsNv1VDdjzOvGmD3GmDXl2poYY+YaYzY5Pxu7WWN1McYkGmO+Nsasd/7O/9ppr/PXb4yJMsYsNsasdK79r057nb/2MsaYUGPMcmPMx87nWnftCmsOY0wicCmwvVxbd2AM0AMYDrxgjAl1p8JqM9Fa29ta2xf4GPgzBM21zwV6Wmt7AxuBCRA01w6wBrgOmF++MRiu37me/wKXA92Bm5zrrsvexPfnWd7DwFfW2k7AV87nuqgU+K21thswCLjf+fMOhusvAi6y1vYB+gLDjTGDCI5rL/NrYH25z7Xu2hXWjngW+D1QfhDfCGCqtbbIWrsVSAUGulFcdbHW5pb7WJ8j1x8M1/6FtbbU+bgISHDe1/lrB7DWrrfWplSyKRiufyCQaq3dYq0tBqbiu+46y1o7H8g6qnkEMNl5PxkYWZM11RRr7U5r7TLnfR6+X9zxBMH1W5+Dzsdw52UJgmsHMMYkAFcCr5ZrrnXXrrAGGGOuATKstSuP2hQP7Cj3Od1pq1OMMY8bY3YAP8PpWSNIrr2cO4DPnPfBdu1HC4brD4ZrPBUtrbU7wRdogBYu11PtjDFJQD/gR4Lk+p3bgCuAPcBca23QXDvwHL6OGG+5tlp37WFuF1BTjDFfAq0q2fQo8AhwWWWHVdJW66bPnujarbUfWmsfBR41xkwAHgAeI0iu3dnnUXy3Sf5Xdlgl+9e6a4dTu/7KDqukrVZe/wkEwzXKUYwxDYAZwG+stbnGVPbXoO6x1nqAvs643A+MMT1dLqlGGGOuAvZYa5caYy5wuZwqCZqwZq29pLJ2Y0wvoB2w0vkXNwFYZowZiO//thPL7Z4AZFZzqX53vGuvxDvAJ/jCWlBcuzFmLHAVcLE98hybOnHtcFp/9uXVmes/gWC4xlOx2xjT2lq70xjTGl/PS51kjAnHF9T+Z62d6TQHzfUDWGuzjTHf4Bu7GAzXPgS4xhhzBRAFxBhj3qYWXnvQ3wa11q621raw1iZZa5Pw/Ue8v7V2FzAbGGOMiTTGtAM6AYtdLNfvjDGdyn28BtjgvA+Gax8O/AG4xlqbX25Tnb/2kwiG6/8J6GSMaWeMicA3oWK2yzW5YTYw1nk/Fjheb2utZnz/J/4asN5a+0y5TXX++o0xzctmuhtjooFL8P13vs5fu7V2grU2wfndPgaYZ629hVp47UHTs3YmrLVrjTHTgXX4bpPd73Qn1yVPGWO64Lufvw24B4Lm2p8HIoG5Tq/qImvtPUFy7RhjrgX+AzQHPjHGrLDWDguG67fWlhpjHgDmAKHA69batS6XVa2MMe8CFwDNjDHp+HrQnwKmG2PuxDcT/gb3KqxWQ4BbgdXO2C3wDX8JhutvDUx2ZkCHANOttR8bYxZS96/9eGrdn7tWMBAREREJYEF/G1REREQkkCmsiYiIiAQwhTURERGRAKawJiIiIhLAFNZEREREApjCmoiIiEgAU1gTERERCWAKayIiIiIB7P8DVqzl5gXL5EsAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model = LinearRegression().fit(x_tranform,y)\n",
    "y_pred = model.predict(x_tranform)\n",
    "plt.plot(x, y_pred,label='pca')\n",
    "plt.plot(x, y_pred_1,label='poly')\n",
    "plt.scatter(x, y)\n",
    "plt.legend()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "4079435b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4.26215222e+63]\n"
     ]
    }
   ],
   "source": [
    "print(pca.explained_variance_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "id": "633b089c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.84571418e+32])"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.singular_values_"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7e7a501a",
   "metadata": {},
   "source": [
    "Ideally, a machine learning model should have low variance and low bias.Therefore to achieve a good model that performs well both on the train and unseen data, a trade-off is made."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1d32949e",
   "metadata": {},
   "source": [
    "<img src='https://randlow.github.io/images/ml/tradeoff_cost_bias.png' alt=\"Italian Trulli\">"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4609d504",
   "metadata": {},
   "source": [
    "<h2> Lasso Regression </h2>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0fd6a4b9",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "519f05a8",
   "metadata": {},
   "outputs": [],
   "source": [
    "linear_model = poly_regression(10)\n",
    "y_predi = linear_model.predict(x_poly)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "7f5338d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "lasso_model =  Lasso(alpha=0)\n",
    "lasso_model.fit(x_poly,y ) \n",
    "y_pred_lasso = lasso_model.predict(x_poly)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "fcecb147",
   "metadata": {},
   "outputs": [],
   "source": [
    "#plt.plot(x, y_pred)  #L = 0.0028\n",
    "plt.scatter(x,y, s=10,color='r')\n",
    "plt.plot(x, y_pred_lasso,label='lasso')\n",
    "plt.plot(x, y_pred,label = 'linear')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "cde8022c",
   "metadata": {},
   "outputs": [],
   "source": [
    "lasso_model.coef_\n",
    "plt.scatter(np.linspace(start=0,stop=25,num=len(lasso_model.coef_) ),lasso_model.coef_)\n",
    "#plt.plot(np.linspace(start=0,stop=25,num=len(linear_model.coef_) ),(linear_model.coef_)/10**10,color='r')\n",
    "plt.scatter(np.linspace(start=0,stop=25,num=linear_model.coef_.size ),(linear_model.coef_)/10**5,color='r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1f2d7a05",
   "metadata": {},
   "outputs": [],
   "source": [
    "key = []\n",
    "for i in range(26):\n",
    "    key.append('w_'+str(i))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6c89371a",
   "metadata": {},
   "outputs": [],
   "source": [
    "linear_model.coef_.size\n",
    "len(key)\n",
    "linear_model.coef_/10**8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c3e1323a",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.bar(key , lasso_model.coef_, color ='maroon',width = 0.4)\n",
    "#plt.bar(key , linear_model.coef_/10**10, color ='red')\n",
    "  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "79e0ea5d",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "488845f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "linear_model.coef_.size\n",
    "lasso_model.coef_.size"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "36642d7a",
   "metadata": {},
   "outputs": [],
   "source": [
    "model =  Ridge(alpha=30)\n",
    "model.fit(x_poly,y ) \n",
    "y_pred_ridge = model.predict(x_poly)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6b15b88b",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.scatter(x,y, s=10,color='r')\n",
    "plt.plot(x, y_pred_ridge)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "50d251c1",
   "metadata": {},
   "outputs": [],
   "source": [
    "#pd.DataFrame(np.cov(x_poly))\n",
    "covMatrix = np.cov(x_poly)\n",
    "import seaborn as sn\n",
    "plt.rcParams[\"figure.figsize\"] = (10,10)\n",
    "sn.heatmap(covMatrix)\n",
    "sn.heatmap(np.corrcoef(x_poly))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b9454b1f",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "5113938c",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1420f966",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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