R_and_Python_Notebook.ipynb

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    "# Using R Functions in Python\n",
    "\n",
    "This notebook provides all of the code present in the Medium article **Guide to R and Python in a Single Jupyter Notebook**. The focus on the notebook is on the use of R functions, libraries, vectors, dataframes, and formula within a Python notebook and how to interface between the Python and R environment. Following this, examples of using these features are given with the examples of smoothing splines, natural and basis splines, as well as generalized additive models (GAMs).\n",
    "\n",
    "**Author:** <a href=\"https://github.com/Srtgn\">Saeed Rastegarian</a> based on <a href=\"https://github.com/mrdragonbear\">Matthew Stewart</a>'s notebook<br>\n",
    "\n",
    "<span style=\"color:red\">\n",
    "If you have configured your python environment based on the instructions in <a href=\"https://github.com/bmcs-group/bmcs_utils/blob/master/docs/README.md\">BMCS development process</a>, please add the following packages to use the \"R\" parts of this notebook:</span>\n",
    "\n",
    "conda install -c r rpy2\n",
    "\n",
    "conda install -c conda-forge tzlocal\n",
    "\n",
    "conda install -c conda-forge r-gam\n"
   ]
  },
  {
   "cell_type": "code",
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   "source": [
    "## RUN THIS CELL TO PROPERLY HIGHLIGHT THE EXERCISES\n",
    "import requests\n",
    "from IPython.core.display import HTML\n",
    "styles = requests.get(\"https://raw.githubusercontent.com/Harvard-IACS/2019-CS109B/master/content/styles/cs109.css\").text\n",
    "HTML(styles)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Learning Goals\n",
    "\n",
    "The main goal of this notebook is to get familiar with calling R functions within Python. Along the way, we'll learn about the \"formula\" interface to statsmodels, which gives an intuitive way of specifying regression models, and we'll review the different approaches to fitting curves.\n",
    "\n",
    "Key Skills:\n",
    "- Importing (base) R functions\n",
    "- Importing R library functions\n",
    "- Populating vectors R understands\n",
    "- Populating dataframes R understands\n",
    "- Populating formulas R understands\n",
    "- Running models in R\n",
    "- Getting results back to Python\n",
    "- Getting model predictions in R\n",
    "- Plotting in R\n",
    "- Reading R's documentation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "%matplotlib inline "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear/Polynomial Regression (Python, Review)\n",
    "Hopefully, you are at least somewhat familiar with using the statsmodels package in Python."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reading data and (some) exploring in Pandas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
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    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "# Variables are:\n",
      "#   subject:   subject ID number\n",
      "#   age:       age diagnosed with diabetes\n",
      "#   acidity:   a measure of acidity called base deficit\n",
      "#   y:         natural log of serum C-peptide concentration\n",
      "#\n",
      "# Original source is Sockett et al. (1987)\n",
      "# mentioned in Hastie and Tibshirani's book \n",
      "# \"Generalized Additive Models\".\n",
      "\n"
     ]
    },
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       "      <th></th>\n",
       "      <th>subject</th>\n",
       "      <th>age</th>\n",
       "      <th>acidity</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>5.2</td>\n",
       "      <td>-8.1</td>\n",
       "      <td>4.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>8.8</td>\n",
       "      <td>-16.1</td>\n",
       "      <td>4.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>10.5</td>\n",
       "      <td>-0.9</td>\n",
       "      <td>5.2</td>\n",
       "    </tr>\n",
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       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>10.6</td>\n",
       "      <td>-7.8</td>\n",
       "      <td>5.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>10.4</td>\n",
       "      <td>-29.0</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
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      "text/plain": [
       "   subject   age  acidity    y\n",
       "0        1   5.2     -8.1  4.8\n",
       "1        2   8.8    -16.1  4.1\n",
       "2        3  10.5     -0.9  5.2\n",
       "3        4  10.6     -7.8  5.5\n",
       "4        5  10.4    -29.0  5.0"
      ]
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       "subject      int64\n",
       "age        float64\n",
       "acidity    float64\n",
       "y          float64\n",
       "dtype: object"
      ]
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>subject</th>\n",
       "      <th>age</th>\n",
       "      <th>acidity</th>\n",
       "      <th>y</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>43.000000</td>\n",
       "      <td>43.000000</td>\n",
       "      <td>43.000000</td>\n",
       "      <td>43.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>22.000000</td>\n",
       "      <td>9.032558</td>\n",
       "      <td>-8.148837</td>\n",
       "      <td>4.746512</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>12.556539</td>\n",
       "      <td>4.022539</td>\n",
       "      <td>7.123080</td>\n",
       "      <td>0.720565</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.900000</td>\n",
       "      <td>-29.000000</td>\n",
       "      <td>3.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>11.500000</td>\n",
       "      <td>5.500000</td>\n",
       "      <td>-12.700000</td>\n",
       "      <td>4.450000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>22.000000</td>\n",
       "      <td>10.400000</td>\n",
       "      <td>-7.800000</td>\n",
       "      <td>4.900000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>32.500000</td>\n",
       "      <td>11.850000</td>\n",
       "      <td>-2.000000</td>\n",
       "      <td>5.100000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>43.000000</td>\n",
       "      <td>15.600000</td>\n",
       "      <td>-0.200000</td>\n",
       "      <td>6.600000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "         subject        age    acidity          y\n",
       "count  43.000000  43.000000  43.000000  43.000000\n",
       "mean   22.000000   9.032558  -8.148837   4.746512\n",
       "std    12.556539   4.022539   7.123080   0.720565\n",
       "min     1.000000   0.900000 -29.000000   3.000000\n",
       "25%    11.500000   5.500000 -12.700000   4.450000\n",
       "50%    22.000000  10.400000  -7.800000   4.900000\n",
       "75%    32.500000  11.850000  -2.000000   5.100000\n",
       "max    43.000000  15.600000  -0.200000   6.600000"
      ]
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   "source": [
    "diab = pd.read_csv(\"data/diabetes.csv\")\n",
    "print(\"\"\"\n",
    "# Variables are:\n",
    "#   subject:   subject ID number\n",
    "#   age:       age diagnosed with diabetes\n",
    "#   acidity:   a measure of acidity called base deficit\n",
    "#   y:         natural log of serum C-peptide concentration\n",
    "#\n",
    "# Original source is Sockett et al. (1987)\n",
    "# mentioned in Hastie and Tibshirani's book \n",
    "# \"Generalized Additive Models\".\n",
    "\"\"\")\n",
    "\n",
    "display(diab.head())\n",
    "display(diab.dtypes)\n",
    "display(diab.describe())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax0 = diab.plot.scatter(x='age',y='y',c='Red',title=\"Diabetes data\") #plotting direclty from pandas!\n",
    "ax0.set_xlabel(\"Age at Diagnosis\")\n",
    "ax0.set_ylabel(\"Log C-Peptide Concentration\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Linear regression with statsmodels. \n",
    "\n",
    "- Previously, we worked from a vector of target values and a design matrix we built ourself (e.g. from PolynomialFeatures). \n",
    "- Now, Statsmodels' *formula interface* can help build the target value and design matrix for you."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Using statsmodels\n",
    "import statsmodels.formula.api as sm\n",
    "\n",
    "\n",
    "model1 = sm.ols('y ~ age',data=diab)\n",
    "fit1_lm = model1.fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Build a data frame to predict values on (sometimes this is just the test or validation set)\n",
    " - Very useful for making pretty plots of the model predcitions -- predict for TONS of values, not just whatever's in the training set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "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>age</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.161616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.323232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.484848</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.646465</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        age\n",
       "0  0.000000\n",
       "1  0.161616\n",
       "2  0.323232\n",
       "3  0.484848\n",
       "4  0.646465"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_pred = np.linspace(0,16,100)\n",
    "\n",
    "predict_df = pd.DataFrame(data={\"age\":x_pred})\n",
    "predict_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use `get_prediction(<data>).summary_frame()` to get the model's prediction (and error bars!)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "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>mean</th>\n",
       "      <th>mean_se</th>\n",
       "      <th>mean_ci_lower</th>\n",
       "      <th>mean_ci_upper</th>\n",
       "      <th>obs_ci_lower</th>\n",
       "      <th>obs_ci_upper</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>3.996031</td>\n",
       "      <td>0.244590</td>\n",
       "      <td>3.502071</td>\n",
       "      <td>4.489991</td>\n",
       "      <td>2.600828</td>\n",
       "      <td>5.391235</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.009459</td>\n",
       "      <td>0.240929</td>\n",
       "      <td>3.522892</td>\n",
       "      <td>4.496026</td>\n",
       "      <td>2.616856</td>\n",
       "      <td>5.402063</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.022887</td>\n",
       "      <td>0.237280</td>\n",
       "      <td>3.543691</td>\n",
       "      <td>4.502084</td>\n",
       "      <td>2.632842</td>\n",
       "      <td>5.412932</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.036315</td>\n",
       "      <td>0.233642</td>\n",
       "      <td>3.564466</td>\n",
       "      <td>4.508165</td>\n",
       "      <td>2.648786</td>\n",
       "      <td>5.423845</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.049743</td>\n",
       "      <td>0.230016</td>\n",
       "      <td>3.585216</td>\n",
       "      <td>4.514270</td>\n",
       "      <td>2.664687</td>\n",
       "      <td>5.434800</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean   mean_se  mean_ci_lower  mean_ci_upper  obs_ci_lower  \\\n",
       "0  3.996031  0.244590       3.502071       4.489991      2.600828   \n",
       "1  4.009459  0.240929       3.522892       4.496026      2.616856   \n",
       "2  4.022887  0.237280       3.543691       4.502084      2.632842   \n",
       "3  4.036315  0.233642       3.564466       4.508165      2.648786   \n",
       "4  4.049743  0.230016       3.585216       4.514270      2.664687   \n",
       "\n",
       "   obs_ci_upper  \n",
       "0      5.391235  \n",
       "1      5.402063  \n",
       "2      5.412932  \n",
       "3      5.423845  \n",
       "4      5.434800  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prediction_output = fit1_lm.get_prediction(predict_df).summary_frame()\n",
    "prediction_output.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the model and error bars"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax1 = diab.plot.scatter(x='age',y='y',c='Red',title=\"Diabetes data with least-squares linear fit\")\n",
    "ax1.set_xlabel(\"Age at Diagnosis\")\n",
    "ax1.set_ylabel(\"Log C-Peptide Concentration\")\n",
    "\n",
    "\n",
    "ax1.plot(predict_df.age, prediction_output['mean'],color=\"green\")\n",
    "ax1.plot(predict_df.age, prediction_output['mean_ci_lower'], color=\"blue\",linestyle=\"dashed\")\n",
    "ax1.plot(predict_df.age, prediction_output['mean_ci_upper'], color=\"blue\",linestyle=\"dashed\");\n",
    "\n",
    "ax1.plot(predict_df.age, prediction_output['obs_ci_lower'], color=\"skyblue\",linestyle=\"dashed\")\n",
    "ax1.plot(predict_df.age, prediction_output['obs_ci_upper'], color=\"skyblue\",linestyle=\"dashed\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"exercise\"><b>Exercise 1</b></div>\n",
    "\n",
    "1. Fit a 3rd degree polynomial model and plot the model+error bars\n",
    " - Route1: Build a design df with a column for each of `age`, `age**2`, `age**3`\n",
    " - Route2: Just edit the formula"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "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>mean</th>\n",
       "      <th>mean_se</th>\n",
       "      <th>mean_ci_lower</th>\n",
       "      <th>mean_ci_upper</th>\n",
       "      <th>obs_ci_lower</th>\n",
       "      <th>obs_ci_upper</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.740481</td>\n",
       "      <td>0.508197</td>\n",
       "      <td>1.712556</td>\n",
       "      <td>3.768406</td>\n",
       "      <td>1.156238</td>\n",
       "      <td>4.324724</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.846265</td>\n",
       "      <td>0.472858</td>\n",
       "      <td>1.889819</td>\n",
       "      <td>3.802710</td>\n",
       "      <td>1.307439</td>\n",
       "      <td>4.385090</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.948751</td>\n",
       "      <td>0.439558</td>\n",
       "      <td>2.059661</td>\n",
       "      <td>3.837841</td>\n",
       "      <td>1.450860</td>\n",
       "      <td>4.446641</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3.047990</td>\n",
       "      <td>0.408303</td>\n",
       "      <td>2.222119</td>\n",
       "      <td>3.873860</td>\n",
       "      <td>1.586737</td>\n",
       "      <td>4.509242</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.144031</td>\n",
       "      <td>0.379104</td>\n",
       "      <td>2.377221</td>\n",
       "      <td>3.910841</td>\n",
       "      <td>1.715328</td>\n",
       "      <td>4.572735</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       mean   mean_se  mean_ci_lower  mean_ci_upper  obs_ci_lower  \\\n",
       "0  2.740481  0.508197       1.712556       3.768406      1.156238   \n",
       "1  2.846265  0.472858       1.889819       3.802710      1.307439   \n",
       "2  2.948751  0.439558       2.059661       3.837841      1.450860   \n",
       "3  3.047990  0.408303       2.222119       3.873860      1.586737   \n",
       "4  3.144031  0.379104       2.377221       3.910841      1.715328   \n",
       "\n",
       "   obs_ci_upper  \n",
       "0      4.324724  \n",
       "1      4.385090  \n",
       "2      4.446641  \n",
       "3      4.509242  \n",
       "4      4.572735  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fit2_lm = sm.ols(formula=\"y ~ age + np.power(age, 2) + np.power(age, 3)\",data=diab).fit()\n",
    "\n",
    "poly_predictions = fit2_lm.get_prediction(predict_df).summary_frame()\n",
    "poly_predictions.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax2 = diab.plot.scatter(x='age',y='y',c='Red',title=\"Diabetes data with least-squares cubic fit\")\n",
    "ax2.set_xlabel(\"Age at Diagnosis\")\n",
    "ax2.set_ylabel(\"Log C-Peptide Concentration\")\n",
    "\n",
    "ax2.plot(predict_df.age, poly_predictions['mean'],color=\"green\")\n",
    "ax2.plot(predict_df.age, poly_predictions['mean_ci_lower'], color=\"blue\",linestyle=\"dashed\")\n",
    "ax2.plot(predict_df.age, poly_predictions['mean_ci_upper'], color=\"blue\",linestyle=\"dashed\");\n",
    "\n",
    "ax2.plot(predict_df.age, poly_predictions['obs_ci_lower'], color=\"skyblue\",linestyle=\"dashed\")\n",
    "ax2.plot(predict_df.age, poly_predictions['obs_ci_upper'], color=\"skyblue\",linestyle=\"dashed\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Linear/Polynomial Regression, but make it R"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the meat of the lab. After this section we'll know everything we need to in order to work with R models. The rest of the lab is just applying these concepts to run particular models. This section therefore is your 'cheat sheet' for working in R.\n",
    "\n",
    "What we need to know:\n",
    "- Importing (base) R functions\n",
    "- Importing R Library functions\n",
    "- Populating vectors R understands\n",
    "- Populating DataFrames R understands\n",
    "- Populating Formulas R understands\n",
    "- Running models in R\n",
    "- Getting results back to Python\n",
    "- Getting model predictions in R\n",
    "- Plotting in R\n",
    "- Reading R's documentation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Importing R functions**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# if you're on JupyterHub you may need to specify the path to R\n",
    "\n",
    "# import os\n",
    "# os.environ['R_HOME'] = \"/home/matt.stewart/anaconda3/bin/R\"\n",
    "\n",
    "import rpy2.robjects as robjects"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "r_lm = robjects.r[\"lm\"]\n",
    "r_predict = robjects.r[\"predict\"]\n",
    "#r_plot = robjects.r[\"plot\"] # more on plotting later\n",
    "\n",
    "#lm() and predict() are two of the most common functions we'll use"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Importing R libraries**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "from rpy2.robjects.packages import importr\n",
    "#r_cluster = importr('cluster')\n",
    "#r_cluster.pam;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Populating vectors R understands**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "r_y = robjects.FloatVector(diab['y'])\n",
    "r_age = robjects.FloatVector(diab['age'])\n",
    "# What happens if we pass the wrong type?\n",
    "# How does r_age display?\n",
    "# How does r_age print?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Populating Data Frames R understands**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "diab_r = robjects.DataFrame({\"y\":r_y, \"age\":r_age})\n",
    "# How does diab_r display?\n",
    "# How does diab_r print?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Populating formulas R understands**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "simple_formula = robjects.Formula(\"y~age\")\n",
    "simple_formula.environment[\"y\"] = r_y #populate the formula's .environment, so it knows what 'y' and 'age' refer to\n",
    "simple_formula.environment[\"age\"] = r_age"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Running Models in R**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "diab_lm = r_lm(formula=simple_formula) # the formula object is storing all the needed variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "simple_formula = robjects.Formula(\"y~age\") # reset the formula\n",
    "diab_lm = r_lm(formula=simple_formula, data=diab_r) #can also use a 'dumb' formula and pass a dataframe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Getting results back to Python**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <span>ListVector with 12 elements.</span>\n",
       "    <table>\n",
       "      <tbody>\n",
       "      \n",
       "      <tr>\n",
       "      <th>\n",
       "        coefficients\n",
       "      </th>\n",
       "      <td>\n",
       "        \n",
       "    <span>FloatVector with 2 elements.</span>\n",
       "    <table>\n",
       "      <tbody>\n",
       "      <tr>\n",
       "      \n",
       "      <td>\n",
       "        3.996031\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        0.083086\n",
       "      </td>\n",
       "      \n",
       "      </tr>\n",
       "      </tbody>\n",
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       "    \n",
       "      </td>\n",
       "      </tr>\n",
       "      \n",
       "      <tr>\n",
       "      <th>\n",
       "        residuals\n",
       "      </th>\n",
       "      <td>\n",
       "        \n",
       "    <span>FloatVector with 43 elements.</span>\n",
       "    <table>\n",
       "      <tbody>\n",
       "      <tr>\n",
       "      \n",
       "      <td>\n",
       "        0.371921\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        -0.627189\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        0.331564\n",
       "      </td>\n",
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       "      <td>\n",
       "        0.623256\n",
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       "        ...\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        -0.934608\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        -0.492768\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        0.164502\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        0.206638\n",
       "      </td>\n",
       "      \n",
       "      </tr>\n",
       "      </tbody>\n",
       "    </table>\n",
       "    \n",
       "      </td>\n",
       "      </tr>\n",
       "      \n",
       "      <tr>\n",
       "      <th>\n",
       "        effects\n",
       "      </th>\n",
       "      <td>\n",
       "        \n",
       "    <span>FloatVector with 43 elements.</span>\n",
       "    <table>\n",
       "      <tbody>\n",
       "      <tr>\n",
       "      \n",
       "      <td>\n",
       "        -31.124958\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        -2.165975\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        0.333051\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        0.627310\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        ...\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        -0.881769\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        -0.421956\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        0.124907\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        0.215828\n",
       "      </td>\n",
       "      \n",
       "      </tr>\n",
       "      </tbody>\n",
       "    </table>\n",
       "    \n",
       "      </td>\n",
       "      </tr>\n",
       "      \n",
       "      <tr>\n",
       "      <th>\n",
       "        ...\n",
       "      </th>\n",
       "      <td>\n",
       "        ...\n",
       "      </td>\n",
       "      </tr>\n",
       "      \n",
       "      <tr>\n",
       "      <th>\n",
       "        call\n",
       "      </th>\n",
       "      <td>\n",
       "        \n",
       "    <span>Vector with 3 elements.</span>\n",
       "    <table>\n",
       "      <tbody>\n",
       "      <tr>\n",
       "      \n",
       "      <td>\n",
       "        SignatureTrans...\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        Formula\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        DataFrame\n",
       "      </td>\n",
       "      \n",
       "      </tr>\n",
       "      </tbody>\n",
       "    </table>\n",
       "    \n",
       "      </td>\n",
       "      </tr>\n",
       "      \n",
       "      <tr>\n",
       "      <th>\n",
       "        terms\n",
       "      </th>\n",
       "      <td>\n",
       "        y ~ age\n",
       "\r\n",
       "attr(,\"variables\")\n",
       "\r\n",
       "list(y, age)\n",
       "\r\n",
       "attr(,\"factors\")\n",
       "\r\n",
       "    age\n",
       "\r\n",
       "y     0\n",
       "\r\n",
       "age   1\n",
       "\r\n",
       "attr(,\"term.labels\")\n",
       "\r\n",
       "[1] \"age\"\n",
       "\r\n",
       "attr(,\"order\")\n",
       "\r\n",
       "[1] 1\n",
       "\r\n",
       "attr(,\"intercept\")\n",
       "\r\n",
       "[1] 1\n",
       "\r\n",
       "attr(,\"response\")\n",
       "\r\n",
       "[1] 1\n",
       "\r\n",
       "attr(,\".Environment\")\n",
       "\r\n",
       "<environment: R_GlobalEnv>\n",
       "\r\n",
       "attr(,\"predvars\")\n",
       "\r\n",
       "list(y, age)\n",
       "\r\n",
       "attr(,\"dataClasses\")\n",
       "\r\n",
       "        y       age \n",
       "\r\n",
       "\"numeric\" \"numeric\" \n",
       "\n",
       "      </td>\n",
       "      </tr>\n",
       "      \n",
       "      <tr>\n",
       "      <th>\n",
       "        model\n",
       "      </th>\n",
       "      <td>\n",
       "        \n",
       "    <span>R/rpy2 DataFrame (43 x 2)</span>\n",
       "    <table>\n",
       "      <thead>\n",
       "        <tr>\n",
       "        \n",
       "          <th>y</th>\n",
       "        \n",
       "          <th>age</th>\n",
       "        \n",
       "        </tr>\n",
       "      </thead>\n",
       "      <tbody>\n",
       "      \n",
       "      <tr>\n",
       "      \n",
       "      <td>\n",
       "        4.800000\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        5.200000\n",
       "      </td>\n",
       "      \n",
       "      </tr>\n",
       "      \n",
       "      <tr>\n",
       "      \n",
       "      <td>\n",
       "        4.100000\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        8.800000\n",
       "      </td>\n",
       "      \n",
       "      </tr>\n",
       "      \n",
       "      <tr>\n",
       "      \n",
       "      <td>\n",
       "        5.200000\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        10.500000\n",
       "      </td>\n",
       "      \n",
       "      </tr>\n",
       "      \n",
       "      <tr>\n",
       "      \n",
       "      <td>\n",
       "        5.500000\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        10.600000\n",
       "      </td>\n",
       "      \n",
       "      </tr>\n",
       "      \n",
       "      <tr>\n",
       "      \n",
       "      <td>\n",
       "        ...\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        ...\n",
       "      </td>\n",
       "      \n",
       "      </tr>\n",
       "      \n",
       "      <tr>\n",
       "      \n",
       "      <td>\n",
       "        4.100000\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        12.500000\n",
       "      </td>\n",
       "      \n",
       "      </tr>\n",
       "      \n",
       "      <tr>\n",
       "      \n",
       "      <td>\n",
       "        4.600000\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        13.200000\n",
       "      </td>\n",
       "      \n",
       "      </tr>\n",
       "      \n",
       "      <tr>\n",
       "      \n",
       "      <td>\n",
       "        4.900000\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        8.900000\n",
       "      </td>\n",
       "      \n",
       "      </tr>\n",
       "      \n",
       "      <tr>\n",
       "      \n",
       "      <td>\n",
       "        5.100000\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        10.800000\n",
       "      </td>\n",
       "      \n",
       "      </tr>\n",
       "      \n",
       "      </tbody>\n",
       "    </table>\n",
       "    \n",
       "      </td>\n",
       "      </tr>\n",
       "      \n",
       "      </tbody>\n",
       "    </table>\n",
       "    "
      ],
      "text/plain": [
       "R object with classes: ('lm',) mapped to:\n",
       "<ListVector - Python:0x00000231252AF988 / R:0x00000231244551C0>\n",
       "[FloatVector, FloatVector, FloatVector, IntVector, ..., ListVector, Vector, Formula, DataFrame]\n",
       "  coefficients: <class 'rpy2.robjects.vectors.FloatVector'>\n",
       "  R object with classes: ('numeric',) mapped to:\n",
       "<FloatVector - Python:0x00000231258A88C8 / R:0x0000023125B05B98>\n",
       "[3.996031, 0.083086]\n",
       "  residuals: <class 'rpy2.robjects.vectors.FloatVector'>\n",
       "  R object with classes: ('numeric',) mapped to:\n",
       "<FloatVector - Python:0x00000231142FB708 / R:0x0000023125B35248>\n",
       "[0.371921, -0.627189, 0.331564, 0.623256, ..., -0.934608, -0.492768, 0.164502, 0.206638]\n",
       "  effects: <class 'rpy2.robjects.vectors.FloatVector'>\n",
       "  R object with classes: ('numeric',) mapped to:\n",
       "<FloatVector - Python:0x00000231258C4848 / R:0x0000023125B353D8>\n",
       "[-31.124958, -2.165975, 0.333051, 0.627310, ..., -0.881769, -0.421956, 0.124907, 0.215828]\n",
       "  rank: <class 'rpy2.robjects.vectors.IntVector'>\n",
       "  R object with classes: ('integer',) mapped to:\n",
       "<IntVector - Python:0x00000231258C4308 / R:0x0000023125B32A78>\n",
       "[2]\n",
       "...\n",
       "R object with classes: ('lm',) mapped to:\n",
       "<ListVector - Python:0x00000231252AF988 / R:0x00000231244551C0>\n",
       "[FloatVector, FloatVector, FloatVector, IntVector, ..., ListVector, Vector, Formula, DataFrame]\n",
       "  qr: <class 'rpy2.robjects.vectors.Vector'>\n",
       "  R object with classes: ('lm',) mapped to:\n",
       "<Vector - Python:0x00000231258CC908 / R:0x0000023125B03E28>\n",
       "[SignatureTrans..., Formula, DataFrame]\n",
       "  df.residual: <class 'rpy2.robjects.Formula'>\n",
       "  R object with classes: ('terms', 'formula') mapped to:\n",
       "<Formula - Python:0x00000231258AE6C8 / R:0x0000023125B226B0>\n",
       "R object with classes: ('lm',) mapped to:\n",
       "<ListVector - Python:0x00000231252AF988 / R:0x00000231244551C0>\n",
       "[FloatVector, FloatVector, FloatVector, IntVector, ..., ListVector, Vector, Formula, DataFrame]"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diab_lm #the result is already 'in' python, but it's a special object"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [1] \"coefficients\"  \"residuals\"     \"effects\"       \"rank\"         \n",
      "\r\n",
      " [5] \"fitted.values\" \"assign\"        \"qr\"            \"df.residual\"  \n",
      "\r\n",
      " [9] \"xlevels\"       \"call\"          \"terms\"         \"model\"        \n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(diab_lm.names) # view all names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <span>FloatVector with 2 elements.</span>\n",
       "    <table>\n",
       "      <tbody>\n",
       "      <tr>\n",
       "      \n",
       "      <td>\n",
       "        3.996031\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        0.083086\n",
       "      </td>\n",
       "      \n",
       "      </tr>\n",
       "      </tbody>\n",
       "    </table>\n",
       "    "
      ],
      "text/plain": [
       "R object with classes: ('numeric',) mapped to:\n",
       "<FloatVector - Python:0x00000231258D2B48 / R:0x0000023125B05B98>\n",
       "[3.996031, 0.083086]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diab_lm[0] #grab the first element"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <span>FloatVector with 2 elements.</span>\n",
       "    <table>\n",
       "      <tbody>\n",
       "      <tr>\n",
       "      \n",
       "      <td>\n",
       "        3.996031\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        0.083086\n",
       "      </td>\n",
       "      \n",
       "      </tr>\n",
       "      </tbody>\n",
       "    </table>\n",
       "    "
      ],
      "text/plain": [
       "R object with classes: ('numeric',) mapped to:\n",
       "<FloatVector - Python:0x00000231258D23C8 / R:0x0000023125B05B98>\n",
       "[3.996031, 0.083086]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "diab_lm.rx2(\"coefficients\") #use rx2 to get elements by name!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.99603115, 0.08308615])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.array(diab_lm.rx2(\"coefficients\")) #r vectors can be converted to numpy (but rarely needed)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Getting Predictions**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# make a df to predict on (might just be the validation or test dataframe)\n",
    "predict_df = robjects.DataFrame({\"age\": robjects.FloatVector(np.linspace(0,16,100))})\n",
    "\n",
    "# call R's predict() function, passing the model and the data \n",
    "predictions = r_predict(diab_lm, predict_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_vals = predict_df.rx2(\"age\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = diab.plot.scatter(x='age',y='y',c='Red',title=\"Diabetes data\")\n",
    "ax.set_xlabel(\"Age at Diagnosis\")\n",
    "ax.set_ylabel(\"Log C-Peptide Concentration\");\n",
    "\n",
    "ax.plot(x_vals,predictions); #plt still works with r vectors as input!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Plotting in R**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\srate\\miniconda3\\envs\\py37\\lib\\site-packages\\rpy2\\robjects\\pandas2ri.py:17: FutureWarning: pandas.core.index is deprecated and will be removed in a future version.  The public classes are available in the top-level namespace.\n",
      "  from pandas.core.index import Index as PandasIndex\n"
     ]
    }
   ],
   "source": [
    "%load_ext rpy2.ipython"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The above turns on the %R \"magic\"\n",
    "- R's plot() command responds differently based on what you hand to it; Different models get different plots!\n",
    " - For any specific model search for plot.modelname. E.g. for a GAM model, search plot.gam for any details of plotting a GAM model\n",
    "- The %R \"magic\" runs R code in 'notebook' mode, so figures display nicely\n",
    "  - Ahead of the `plot(<model>)` code we pass in the variables R needs to know about (`-i` is for \"input\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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TCd7LFbwywaIsDQxrxOIa9PCdY1broM7FUCItObfBOqh7PrUz+W3SoHR7uE3auVbROsWuJVh8Io7fv+VlJevUi9ZBPfmdWHDxaS5LxgBLZUkYJFgELRpS12q2Cpomjv2zvQygzup8H1wGHZRPLXAkCxwKBoeCwaFgcCgYHAoGh4LBoWBwKBgcCgaHgsGhYHAoGBwKBoeCwaFgcCgYHAoGh4LBoWBwkAWXf9JrlT2+lV/GrvO1e+6rW5cBtODaGQVDopxlj7/Jvwx0+6aWzhbfvhDPlYl10sfXbfmcpvoMGCts09a/JbQ0rkJwVUXvymXoxbdUrDgWDwFlT3982hqH6MPEUwluj35GCbRg0Qbfa3vi+ZNCmzBXVtH7lfjK5SMmWnB1mIdH+yIAWvBJCZbPZt5s5Wb1bNj/xJN8O1EXG4LLw8Tnw/WdABFyVYLLp7h1CT6+/vT0fnheN6to42Fv13cCRMg1CZaNb6GsaoPFk0AreVT21VbVzfvb6jBxJAVHjRZ83Nz+vpG9aFHpHjdlL7p8cFA871X8Kg4ufvrzi+xF31Q197xX4AFkwSSnYHgoGBwKBoeCwRkgWLxfqPVNKGdD+hdDmEHPtukJgQsTAW2vC+sM0piBsIj8PLh1gNZjT6c59qv9qvvXM6wzpcJdcPb03hF31ym7Q/QGDSP47BBnwS7HLlHwbi3uE38qR33EC+TEmIHY9O/n5PZzPRlT7alDbNX2r7+9/f31xyRZpUk1zKAGkcy3b6oZH7lNBmzsLSd66smBv8ldavZHHl2/ckW+SEW8JufuXZ2/TOEXf9lmj3+tIjcnjqqE6xOqn3qvUQyL1Rel0/BZniPPT+axDNJ1uhbbv3zdiqz5j/i1Pb46uL6QEILVq58qMQ9y1EdkY3r3X3O8SO3RIert6yLX74tcuzfjKceRdKLL0aZDPdPT2KsmemrBd+9qhFHNFal9EjGhUGRx8U3vEJHfbFUKjaBKp9ysT6h+6r1GIURflD5VdcTpGFraeIeOfNuSSJDp/iQ+I/jJFXoWLCZRG2J0TaRHfIs8qXK/DmFsF/N04p8+TKW2HgbW48Vqpqe5t5zoqQWvZS1RblRzQfXlF2f/5cf74mx6h4z81Th1Y+JIJ9x4BWkdY8c15rl5UfpUxvC22K6vqoERncaMrxH89Ar7cRYsPknnguUrxvSgr86+Zgi1vUOwMTaYVTM+1UxPc+SwnOipTvHLtnzPmdxoThmVmffby+fH316MuaRqor/ROtQTR3XC9QnLRPRd44kQfSp9DnV8W4/BSJDmJJN08NMr7CeeEqxmdSot5Ye1nulp7BWUlWtVglW5EFXry0nXaff3b4rm7D7XO85KsAqqLrCaNKxOqBPRfY35WYmrj20twc0q2rEEn15hL0PbYDXzoi6gfCfc50b7VF/8SRvcFKzjycpZnUqLbG6yeqansVdN9NSzP7JBqmZ/9GnUwUnZChs7VBtcC25MHJkfXXlC9VPvNTaF6N31Z/B0HqvJrmyDuwSft8GNK+xlSC9aJrmceakuQHaTjxuzh6kvfme+TPBEsBGPntXJ6xmfclsR8Vtjr6o91exP0Ys2Zn/KuSCVltx41WS5Q6Xky7oEi8h3ie6XVglvTDKpzmv7NZbhzItqpEFfuzGP1aTY/SddglvjM4LrC6kO1xWRB8Gur/R0DfFr7wezf6/9sa354RK5j3AmZkfPR3wVg0ayQoY4/mv4Xstji4LQuhjHJXIf4RoYgr3EV8GxaHAoGJz/Aw/eVQ9ekdIlAAAAAElFTkSuQmCC\n"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%R -i diab_lm plot(diab_lm);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The documentation for the `lm()` funciton is [here](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/lm.html), and a prettier version (same content) is [here](https://www.rdocumentation.org/packages/stats/versions/3.5.2/topics/lm). When googling, perfer rdocumentation.org when possible.\n",
    "Sections:\n",
    " - **Usage**: gives the function signature, including all optional arguments\n",
    " - **Arguments**: What each function input controls\n",
    " - **Details**: additional info on what the funciton *does* and how arguments interact. **Often the right place to start reading**\n",
    " - **Value**: the structure of the object returned by the function\n",
    " - **Refferences**: The relevant academic papers\n",
    " - **See Also**: other functions of interest"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"exercise\"><b>Exercise 2</b></div>\n",
    "\n",
    "1. Add confidence intervals calculated in R to the linear regression plot above. Use the `interval=` argument to `r_predict()` (documentation [here](https://stat.ethz.ch/R-manual/R-devel/library/stats/html/predict.lm.html)). You will have to work with a matrix returned by R.\n",
    "2. Fit a 5th degree polynomial to the diabetes data in R. Search the web for an easier method than writing out a formula with all 5 polynomial terms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "CI_matrix = np.array(r_predict(diab_lm, predict_df, interval=\"confidence\"))\n",
    "\n",
    "ax = diab.plot.scatter(x='age',y='y',c='Red',title=\"Diabetes data\")\n",
    "ax.set_xlabel(\"Age at Diagnosis\")\n",
    "ax.set_ylabel(\"Log C-Peptide Concentration\");\n",
    "\n",
    "ax.plot(x_vals,CI_matrix[:,0], label=\"prediction\")\n",
    "ax.plot(x_vals,CI_matrix[:,1], label=\"95% CI\", c='g')\n",
    "ax.plot(x_vals,CI_matrix[:,2], label=\"95% CI\", c='g')\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ploy5_formula = robjects.Formula(\"y~poly(age,5)\") # reset the formula\n",
    "diab5_lm = r_lm(formula=ploy5_formula, data=diab_r) #can also use a 'dumb' formula and pass a dataframe\n",
    "\n",
    "predictions = r_predict(diab5_lm, predict_df, interval=\"confidence\")\n",
    "\n",
    "ax = diab.plot.scatter(x='age',y='y',c='Red',title=\"Diabetes data\")\n",
    "ax.set_xlabel(\"Age at Diagnosis\")\n",
    "ax.set_ylabel(\"Log C-Peptide Concentration\");\n",
    "\n",
    "ax.plot(x_vals,predictions);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lowess Smoothing\n",
    "Lowess Smoothing is implemented in both Python and R. We'll use it as another example as we transition languages. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**In Python**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.nonparametric.smoothers_lowess import lowess as lowess\n",
    "\n",
    "ss1 = lowess(diab['y'],diab['age'],frac=0.15)\n",
    "ss2 = lowess(diab['y'],diab['age'],frac=0.25)\n",
    "ss3 = lowess(diab['y'],diab['age'],frac=0.7)\n",
    "ss4 = lowess(diab['y'],diab['age'],frac=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.9       , 3.22071129],\n",
       "       [1.        , 3.26459047],\n",
       "       [1.8       , 3.62356396],\n",
       "       [1.9       , 3.66837986],\n",
       "       [2.2       , 3.80550938],\n",
       "       [4.2       , 5.0920864 ],\n",
       "       [4.8       , 4.19014581],\n",
       "       [4.8       , 4.19014581],\n",
       "       [5.1       , 4.66468111],\n",
       "       [5.2       , 4.82679775]])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ss1[:10,:] # we get back simple a smoothed y value for each x value in the data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice the clean code to plot different models. We'll see even cleaner code in a minute"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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tqRXLMAxja0pK/IcSCMwcWrw4ZeJsZt48OOGvBfTe8ArL2Z53OY5JHJFVQXD8GIsH41xQl6jqkcABuMhjhmEYacPPGoIAWwWoSRF//glDh8K++8JnMxpxf8EQFlBEK5ZwKzdnVRAcP4pgnaquAxCROqr6A7BHasUy8oYsNa4Z6WXNGjfU41cRpHItgSq8+CLsuSfcdReceSb8OK8GVz53AA3rVXBtnYeYxJF8es0bWeP+2o8iKBWRJsB44AMReR2LImYkgzFj3D+7V6+sM64Z6WXhQrePVREku0cwcyYceaSLd9OiBXz+OTz3HLRsiUssKWHAB6fTskUFt37eM7mNpxA/xuK/quoKVb0F+CcwEjglxXIZuU5ZGfTvz5DyW3ho5blZZ1wz0sv8+W6/yy7+8gcWlSWrR7BiBQweDAcc4JTB8OGuI3vIISEZCwup170zQ66rycSJ8NlnyWk/1URVBCJSQ0RmBY5V9RNVfUNVN0QrZxhVsmABv9ZqzT0M4Qoe4iEuzyrjmpFe/vc/t4/FiVwyppBWVsLTT8Puu8OwYfD3v8OPP8JFF0HNmpHLXXQR7LAD3HprYu2ni6iKQFUrgeki0i5N8hj5QlER767rAUBXvuYKHuL58tOzxrhmpJf5810MgmbN/JdJdHXxlClw8MGuo7rbblBcDI8/7k+G7baDf/wDPvwQvvgifhnShR8bQStgtoh8JCJvBDY/lYvIAhGZKSLfiUhxmPM9RGSld/47Ebkp1gswspTCQiYceCOtWMonDU/i6BoTuaBiBG98mR3GNSO9zJ/vegN+1hAEiHd1cXk5DBgA3bq5KavPP++GeDp1iq2egQOdrTgbegV+4hEkehlHqupvUc5PVtUTE2zDyDI2boT3vm9Pn/8rp+4VbzOu+U70PLMGZ5wB774LPXpkWsI8pKzMDc0VFSU+2yWZdeEUQefQ6OdVEFhUtm4d1K3rv9zgwfDkk3DVVXDzzdCoUWztBqhf3/UKhgyBr76Cgw6Kr5504KdHcLxnG9i8AcenWjAjt/nyS1i5Ek7oUw+6dKHhTs2ZMMEZA08+2XXDjTSSzBlcSZ4NtnGj0ymxBpmJZ+bQqFFOCVx/Pdx3X/xKIMAll0Dz5tW/V+BHEfQKk3acz/oVeF9EporIgAh5DhaR6SLyjojsEyGPkWO8/bazDfcMmmHXrBm8/76b7XHssfD995mTL6/wZnBRXu60cyIzuJJZl8fChVBR4X/GUIBYFcHcuc7I27178h7c9evDNde4Xu433ySnzlQQzfvoxSIyE9hDRGYEbT8DM33Wf6iqdsIpjkvD+CiaBrRX1Y7AMNxahXCyDBCRYhEpLrPphTnBhAnuDxf6xtW6tTOw1aoFxxyzxeOkkUIWLIDatbdOi3cGVzLr8ghMHY21RxBYXezHTlBeDmec4ZzajR7tfn/J4tJL3UtOde4VROsRjAZOAt7w9oHtQFX9m5/KVXWJt18GjAO6hpxfpap/ep8nAAUi0jxMPSNUtbOqdi7MkpV6RmQWLoRZs+D4CAOMu+4K773nolH16gXLlqVXvryjqAg2hMwIj9c9QjLr8ohXEcTSI7jiCpgxA/773y3lkkWDBnD11e7lZ8qU5NadLKK5oV6pqgtUtR9QCmzEDfU08DOdVETqi0jDwGfgGGBWSJ6WIm4egIh09eT5Pd6LMbKDCRPc/oQTIufp2NENH5WWwl/+4kYZjBRRWAgjR7rX4UaN3H7kyPiMvMmsy2P+fDcds2XL2Mr5jVQ2ejSMGOH8Bh17bNxiRuWyy5ws//pXaupPGFWNugGXAb8Bs3FDQjOBGT7K7QxM97bZwA1e+kBgYFDds708XwGHVFXvgQceqEZ2c+KJqjvtpFpZWXXed95RLShQ7d5ddc2a1MuW1yxbpvrNN25fjeo68UTVDh3iK9uhg+pJJ0U+/8MPqg0aqB52mOrGjfG14Zfbb1cF1eLi1LYTCaBYIzxXxZ2PjIjMB7qparV4U+/cubMW25SSrGXdOvdm1L+/W6nph5decm5cjj8exo1zQ85G/rD33s7B29ixsZc94QRYuhSmTdv2XHm5m9K5eDF8913yh4RCWbXKjZB17w6vZyDGo4hMVdWwk3D9zBpaBFjH3EgKkya5P2Ak+0A4+vZ1KzrffhvOO88t+zfyg4oK514iVvtAgLZtIxuLU2kXCEejRnDllfDGG/Dtt6lvLxb82MZ/AiaJyNvA+kCiqt6fMqmMnGXCBDdsHOuCsYsuguXL3Tju9tu73kQsq0yN7GTxYmd7jlcRtGkTflFZwC5w3XVwnN/J8Eng8svh/vudrWDcuPS1WxV+egQLgQ+A2kDDoM0wYkLVvdUfdZRTBrFy7bVupeajj7oVn0bu8+67br/ffvGVD0whDY5UFlgvcOihcNttickXK40bu57I+PEwfXp6245GlT0CVb0V3MwfVV2TepGMXOXHH+Gnn9wCm3gQgbvvhj/+cH/g7bd3Xe1qTZJdLeQTGzfCnXdC167xu2cIDlCzyy5b1gvUqeOCyyRzvYBfBg+GBx5wvYLXXkt/++HwE7P4YBGZA3zvHXcUkcdSLpmRc7z9ttvHYh8IRQSeeAL69HG+YJ59NimipQYLvJMQL7zgdOhNN8U/DBgasjJgF3j++fTYBcLRpIlTBmPHOlmqBZGmE+mWaaBfA22Bb4PSZlVVLlWbTR/NXo4+WnWffZJT17p1qj17qtaooTpuXHLqTCrLlqnWq+fmCwa2evWSMzUzD9i4UXWXXVQ7dfI3zTgSf/7pbv2//606apT7fO21yZMzXn7/XbVhQ9XTTktfm0SZPurHRoCqhtrdK5KpjIzcZ/Vq+PTTxHoDwdSp44xtXbq4WUUTJyan3qSRAlcL2cSbbyY2Bj5mjJst9M9/JjYpoH59N4T48ceZswuEo2lTZzh+9VW3yj7T+Jo+KiKHACoitUXkGrxhIsPwywcfuDHfaKuJY6VBAzcLaffdoXfvarZ8PwWuFrKFqVPhlFPc8N2mTbGXr6iAO+6ADh2cJ9pEadvW/f7q1HEKprqsQ7nySvcbrg6KyY8iGAhcCrTGuZrY3zs2DN9MmOBmTGwT4zVBmjZ1fokKC900wDlzklt/VMrKnPYJ5wgxBa4WUka064iRigr35l1Q4N7oX3op9jpeecXN7PnnP6FGjcTlC9gCnn9+i82gOtCsGQwa5K43rb/bcEQaM6qum9kIso/KStVWrVRPPz11bcyfr9qypWrr1qo//5y6djYzerQb82/c2O1Hjw6fL5luG1KB3+vwyUMPuXH40aNV991Xda+9VCsq/JevqHB2pL339solQb7Jk1X/+9+Yi6WFsjLV+vVVzzwz9W0RxUbgx1j8HNAk6Hh74OmqyqVqM0WQfUyb5n5pzzyT2nZmzFBt0kR1111Vf/klhQ3liiE4ydexaJHz23PssU75jxnjqnzlFf91vPrqFkWSM/e5Cq69VlVEdc6c1LYTTRH4GRrqoKorgnoQy4EDkt41MXKWwLTRVK/g3G8/NwS1ZInzWLpiRYoayhVDcJKv4/LL3dDQY485A+/ppzv7ze23u6d4VVRWurn1u+/u5vrnzH2ugquvdiOHt9+eORn8KIIaIrJ94EBEmuLPNYVhAO7h3Lkz7LBD6ts6+GA3m2jOHDjxRFiTiiWQuWIITuJ1vP66u+833ww77eTSatZ0IR+nT4e33qq6jjffdPPqb7jBlc2Z+1wFhYUueM2LLzrbSEaI1FUIbMA5uFlCt3nbD8DZVZVL1WZDQ9lFWZnr9t58c3rbfeUVt8agUyfVkpIUNBAYu27UKClj6xkj6DpK6uymHwz9KOYqNm1SbdfO2QQ2bNj63IYNzuV4167R1wNUVqoeeKDqzjuHuIPOlftcBb/+qrrddqpnnZW6NkjERuDKsw8udsAgYG8/ZVK1mSJIImkwZL7wgvuVff11ypqIyFujVmij+hu1RfMKnTw5BQ1Ucf8WLHB/7PfeS0HbSaTy12U6/LqftUH9CgXVKVO8E9GuL+hccbH7jv976//C5n3iCXd+q/sQUvfbb7s8I0eGEbC6G9yTxNVXu5eXuXNTU38yFEFNYEegXWDzUy4VmymCJJHk2SKR6NdPtbAwtpkjScG7vu8bdNbdZa4W1NykTzyRnqYrK1VHjHCGU1AtKlJdvz49bcfD4MFOzqOPVm3e3O2j/j5Czt1zyFgF1cUN9wj7W1q3TrVNGxdcKFz5ylGjtVs31fbtt+1R5BO//OJuyznnpKb+hBSB1wsIRCibgc8IZanaTBEkgWXLdFPd+noV9+rXdNFUzcbYtEl1++1T98OOSMhsk+U01mNrvKegesklqX3YLFyoeswxWx6sgbfhxx5LXZuJ8NFHTr6LL3YK7IEH3PH7tU/YfP+2+n2EmclzHG/rnszZNm8QDz/sTk0av3yb8u/XPkFBdfjwjNyCasWVV6rWrKk6b17y605UEcwHmlWVL12bKYIk8M03OqLeIAXVs3nO/QwaNXLd7yTy2Weu6pdeSmq1VfPNN+5tM+hhs6lhEx1y9hIF1cMPT/4oQ2WlG9Zo1MjNC3/8cZdWWal66KGqO+6ounZtcttMlFWrXG9lt922hAFdt061fat12qnGt1qBbLmHgd9HyL3dQC1twCq9mEe3zRvE2rWqO+yg2rPriq3KV4IeWvMLbdNiva5bl/ZbUO1YulS1bl3V885Lft2JKoKPgVpV5UvXZoogcf74sUybs0xBtS0lWpmiHsH117u3m+XLk1pt1USZfz5qlPujtWun+u23yWmutFT1uONcMz16qP7009bnJ01y5+69NzntJYNNm9ywnYjq559vfe65YSudAuf0KnsEX3CQWytAn6g9AlXVe+5xp7+sc/jmvBPpoaD6yJ2r0nTl1Z/Bg93/Zv785NabqCIYCXwGDAWuCmxVlfPKLvCGkr4LJwQgwMNer2MG0KmqOk0RJM7ll6vWkAr9e82RCqr/q7NXSmwEHTu6t++MEGW2SXGxG7PebjvVl19OrJnnnnMvuNttpzpsWGRbSK9ebvx9VTV43lVUqF54ofv333npwm0e2ps2qe7bdrnuKvN0Q8OmkW0EjRrpHbVuUlAtq9umypk9q1erNmumemzHxZvL96gxSVs1WaPl5am84uxi8WLVOnVUL7ggufUmqghuDrdVVU63KILmUc4fD7zjKYSDgK+rqtMUQWLMnOneNi6+WHX25N/dTI0Hk/90Ki11v66770561f6JMttk6VLVQw5xMt5wQ3zG7LfecuUPO6zqMd2vv3Z5b7st9naSSWWl6mWXOVlurHVnxMkCb7zh8jx+7c9RZw0d3X29duigvmf2BHoFb76wQj99Yo6Cs0sYWzNokGqtWtv2LhMh4VlDrg4aAg385ld/iuAJoF/Q8VygVbQ6TRHET2Wl6lFHOQPub7+54xYtUjN3ecQI9+uaOTP5dSeLdeu2vBmfdJLqypWxle/Z0/Us/Bqfe/d2z90//ohV0uRQWal6zTXueq+u9YAbEowwnBOwbbRs6Xz6h2PdOjfMNniwfxnWr3f+h3bayQ2jtWixxT5hbKG0VLV2bff7TBaJ9gj2Bb4FSrxtKrBPVeW8sj8D07wyA8Kcfws4LOj4I6BzmHwDgGKguF27dsm7M3lGwI/Lo49uSTvjDPcwSyT4RzhOOcWNwye73mRTWan6yCOul7TXXqo//uiv3Bxvkswdd/hva8YMNyY/dGh8sibKP//pZL709F+0slHjLUoggoE3YOz/17/C1xewfbz+emxyBGYqgep//hPfteQDl17qegXJcqKYqCL4Ajgy6LgH8EVV5by8O3r7FsB04PCQ82+HUQQHRqvTegTxsWaNezB36LD1ys3HHnO/gmQaptatczNnBg5MXp2p5uOP3fh1kyaq775bdf5LLnHjuLHa188809kTUuoULwy33+6+5wsvVK34xb8zt1NPdd/l0qXb1nnzzW4BVDyTAc49172ArF4de9l8YdEi1ysYMCA59SWqCKb7SfNRzy3ANSFpNjSUJm65xX3bkyZtnR54s33qqeS19cEHrs4330xenengp5+coqxRw83widSbWbHCPRzPPTf2NubOdb2PWIZTEuW++9z3cdZZzhCsqr5dN/z4o3srveiibc91767auXN8MlVWRh5yMrZw8cWqBQXJcZOSqCIYB/wTKPK2G4HxPsrVBxoGff4CODYkzwkhxuJvqqrXFEHsLFjgxnL79t32XGWlm9+dFDuBZzC84qI1WqdOdv7RV69W7dNny4Mz3Nz/gM/94uL42rjgAvemt3ChpsZ9QlCdjzziZD399BAfPiH5ojFokFOOs2dvSVuzxj2ghgxJntjGtixcqFpQUKkX/fVX99aWwG8lUUWwvTfFc5q3PQhs76Pczt5w0HTcquQbvPSBwEDvswCPAv/DTTPdxj4QupkiiJ0+fdxL38KF4c/37esCuiQ0nh/kNmB3meumCGYplZVuXBxUu3RxhrsAFRVuAdZBB8Vf/4IF7iF6/hH/S76bj6Dv4amCgQqqJ5+c2GrqsjLXcTjhhC1p77/v7s877yQushGF0aN1YM0RWsB6LaGt+27j/K3EpQiAukBhmPQdgLqRyqV6M0UQGx9+qFVOW3z8cZcn7mXtQYuM5rGLgurDBVdmvZOw8eOdv6CWLVW/+MKlvfOOu1ejRiVW95DL1iiovovnjyIZi/qCvocX+D8VKvQvNd7XdYsS/x7uvtuJ+JHnnHToUDdkZGP8KcT7PktoqwWs14E8ltBvJZoiiBaP4GGge5j0nsADUcoZ1YSNG2HwYOcf/pprIufr0cPtJ02Ks6GgACITOB6AE+p8lPUBRHr3hq++gvr13T16+mkYNgxatoTTTkus7lv7zmGvGj/Qn5Esp4lLTDToivc9vEofzuF5juATxtY/mzpLE6jT4/LLoV079ztavx4mToSuXV3wdSNFeN9nOxbRn5GMpD8L8YIuJztATyQNAcyJcm52pHOp3qxH4J/AWPb48dHzVVa6t96//S3OhoLeRI/hXd2D73MqpODvv7s1A4GXsaTEVli2TKfUOVRrslH3YaaeyWi9vOYjett1f+oTT6iOHeumb86d62bl+Bq2W7ZMX619ptZigx7CZ7qa+kn9HgIuxQsK3DTYG29MSrVGJIL+V4FewaUMS0mPIFqkMYlyzk9kMyODlJXBTTfBMcfAySdHzyvi3ngnTXKPOon2zYejsBBGjmTNBYOYtK4Hl9UaDiNHuvQcoGlTeOcdGHLh77zyZl0uOmoJsFtilRYW0vmZS3ny3Et5svICiiu7sKx2O1bdVTts9oICaN4cWrRwtzXcfsncugzaNIpuNb7mnfp9abCpMqnfw//9n7sXkybBDz/A2WcnpVojEt7/iv79acdvjCnvR/c6U6BGvaT/v6IpgmUi0lVVvwlOFJEuQFnSJDBSwg03uDCNDz7o78Heo4cLlTd/PuwW5zNuUkV3NlCH4+Q9ILeeErWuHMT9zz3CfYAcAVx2mRsnSoR+/Ti/Z0/OX7AAihpDYW3Wr3dKPLAtWxZ+/9NPbr96dXCFDele8wvertWbhkMGw0UXJfVhIeLiTqc69rQRRL9+0LMnLFhAnwYN4M8/XajOZL9kReoqAF1xLiJuAU7ytltxq4W7RSqX6s2GhqqmuNh13a+6yn+ZH35wPc4RI+Jo0OvCXsudWsB6XUvdnBoa2rzYInSbMyfTkml5uerCb3/T4jqH6ER6aDl1kmN4NnIO4jEWq+sJdMUNEZ3nbeIpga+Tq46MZKEKgwa5F4abbvJfbvfdnRE0LoOxZ9T6jMM4kKnUY13yjVmZ5JtvYktPI3XrQtuNP3Fg3dkcySTqst6dyKX7b6ScaENDqOoynLdRI0sYNQq+/NLNcGnc2H+5hOwERUWsWy9MoQuD8IZLNm50XdhcoGvX2NLTTVERbNiwdVou3X8j5ZjRN4dYvRqGDIEuXeDcc2Mvf+SRsGQJzJsXY8HCQqZe+zIbqMNh9aZBveQbszLKXns5m0Awl13m0qsDAaNivXrQqFHu3X8j5UTtERjZxR13wNKlMG4c1IhDxQevJ9h999jKfr5dLwAOGfcP6PRQ7j2Ehg2DSy5xw0Fdu1YfJRAgyKiYEmNiKGVl6WvLSDm+HxciUj+VghiJMW8e3H8/nHcedOsWXx277QatWsVnJ/jsM6c8WvzlgNx9MOy1l+tqVTclEKCw0HUHU33/x4yB9u2hVy+3HzMmte0ZKadKRSAih4jIHOB777ijiDyWcsmMmLjySmc4vPPO+OsItRP4pbISvvgCDj00/raNLKGsDPr3h/JyWLnS7fv3d+lG1uKnR/AA8BfgdwBVnQ4cnkqhjNh4+2233Xyzm/mTCEce6YaXYrETzJ0Lv/8Ohx2WWNtGFhDkTmQzNkMp6/E1NKSqi0KSKlIgixEH69e73sAee7hpo4kSsBN8/LH/Mp995vbWI8gDbIZSTuJHESwSkUMAFZHaInIN3jCRkXkefNC9vT/44LYvavGw666w446x2Qkmf7COFk03svv2NjyQ8yQ6Q6msDKZMSe9QUibazDL8KIKBwKVAa6AU2N87NjLMkiVw223Ol9CxxyanzpjtBGPGMPnVXzhs1TtIkRkO84J+/aCkBD780O379fNXLhNGZjNs+0I0FqtgNaBz585aXFycaTGqBWefDa+8AnPmwM47J6/eJ5+EAQOcY7E99oiSsayM0naH0HbdPB7gCq7gIfeGWFKSuzOHjPgoK3MP4vLyLWmp/q1kos1qjIhMVdXO4c5FXEcgIsOAiFpCVS9PgmxGnHz+ObzwgnMul0wlAM5gDK5XEFURLFjAZHHzBroz2aUFDId5+EczohAwMgc/lFP9W8lEm1lKtKGhYmAqLlJZJ2Cet+2PGYszSkWFCxTSujUMHZr8+nfZxdVdpcG4qIjJG7rRgNV0ZLpLM8OhEY5MGJnNsO2baE7nnlPV53CO149U1WGqOgw4GqcMfCEiNUXkWxF5K8y5HiKyUkS+87YY3KTlL08/DdOmwb33uuhZyca3naCwkMk7nsEhNb6iVqP65trAiEwm3GCY6w3f+HExsSPQEPjDO27gpfllMG6WUaMI5yer6okx1JfXLF8O118P3btD376pa6dHD+fAbu5c2HNPLzHErcAff8CsRU3oe90hcOqH5m4g20m124h0u8HIVJtZiJ9ZQ3cB34rIsyLyLDAN+LefykWkDXAC8FTcEhpbccst8Mcf8PDDcUQSi4Ft4hiHmX3x+efuVPdj66fHtYGROtI1uyZdbjAy3WaWUaUiUNVngG7AOG872Bsy8sODwBCgMkqeg0Vkuoi8IyL7+Kw3L5k1Cx591AWe2n//1La1yy7Qpo2nCCK4FZj83loKCqqPN2YjTsxtRN4TURGIyJ7evhNuKGiRt+3opUVFRE4Elqnq1CjZpgHtVbUjMAwYH6GuASJSLCLFZXn641SFwYPdUOdtt6W+va3sBD8vCOtWYPInlXTp4oZejSzG3EbkPdF6BFd5+/vCbPf6qPtQ4GQRWQC8CBwlIi8EZ1DVVar6p/d5AlAgIs1DK1LVEaraWVU7F+Zp927sWJg4EW6/HZo1S0+bPXrAr7/CDxt32Wb2xdoNtSj+oT7du6dHFiOF2OyavCfarKEB3sfjVPXI4A04vqqKVXWoqrZR1SLgTGCiqp4VnEdEWoq4kW4R6erJ83uc15KzrF0LV10FHTq4hV7pYrOdYEbTbWZffH31y2zaJKYIcoFYZteYu4acxI+x+Aufab4QkYEiMtA7PA2YJSLTgYeBMzXbljqngXvugYULnYG4VhpDCe28M7Rt69kJQtwKTK59NCLmaC5n8OM2wtw15CwRXUyISEucf6EXgP/DBa4HNw10uKruGbZgisk3FxMlJW76Zu/e8OKL6W//nHPgvffgl1+2nqXUqxcsWwbTp6dfJiMDmLuGrCeai4loPYK/4GwBbYD72WIfuAq4PtlCGuG55hr3AL7nnsy036OHe+B/H+RvdtMm+PJLbFgonzCDck4TcaDBmyL6nIj0UdXX0iiT4TFxIrz6qpsl1LZtZmQIXk+w997u87ffwpo1pgjyCjMo5zR+bASTRORhEZkmIlNF5CERSdO8lfxl40bnT2innVyvIFPstFOQncBjsudfzhRBHmHuGnIaP6bHF4FPgT7e8d+Al4CeqRLKgMcfh9mzYfx4F4s4U4g4b6TvvOPWMog4RbDzzi6AjZFHmLuGnMVPj6Cpqt6mqj972+1AkxTLldeUlcFNN8Exx7igM5mmRw8n05w5Thl89pn1BvIWc9eQk/jpEXwsImcCL3vHpwFvp04k44Yb3Bj8gw+m1p+QX4LtBDVqwG+/mSIwjFzCjyK4CDdT6AVcoJqawBoRuQpQVY3kVdSIg6lT4amnXED6vfbKtDSOoiJo184pgoICl2aKwDByhyoVgao2TIcghht2GTTI9bpvqkaRGQJ+hyZMgDp1oEUL2G23TEtlGEayqNJGII6zROSf3nFbzx2EkWRGjXLz8++6Cxo3zrQ0W3PkkW5IaOxY1xuoDkNWhmEkBz/G4seAg3GriwH+BB5NmUR5yurVMGSIs8Ode26mpdmWgJ2gvNyGhQwj1/BjI+imqp1E5FsAVV0uIrWrKmTExh13wNKlMG6cM8hWN4qKnIeBkhJTBIaRa/h55GwUkZo4QzEiUkj0QDNGjMybB/ffD+edB926ZVqayPTqBU2bQseOmZbEMIxk4kcRPIyLTNZCRO4APsNnqErDH1de6RaN3XlnpiWJzj33wFdfQc2amZbEMIxk4mfW0CgRmQocjfNAeoqqfl9FMcMnb7/ttnvvhZYtMy1NdJo0cZthGLlFREUgIt2AEcAuwEygv6rOSZdg+cD69a43sMcebtqokUeUlZmrhlixe5Yyog0NPQpcAzTDuaF+IC0S5REPPeTsAw8+uK2HXyOHsQAvsWP3LKVEC0wzTVU7RTrOFLkSmGbJEtcTOOooeP31TEtjpA0L8BI7ds+SQrTANNFsBE1E5NRIx6o6NlkC5iPXXutcTd9/f6YlMdJKIMBL8EMtEODFHmrhsXuWcqIpgk+AkyIcK2CKIE4+/xxeeME5l9tll0xLY6QVC/ASO3bPUk60CGXnJ6MBbw1CMbBYVU8MOSfAQ8DxwFrgPFWdlox2qysVFS7gTOvWMHRopqUx0k4gwEv//u6tduNGC/BSFXbPUo6flcWbEZG3Qh/mPhgMfI8Leh/KccBu3tYNeNzb5yxPPw3TpjlbV/36mZbGyAgW4CV27J6llJgUAdA6lswi0gY4AbgD58o6lN7A8+os1l+JSBMRaaWqS2OUKytYvhyuv965aOjbN9PSGBmlsNAeZrFi9yxlxOrV5tsY8z8IDCGyS4rWwKKg41LCKBsRGSAixSJSXFZWFqMI1YdbboE//oCHHzbvnYZhVB8iKgIRKRSRvYPTVPUCEdnH8zcUFRE5EVimqlOjZQuTts18VlUdoaqdVbVzYZa+EcyaBY8+ChddBPvvn2lpDMMwthCtRzAMCPfUbYMz8FbFocDJIrIAeBE4SkReCMlTCrQNqXuJj7rjp6wMpkxx+zS1oQqDB0OjRnDbbalrNuWk494ZhpF2oimC/VT1k9BEVX0P6FBVxao6VFXbqGoRcCYwUVXPCsn2BnCOF/zmIGBlSu0D6VidGKaNsWNh4kS4/XZo1iz5TaYFW9lpGDlLtJXFP6rq7hHOzVXVPXw3ItIDuEZVTxSRgQCqOtybPvoIcCxu+uj5qhp12XDcK4vTsToxTBtr6zZlr+bLaNK0JlOnQq1YzfPVAVvZaRhZT7wri+eJyPGqOiGksuOAn2IRQFUnAZO8z8OD0hW4NJa64iYdqxPDtHGPXs3C0po8/0KWKgGwlZ2GkeNEezRdCbwlImcAAYNvZ1zYyljXEmSedKxODGmjhHbctf5K+p6yjiOOqJu8dtKNrew0jJwmoo1AVX8E9sO5lijytk+ADt657CKwOrFePWe1rVcv+asTQ9q4psYDSO0C7nk4i5UApOfeGYaRMSLaCKorCXsfTYdP87IyJr7yO0dfuie33QY33piaZtKO+YM3jKwlmo0g/xRBGti0ya0VWLsW5sxxYSgNwzAySbzGYiNO7rgDZs+GceNMCRiGUf2J1cWEUQVjxzpXEmedBb17Z1oawzCMqqmyRyAiM9nW7cNKnGvp21X191QIlo189x2cfTZ06wZPPmn+hAzDyA78DA29A1QAo73jM739KuBZtg5ek18EGU+XaSG9e8P229uQkGFkPXk2McKPIjhUVQ8NOp4pIp+r6qEiEuoyIn8YM8YFyqhdm/Xr4dR28ygrK2TyZGjVKtPCGYYRN0H/bTZscFOl+/XLtFQpxY+NoIGIbA4WIyJdgQbe4aaUSFXdKStzP5TycnTlSi5Zdx+f/1jIMw+t4sADMy2cYRhxE/TfZuVKt+/fP+cdLfpRBBcCT4nIz54n0aeAC0WkPnBnKoWrtgRcLgAPMZin6c+Ntf9D3/3nZlYuwzASI+i/vZmAO5UcpsqhIVWdAuwnIo1x6w5WBJ1+OVWCVWs8lwvvcQxXcx9/ZSy31rgVipIS5tkwjEyRp+5UquwRiEhjEbkf+Aj4UETu85RC/lJYyJxbX+EMXmbfGnN4vu5F1Hj6qbwwKhlGTpOn7lSqXFksIq8Bs4DnvKSzgY6qemqKZQtLdVhZ/NtvboromtWVfDNyJu0O2jHnfyiGkVfk4KyhRFcW76KqfYKObxWR75IiWRayfj2ceiosXgyffFKDdt06ZlokwzCSTWFhzigAP/gxFpeLyGGBAxE5FCiPkj9nUYWBA2HyZHj2WdcrMAzDyHb89AgGAs8H2QWWA+emTqTqyz33OAVw881w5plVZjcMw8gK/Mwamg50FJFG3vEqEbkCmJFi2aoV48fDdddB375OERiGYeQKvp3OqeoqVV3lHV5VVX4RqSsi34jIdBGZLSK3hsnTQ0RWish33nZTDLKnje++g7/9Dbp0gWeeMR9ChmHkFvG6ofbzKFwPHKWqf4pIAfCZiLyjql+F5JusqtU29OXSpXDSSdCsGbz+uptNZhiGkUvEqwiqjGbjBab/0zss8LasioJTXu5cSS9fDp9/Di1bZloiwzCM5BNxaEhEVovIqjDbamBHP5WLSE1vquky4ANV/TpMtoO94aN3RGSfCPUMEJFiESkuS5PPj8pKOO88KC6G0aOho80SNQwjR4kWvL6hqjYKszVUVV89CVWtUNX9gTZAVxHZNyTLNKC9qnYEhgHjI9QzQlU7q2rnwjTN7b31Vnj5Zbj7bjj55LQ0aRiGkRHSEqHM8080CTg2JH2Vqv7pfZ4AFIhI83TIFI0xY+Bf/4Lzz4drrsm0NIZhGKklZYpARApFpIn3uR7QE/ghJE9LETcHx3NvXQPIaMSzr75yCuDww2H48AgzhMrKYMqUnHdNaxjVGvsfJo1U9ghaAR+LyAxgCs5G8JaIDBSRgV6e04BZIjIdeBg4U6tyfpRCFi6EU06B1q3htde29UYLuO5C+/bQq5fbjxmTbjENw7D/YVKp0ulcdSNVTudWr4bDDoOSEvjyS9hrrzCZysrcj648yMNGvXquUB75JTGMjGL/w7iI5nQuLTaC6k5FhVswNnu2MxCHVQKQt0ErDKNaYf/DpBPvOoKc4tpr4c034dFH4ZhjomTM06AVhlGtsP9h0sn7HsHIkXDffXDZZXDJJVVkztOgFYZRrbD/YdLJaxvBpEnO1nT00fDWW1DLb/8oB4NWGEbWYf/DmEg0ME1OMn8+9OkDu+0GL70UgxKAvAtaYRjVEvsfJo28HBpavhxOPNGtEXjzTWic3xGYDcPIc/KuR7BxI5xxBvz0E3z0EeyyS6YlMgzDyCx5pQhU4dJL4cMPXVyB7t0zLZFhGEbmyauhoXvvhSefhOuvd55FDcMwjDxSBOPHw5AhLtTkbbdlWhrDMIzqQ94ogs6d4e9/d0NCNfLmqg3DMKomb2wEbdrAiBGZlsIwDKP6Ye/GhmEYeY4pAsMwjDzHFIFhGEaeY4rAMAwjzzFFYBiGkeeYIjAMw8hzTBEYhmHkOSlTBCJSV0S+EZHpIjJbRG4Nk0dE5GERmS8iM0SkU6rkoawMpkxxe8MwDGMzqewRrAeOUtWOwP7AsSJyUEie44DdvG0A8HhKJBkzxgW77tXL7ceMSUkzhmEY2UjKFIE6/vQOC7wtNBxab+B5L+9XQBMRaZVUQcrKoH9/KC+HlSvdvn9/6xkYhmF4pNRGICI1ReQ7YBnwgap+HZKlNbAo6LjUSwutZ4CIFItIcVmsD/AFC6B27a3TCgpcumEYhpFaRaCqFaq6P9AG6Coi+4ZkkXDFwtQzQlU7q2rnwlhD0xUVwYYNW6dt3OjSDcMwjPTMGlLVFcAk4NiQU6VA26DjNsCSpDZeWAgjR0K9etCokduPHGmxTg3DMDxSOWuoUESaeJ/rAT2BH0KyvQGc480eOghYqapLky5Mv35QUuJCk5WUuGPDMAwDSK0b6lbAcyJSE6dwXlbVt0RkIICqDgcmAMcD84G1wPkpk6aw0HoBhmEYYUiZIlDVGcABYdKHB31W4NJUyWAYhmFUja0sNgzDyHNMERiGYeQ5pggMwzDyHFMEhmEYeY44e232ICJlQEmm5QhDc+C3TAvhg2yQ02RMHtkgZzbICNkhZzQZ26tq2KmTWacIqisiUqyqnTMtR1Vkg5wmY/LIBjmzQUbIDjnjldGGhgzDMPIcUwSGYRh5jimC5DEi0wL4JBvkNBmTRzbImQ0yQnbIGZeMZiMwDMPIc6xHYBiGkeeYIjAMw8hzTBEkiIi0FZGPReR7EZktIoMzLVMkvIhx34rIW5mWJRIi0kREXhWRH7x7enCmZQpFRK70vutZIjJGROpmWiYAEXlaRJaJyKygtKYi8oGIzPP221dDGe/xvu8ZIjIu4L4+U4STMejcNSKiItI8E7KFyBJWThEZJCJzvd/of/zUZYogcTYBV6vqXsBBwKUisneGZYrEYOD7TAtRBQ8B76rqnkBHqpm8ItIauBzorKr7AjWBMzMr1WaeZdvgT9cBH6nqbsBH3nEmeZZtZfwA2FdVOwA/AkPTLVQIz7KtjIhIW6AXsDDdAkXgWULkFJEjcbHgO6jqPsC9fioyRZAgqrpUVad5n1fjHlzbxF3ONCLSBjgBeCrTskRCRBoBhwMjAVR1gxfdrrpRC6gnIrWA7Uh2VL04UdVPgT9CknsDz3mfnwNOSadMoYSTUVXfV9VN3uFXuEiFGSPCfQR4ABhCmHC6mSCCnBcDd6nqei/PMj91mSJIIiJShIvB8HWGRQnHg7gfcWWG5YjGzkAZ8Iw3hPWUiNTPtFDBqOpi3FvWQmApLqre+5mVKio7BKL+efsWGZanKi4A3sm0EKGIyMnAYlWdnmlZqmB3oLuIfC0in4hIFz+FTBEkCRFpALwGXKGqqzItTzAiciKwTFWnZlqWKqgFdAIeV9UDgDVkfihjK7wx9t7ATsCOQH0ROSuzUuUGInIDbqh1VKZlCUZEtgNuAG7KtCw+qAVsjxum/gfwsohIVYVMESQBESnAKYFRqjo20/KE4VDgZBFZALwIHCUiL2RWpLCUAqWqGuhRvYpTDNWJnsDPqlqmqhuBscAhGZYpGr+KSCsAb+9rqCDdiMi5wInA37T6LW7aBaf4p3v/oTbANBFpmVGpwlMKjFXHN7gRgCoN26YIEsTTtiOB71X1/kzLEw5VHaqqbVS1CGfYnKiq1e4tVlV/ARaJyB5e0tHAnAyKFI6FwEEisp333R9NNTNoh/AGcK73+Vzg9QzKEhYRORa4FjhZVddmWp5QVHWmqrZQ1SLvP1QKdPJ+r9WN8cBRACKyO1AbHx5TTREkzqHA2bi37O+87fhMC5XFDAJGicgMYH/g35kVZ2u83sqrwDRgJu4/VC1cD4jIGOBLYA8RKRWR/sBdQC8RmYeb8XJXNZTxEaAh8IH3/xketZLMyFjtiCDn08DO3pTSF4Fz/fSwzMWEYRhGnmM9AsMwjDzHFIFhGEaeY4rAMAwjzzFFYBiGkeeYIjAMw8hzTBEYWYOI/NXz/LhnGtrqISJhF4qJyHkiUua5wZgnIu8F5xWRf4lIz1TLGI3qIIORPdj0USNrEJGXgVY4b5q3pLitW4A/VXUb740ich7O++hl3vGRwBjgSFWtzovLDCMs1iMwsgLPl9OhQH+C3D6LSA0Reczzvf6WiEwQkdO8cwd6jremem/trcLUe5LnoOtbEflQRHbwnAcOBK70Fjh1jyabqn6MW1Q2wKvz2SAZbhKRKeJiF4wI+H0RkS6e//0vxfnjn+WlnyciY0XkXa+3sdmfvIj0E5GZXl13e2k1vfZmeeeuDCPDXSIyx2vPl1tiI78wRWBkC6fg4hT8CPwhIgEfRKcCRcB+wIXAwbDZ/9Mw4DRVPRC34vKOMPV+BhzkObl7ERiiqguA4cADqrq/qk72Id80INyQ1SOq2sWLXVAP508H4BlgoKoeDFSElNkf6OtdU19xwY92BO7GuQ/YH+giIqd4n1ur6r6qup9X72ZEpCnwV2Afz9//7T6uxcgzTBEY2UI/3IMab9/P+3wY8IqqVnq+Xz720vcA9sVzWwDcSHg/922A90RkJs5b4z5xyhfJw+ORXo9jJu4hvo+4CFwNVfULL8/okDIfqepKVV2H87XUHugCTPKc3QU8dB4O/IRzKTDM89kT6vl2FbAOeEpETgWqnS8fI/PUyrQAhlEVItIM9xDdV0QUFxVMRWQIkR/AAsz23rijMQy4X1XfEJEewC1xinkAIc7nxIWwfAxnT1jk2R3qRpE5wPqgzxW4/2nYMqq6XEQ6An8BLgXOwPn0D5zfJCJdcc7xzgQuw3NKZhgBrEdgZAOnAc+ranvPA2Rb4Gdcb+AzoI9nK9gB6OGVmQsUihfzWEQKRCTc235jYLH3+dyg9NU4R2hVIiJH4OwDT4acCsQy/s2zcZwG7uENrBaRg7zzfkJdfg0cISLNRaQmrkf0ibjYuTVU9TXgn4S47fbabayqE4ArcENJhrEV1iMwsoF+bOs18zXg/3BvwUcDs3Dxbr/GRQ3b4BlLHxaRxrjf+oPA7JB6bgFeEZHFuDCJO3npbwKvikhvYFAYO0FfETkMF6ryZ6BP6IwhVV0hIk/ivJQuAKYEne4PPCkia4BJwMpoN0BVl4rIUNzQlwATVPV1rzfwjIgEXupC4/02BF73eicCXBmtHSM/semjRtYjIg1U9U9vCOkb4NBq6it+MwGZvc/XAa1UdXCGxTLyFOsRGLnAW54BtjZwW3VXAh4neG/4tYAS4LzMimPkM9YjMAzDyHPMWGwYhpHnmCIwDMPIc0wRGIZh5DmmCAzDMPIcUwSGYRh5zv8DLjPOVXS9OmEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for cur_model, cur_frac in zip([ss1,ss2,ss3,ss4],[0.15,0.25,0.7,1]):\n",
    "\n",
    "    ax = diab.plot.scatter(x='age',y='y',c='Red',title=\"Lowess Fit, Fraction = {}\".format(cur_frac))\n",
    "    ax.set_xlabel(\"Age at Diagnosis\")\n",
    "    ax.set_ylabel(\"Log C-Peptide Concentration\")\n",
    "    ax.plot(cur_model[:,0],cur_model[:,1],color=\"blue\")\n",
    "    \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**In R**  \n",
    "\n",
    "We need to:\n",
    " - Import the loess function\n",
    " - Send data over to R\n",
    " - Call the function and get results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "r_loess = robjects.r['loess.smooth'] #extract R function\n",
    "r_y = robjects.FloatVector(diab['y'])\n",
    "r_age = robjects.FloatVector(diab['age'])\n",
    "\n",
    "ss1_r = r_loess(r_age,r_y, span=0.15, degree=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "    <span>ListVector with 2 elements.</span>\n",
       "    <table>\n",
       "      <tbody>\n",
       "      \n",
       "      <tr>\n",
       "      <th>\n",
       "        x\n",
       "      </th>\n",
       "      <td>\n",
       "        \n",
       "    <span>FloatVector with 50 elements.</span>\n",
       "    <table>\n",
       "      <tbody>\n",
       "      <tr>\n",
       "      \n",
       "      <td>\n",
       "        0.900000\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        1.200000\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        1.500000\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        1.800000\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        ...\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        14.700000\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        15.000000\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        15.300000\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        15.600000\n",
       "      </td>\n",
       "      \n",
       "      </tr>\n",
       "      </tbody>\n",
       "    </table>\n",
       "    \n",
       "      </td>\n",
       "      </tr>\n",
       "      \n",
       "      <tr>\n",
       "      <th>\n",
       "        y\n",
       "      </th>\n",
       "      <td>\n",
       "        \n",
       "    <span>FloatVector with 50 elements.</span>\n",
       "    <table>\n",
       "      <tbody>\n",
       "      <tr>\n",
       "      \n",
       "      <td>\n",
       "        3.311816\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        3.420293\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        3.530318\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        3.640274\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        ...\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        5.545358\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        5.316981\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        5.090513\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        4.864094\n",
       "      </td>\n",
       "      \n",
       "      </tr>\n",
       "      </tbody>\n",
       "    </table>\n",
       "    \n",
       "      </td>\n",
       "      </tr>\n",
       "      \n",
       "      </tbody>\n",
       "    </table>\n",
       "    "
      ],
      "text/plain": [
       "R object with classes: ('list',) mapped to:\n",
       "<ListVector - Python:0x0000023128728348 / R:0x0000023125F05E48>\n",
       "[FloatVector, FloatVector]\n",
       "  x: <class 'rpy2.robjects.vectors.FloatVector'>\n",
       "  R object with classes: ('numeric',) mapped to:\n",
       "<FloatVector - Python:0x0000023128721388 / R:0x00000231259D23D8>\n",
       "[0.900000, 1.200000, 1.500000, 1.800000, ..., 14.700000, 15.000000, 15.300000, 15.600000]\n",
       "  y: <class 'rpy2.robjects.vectors.FloatVector'>\n",
       "  R object with classes: ('numeric',) mapped to:\n",
       "<FloatVector - Python:0x0000023128728608 / R:0x00000231230D2950>\n",
       "[3.311816, 3.420293, 3.530318, 3.640274, ..., 5.545358, 5.316981, 5.090513, 4.864094]"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ss1_r #again, a smoothed y value for each x value in the data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Varying span**  \n",
    "Next, some extremely clean code to fit and plot models with various parameter settings. (Though the `zip()` method seen earlier is great when e.g. the label and the parameter differ)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for cur_frac in [0.15,0.25,0.7,1]:\n",
    "    \n",
    "    cur_smooth = r_loess(r_age,r_y, span=cur_frac)\n",
    "\n",
    "    ax = diab.plot.scatter(x='age',y='y',c='Red',title=\"Lowess Fit, Fraction = {}\".format(cur_frac))\n",
    "    ax.set_xlabel(\"Age at Diagnosis\")\n",
    "    ax.set_ylabel(\"Log C-Peptide Concentration\")\n",
    "    ax.plot(cur_smooth[0], cur_smooth[1], color=\"blue\")\n",
    "    \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Smoothing Splines\n",
    "From this point forward, we're working with R functions; these models aren't (well) supported in Python.\n",
    "\n",
    "For clarity: this is the fancy spline model that minimizes $MSE - \\lambda\\cdot\\text{wiggle penalty}$ $=$ $\\sum_{i=1}^N \\left(y_i - f(x_i)\\right)^2 - \\lambda \\int \\left(f''(x)\\right)^2$, across all possible functions $f$. The winner will always be a continuous, cubic polynomial with a knot at each data point"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "r_smooth_spline = robjects.r['smooth.spline'] #extract R function\n",
    "\n",
    "# run smoothing function\n",
    "spline1 = r_smooth_spline(r_age, r_y, spar=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"exercise\"><b>Exercise 3</b></div>\n",
    "\n",
    "1. We actually set the spar parameter, a scale-free value that translates to a $\\lambda$ through a complex expression. Inspect the 'spline1' result and extract the implied value of $\\lambda$\n",
    "2. Working from the fitting/plotting loop examples above, produce a plot like the one below for spar = [0,.5,.9,2], including axes labels and title."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "lambda1 = spline1.rx2(\"lambda\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for cur_spar in [0,0.5,0.9,2]:\n",
    "    \n",
    "    cur_model = r_smooth_spline(r_age, r_y, spar= cur_spar)\n",
    "    cur_lambda = cur_model.rx2(\"lambda\")[0]\n",
    "    \n",
    "    ax = diab.plot.scatter(x='age',y='y',c='Red',title=\"$\\lambda=$\"+str(cur_lambda)) #can use TeX style in labels\n",
    "    ax.set_xlabel(\"Age at Diagnosis\")\n",
    "    ax.set_ylabel(\"Log C-Peptide Concentration\")\n",
    "    ax.plot(cur_model.rx2(\"x\"),cur_model.rx2(\"y\"),color=\"darkgreen\")\n",
    "    \n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**CV**  \n",
    "R's `smooth_spline` funciton has built-in CV to find a good lambda. See package [docs](https://www.rdocumentation.org/packages/stats/versions/3.5.2/topics/smooth.spline)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "spline_cv = r_smooth_spline(r_age, r_y, cv=True) \n",
    "\n",
    "lambda_cv = spline_cv.rx2(\"lambda\")[0]\n",
    "\n",
    "ax19 = diab.plot.scatter(x='age',y='y',c='Red',title=\"smoothing spline with $\\lambda=$\"+str(np.round(lambda_cv,4))+\", chosen by cross-validation\")\n",
    "ax19.set_xlabel(\"Age at Diagnosis\")\n",
    "ax19.set_ylabel(\"Log C-Peptide Concentration\")\n",
    "ax19.plot(spline_cv.rx2(\"x\"),spline_cv.rx2(\"y\"),color=\"darkgreen\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Natural & Basis Splines\n",
    "Here, we take a step backward on model complexity, but a step forward in coding complexity. We'll be working with R's formula interface again, so we will need to populate Formulas and DataFrames."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [],
   "source": [
    "#We will now work with a new dataset, called GAGurine.\n",
    "#The dataset description (from the R package MASS) is below:\n",
    "#Data were collected on the concentration of a chemical GAG \n",
    "# in the urine of 314 children aged from zero to seventeen years. \n",
    "# The aim of the study was to produce a chart to help a paediatrican\n",
    "# to assess if a child's GAG concentration is ‘normal’.\n",
    "\n",
    "#The variables are:\n",
    "# Age: age of child in years.\n",
    "# GAG: concentration of GAG (the units have been lost)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "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>Age</th>\n",
       "      <th>GAG</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00</td>\n",
       "      <td>23.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.00</td>\n",
       "      <td>23.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.00</td>\n",
       "      <td>16.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.00</td>\n",
       "      <td>18.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.01</td>\n",
       "      <td>17.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Age   GAG\n",
       "0  0.00  23.0\n",
       "1  0.00  23.8\n",
       "2  0.00  16.9\n",
       "3  0.00  18.6\n",
       "4  0.01  17.9"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "GAGurine = pd.read_csv(\"data/GAGurine.csv\")\n",
    "display(GAGurine.head())\n",
    "\n",
    "ax31 = GAGurine.plot.scatter(x='Age',y='GAG',c='black',title=\"GAG in urine of children\")\n",
    "ax31.set_xlabel(\"Age\");\n",
    "ax31.set_ylabel(\"GAG\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Standard stuff: import function, convert variables to R format, call function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [],
   "source": [
    "from rpy2.robjects.packages import importr\n",
    "r_splines = importr('splines')\n",
    "\n",
    "# populate R variables\n",
    "r_gag = robjects.FloatVector(GAGurine['GAG'].values)\n",
    "r_age = robjects.FloatVector(GAGurine['Age'].values)\n",
    "r_quarts = robjects.FloatVector(np.quantile(r_age,[.25,.5,.75])) #woah, numpy functions run on R objects!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What happens when we call the ns or bs functions from r_splines?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "ns_design = r_splines.ns(r_age, knots=r_quarts)\n",
    "bs_design = r_splines.bs(r_age, knots=r_quarts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                  1            2           3            4\n",
      "\r\n",
      "  [1,] 0.000000e+00  0.000000000 0.000000000  0.000000000\n",
      "\r\n",
      "  [2,] 0.000000e+00  0.000000000 0.000000000  0.000000000\n",
      "\r\n",
      "  [3,] 0.000000e+00  0.000000000 0.000000000  0.000000000\n",
      "\r\n",
      "  [4,] 0.000000e+00  0.000000000 0.000000000  0.000000000\n",
      "\r\n",
      "  [5,] 3.064149e-08 -0.001934587 0.004727391 -0.002792803\n",
      "\r\n",
      "  [6,] 3.064149e-08 -0.001934587 0.004727391 -0.002792803\n",
      "\r\n",
      "  [7,] 3.064149e-08 -0.001934587 0.004727391 -0.002792803\n",
      "\r\n",
      "  [8,] 3.064149e-08 -0.001934587 0.004727391 -0.002792803\n",
      "\r\n",
      "  [9,] 3.064149e-08 -0.001934587 0.004727391 -0.002792803\n",
      "\r\n",
      " [10,] 3.064149e-08 -0.001934587 0.004727391 -0.002792803\n",
      "\r\n",
      " [11,] 3.064149e-08 -0.001934587 0.004727391 -0.002792803\n",
      "\r\n",
      " [12,] 2.451319e-07 -0.003869017 0.009454395 -0.005585378\n",
      "\r\n",
      " [13,] 2.451319e-07 -0.003869017 0.009454395 -0.005585378\n",
      "\r\n",
      " [14,] 8.273203e-07 -0.005803130 0.014180627 -0.008377497\n",
      "\r\n",
      " [15,] 8.273203e-07 -0.005803130 0.014180627 -0.008377497\n",
      "\r\n",
      " [16,] 8.273203e-07 -0.005803130 0.014180627 -0.008377497\n",
      "\r\n",
      " [17,] 1.961055e-06 -0.007736769 0.018905700 -0.011168931\n",
      "\r\n",
      " [18,] 1.961055e-06 -0.007736769 0.018905700 -0.011168931\n",
      "\r\n",
      " [19,] 1.961055e-06 -0.007736769 0.018905700 -0.011168931\n",
      "\r\n",
      " [20,] 3.830186e-06 -0.009669775 0.023629228 -0.013959452\n",
      "\r\n",
      " [21,] 3.830186e-06 -0.009669775 0.023629228 -0.013959452\n",
      "\r\n",
      " [22,] 3.830186e-06 -0.009669775 0.023629228 -0.013959452\n",
      "\r\n",
      " [23,] 3.830186e-06 -0.009669775 0.023629228 -0.013959452\n",
      "\r\n",
      " [24,] 3.830186e-06 -0.009669775 0.023629228 -0.013959452\n",
      "\r\n",
      " [25,] 3.830186e-06 -0.009669775 0.023629228 -0.013959452\n",
      "\r\n",
      " [26,] 6.618562e-06 -0.011601992 0.028350825 -0.016748833\n",
      "\r\n",
      " [27,] 1.051003e-05 -0.013533260 0.033070104 -0.019536844\n",
      "\r\n",
      " [28,] 3.064149e-05 -0.019319792 0.047210174 -0.027890381\n",
      "\r\n",
      " [29,] 3.064149e-05 -0.019319792 0.047210174 -0.027890381\n",
      "\r\n",
      " [30,] 8.408025e-05 -0.027012302 0.066007721 -0.038995419\n",
      "\r\n",
      " [31,] 8.408025e-05 -0.027012302 0.066007721 -0.038995419\n",
      "\r\n",
      " [32,] 1.034150e-04 -0.028930292 0.070694554 -0.041764262\n",
      "\r\n",
      " [33,] 1.505416e-04 -0.032759001 0.080050453 -0.047291452\n",
      "\r\n",
      " [34,] 1.787012e-04 -0.034669404 0.084718746 -0.050049342\n",
      "\r\n",
      " [35,] 3.728150e-04 -0.044175579 0.107948196 -0.063772617\n",
      "\r\n",
      " [36,] 4.235880e-04 -0.046066539 0.112568979 -0.066502440\n",
      "\r\n",
      " [37,] 4.235880e-04 -0.046066539 0.112568979 -0.066502440\n",
      "\r\n",
      " [38,] 4.787733e-04 -0.047953706 0.117180492 -0.069226786\n",
      "\r\n",
      " [39,] 6.031165e-04 -0.051716026 0.126374162 -0.074658136\n",
      "\r\n",
      " [40,] 6.726420e-04 -0.053590864 0.130955546 -0.077364683\n",
      "\r\n",
      " [41,] 7.473153e-04 -0.055461275 0.135526116 -0.080064841\n",
      "\r\n",
      " [42,] 7.473153e-04 -0.055461275 0.135526116 -0.080064841\n",
      "\r\n",
      " [43,] 8.273203e-04 -0.057327103 0.140085484 -0.082758381\n",
      "\r\n",
      " [44,] 1.101163e-03 -0.062895500 0.153692516 -0.090797015\n",
      "\r\n",
      " [45,] 1.101163e-03 -0.062895500 0.153692516 -0.090797015\n",
      "\r\n",
      " [46,] 1.961055e-03 -0.075698483 0.184978102 -0.109279619\n",
      "\r\n",
      " [47,] 2.111842e-03 -0.077503454 0.189388760 -0.111885306\n",
      "\r\n",
      " [48,] 2.792206e-03 -0.084656950 0.206869163 -0.122212213\n",
      "\r\n",
      " [49,] 2.982520e-03 -0.086427936 0.211196775 -0.124768839\n",
      "\r\n",
      " [50,] 3.181292e-03 -0.088191651 0.215506620 -0.127314969\n",
      "\r\n",
      " [51,] 3.830186e-03 -0.093437589 0.228325683 -0.134888094\n",
      "\r\n",
      " [52,] 3.830186e-03 -0.093437589 0.228325683 -0.134888094\n",
      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
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      "\r\n",
      "[189,] 6.933792e-01  0.139906562 0.140014158 -0.081515371\n",
      "\r\n",
      "[190,] 6.933792e-01  0.139906562 0.140014158 -0.081515371\n",
      "\r\n",
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      "\r\n",
      "[192,] 6.929131e-01  0.144116530 0.138460233 -0.080501756\n",
      "\r\n",
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      "\r\n",
      "[194,] 6.917160e-01  0.152524223 0.135526439 -0.078562398\n",
      "\r\n",
      "[195,] 6.797155e-01  0.196979914 0.123605120 -0.070044971\n",
      "\r\n",
      "[196,] 6.729613e-01  0.213425405 0.120649643 -0.067562760\n",
      "\r\n",
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      "\r\n",
      "[198,] 6.643865e-01  0.231061867 0.118308372 -0.065255035\n",
      "\r\n",
      "[199,] 6.553877e-01  0.247151580 0.116898335 -0.063442787\n",
      "\r\n",
      "[200,] 6.545932e-01  0.248483409 0.116812067 -0.063304508\n",
      "\r\n",
      "[201,] 6.488475e-01  0.257765056 0.116338382 -0.062388008\n",
      "\r\n",
      "[202,] 6.462886e-01  0.261720133 0.116203838 -0.062021774\n",
      "\r\n",
      "[203,] 6.436736e-01  0.265661033 0.116109461 -0.061670753\n",
      "\r\n",
      "[204,] 6.427896e-01  0.266971454 0.116086820 -0.061557041\n",
      "\r\n",
      "[205,] 6.418996e-01  0.268280247 0.116068548 -0.061444946\n",
      "\r\n",
      "[206,] 6.418996e-01  0.268280247 0.116068548 -0.061444946\n",
      "\r\n",
      "[207,] 6.418996e-01  0.268280247 0.116068548 -0.061444946\n",
      "\r\n",
      "[208,] 6.373596e-01  0.274799329 0.116041919 -0.060908077\n",
      "\r\n",
      "[209,] 6.345654e-01  0.278690396 0.116076886 -0.060604179\n",
      "\r\n",
      "[210,] 6.317199e-01  0.282565742 0.116149290 -0.060313342\n",
      "\r\n",
      "[211,] 6.297949e-01  0.285140395 0.116218048 -0.060126461\n",
      "\r\n",
      "[212,] 6.288242e-01  0.286425009 0.116258503 -0.060035068\n",
      "\r\n",
      "[213,] 6.258795e-01  0.290267842 0.116403893 -0.059768861\n",
      "\r\n",
      "[214,] 6.198475e-01  0.297902779 0.116800687 -0.059270660\n",
      "\r\n",
      "[215,] 6.028944e-01  0.317912575 0.118515632 -0.058138154\n",
      "\r\n",
      "[216,] 6.006925e-01  0.320376100 0.118793815 -0.058013989\n",
      "\r\n",
      "[217,] 5.871306e-01  0.334970230 0.120741121 -0.057334739\n",
      "\r\n",
      "[218,] 5.669954e-01  0.355062817 0.124256767 -0.056518503\n",
      "\r\n",
      "[219,] 5.459644e-01  0.374414067 0.128556485 -0.055791940\n",
      "\r\n",
      "[220,] 5.099186e-01  0.404498805 0.137043787 -0.054551145\n",
      "\r\n",
      "[221,] 5.059839e-01  0.407580386 0.138039513 -0.054401257\n",
      "\r\n",
      "[222,] 4.980864e-01  0.413656825 0.140073347 -0.054085514\n",
      "\r\n",
      "[223,] 4.835361e-01  0.424488423 0.143934262 -0.053439889\n",
      "\r\n",
      "[224,] 4.808841e-01  0.426413819 0.144652710 -0.053311705\n",
      "\r\n",
      "[225,] 4.742498e-01  0.431166712 0.146468538 -0.052974777\n",
      "\r\n",
      "[226,] 4.742498e-01  0.431166712 0.146468538 -0.052974777\n",
      "\r\n",
      "[227,] 4.517095e-01  0.446659282 0.152818072 -0.051625729\n",
      "\r\n",
      "[228,] 4.503873e-01  0.447537585 0.153198421 -0.051535310\n",
      "\r\n",
      "[229,] 4.306587e-01  0.460254365 0.158964145 -0.050007217\n",
      "\r\n",
      "[230,] 4.306587e-01  0.460254365 0.158964145 -0.050007217\n",
      "\r\n",
      "[231,] 4.306587e-01  0.460254365 0.158964145 -0.050007217\n",
      "\r\n",
      "[232,] 4.202477e-01  0.466675986 0.162068401 -0.049046976\n",
      "\r\n",
      "[233,] 4.189533e-01  0.467460572 0.162457022 -0.048919178\n",
      "\r\n",
      "[234,] 4.022940e-01  0.477285038 0.167505412 -0.047088453\n",
      "\r\n",
      "[235,] 3.934737e-01  0.482280085 0.170209517 -0.045963387\n",
      "\r\n",
      "[236,] 3.884880e-01  0.485039347 0.171746136 -0.045273480\n",
      "\r\n",
      "[237,] 3.798644e-01  0.489700180 0.174416822 -0.043981377\n",
      "\r\n",
      "[238,] 3.786429e-01  0.490348631 0.174796426 -0.043788004\n",
      "\r\n",
      "[239,] 3.737834e-01  0.492899168 0.176310057 -0.042992643\n",
      "\r\n",
      "[240,] 3.665724e-01  0.496595679 0.178566203 -0.041734245\n",
      "\r\n",
      "[241,] 3.352690e-01  0.511335526 0.188509323 -0.035113839\n",
      "\r\n",
      "[242,] 3.263488e-01  0.515116451 0.191390570 -0.032855803\n",
      "\r\n",
      "[243,] 3.047435e-01  0.523419773 0.198466605 -0.026629916\n",
      "\r\n",
      "[244,] 3.005402e-01  0.524885850 0.199860289 -0.025286378\n",
      "\r\n",
      "[245,] 2.771193e-01  0.532079683 0.207737257 -0.016936201\n",
      "\r\n",
      "[246,] 2.771193e-01  0.532079683 0.207737257 -0.016936201\n",
      "\r\n",
      "[247,] 2.692675e-01  0.534094970 0.210423216 -0.013785663\n",
      "\r\n",
      "[248,] 2.512169e-01  0.537893957 0.216693168 -0.005804062\n",
      "\r\n",
      "[249,] 2.235290e-01  0.541178884 0.226600852  0.008691236\n",
      "\r\n",
      "[250,] 2.117225e-01  0.541509500 0.230947774  0.015820271\n",
      "\r\n",
      "[251,] 2.100705e-01  0.541499337 0.231562415  0.016867716\n",
      "\r\n",
      "[252,] 2.043565e-01  0.541351897 0.233701285  0.020590323\n",
      "\r\n",
      "[253,] 2.035488e-01  0.541316691 0.234005273  0.021129273\n",
      "\r\n",
      "[254,] 2.019397e-01  0.541235716 0.234612082  0.022212512\n",
      "\r\n",
      "[255,] 1.995420e-01  0.541087921 0.235519383  0.023850682\n",
      "\r\n",
      "[256,] 1.893713e-01  0.540085223 0.239410952  0.031132532\n",
      "\r\n",
      "[257,] 1.802952e-01  0.538643690 0.242946101  0.038115052\n",
      "\r\n",
      "[258,] 1.736817e-01  0.537242463 0.245562061  0.043513735\n",
      "\r\n",
      "[259,] 1.637189e-01  0.534526202 0.249571985  0.052182917\n",
      "\r\n",
      "[260,] 1.588836e-01  0.532926533 0.251550231  0.056639602\n",
      "\r\n",
      "[261,] 1.514793e-01  0.530092341 0.254623464  0.063804934\n",
      "\r\n",
      "[262,] 1.300540e-01  0.518917796 0.263855512  0.087172722\n",
      "\r\n",
      "[263,] 1.129151e-01  0.506139830 0.271678685  0.109266395\n",
      "\r\n",
      "[264,] 1.118294e-01  0.505193972 0.272189834  0.110786819\n",
      "\r\n",
      "[265,] 1.075561e-01  0.501295529 0.274221708  0.116926651\n",
      "\r\n",
      "[266,] 9.587971e-02  0.489080717 0.279951991  0.135087582\n",
      "\r\n",
      "[267,] 9.250171e-02  0.485072824 0.281663877  0.140761584\n",
      "\r\n",
      "[268,] 9.013807e-02  0.482128717 0.282877657  0.144855552\n",
      "\r\n",
      "[269,] 8.644057e-02  0.477278793 0.284804293  0.151476342\n",
      "\r\n",
      "[270,] 7.892200e-02  0.466413120 0.288836502  0.165828381\n",
      "\r\n",
      "[271,] 7.554010e-02  0.461041646 0.290705453  0.172712806\n",
      "\r\n",
      "[272,] 7.185255e-02  0.454805237 0.292786620  0.180555595\n",
      "\r\n",
      "[273,] 6.906891e-02  0.449815133 0.294389869  0.186726090\n",
      "\r\n",
      "[274,] 6.635811e-02  0.444704658 0.295979804  0.192957430\n",
      "\r\n",
      "[275,] 6.371918e-02  0.439475408 0.297556603  0.199248808\n",
      "\r\n",
      "[276,] 5.588254e-02  0.422285187 0.302428700  0.219403573\n",
      "\r\n",
      "[277,] 5.419606e-02  0.418222028 0.303518709  0.224063204\n",
      "\r\n",
      "[278,] 5.156884e-02  0.411603395 0.305249717  0.231578047\n",
      "\r\n",
      "[279,] 5.124654e-02  0.410765988 0.305464979  0.232522496\n",
      "\r\n",
      "[280,] 4.871631e-02  0.403987066 0.307178259  0.240118363\n",
      "\r\n",
      "[281,] 4.390848e-02  0.390011758 0.310558646  0.255521118\n",
      "\r\n",
      "[282,] 3.653124e-02  0.365212166 0.316128525  0.282128066\n",
      "\r\n",
      "[283,] 3.602032e-02  0.363316423 0.316534612  0.284128641\n",
      "\r\n",
      "[284,] 2.869918e-02  0.332943999 0.322719640  0.315637181\n",
      "\r\n",
      "[285,] 2.869918e-02  0.332943999 0.322719640  0.315637181\n",
      "\r\n",
      "[286,] 2.474427e-02  0.313449080 0.326413180  0.335393471\n",
      "\r\n",
      "[287,] 2.376764e-02  0.308212853 0.327373442  0.340646068\n",
      "\r\n",
      "[288,] 2.099258e-02  0.292248284 0.330225925  0.356533208\n",
      "\r\n",
      "[289,] 1.926807e-02  0.281397812 0.332104638  0.367229485\n",
      "\r\n",
      "[290,] 1.344451e-02  0.237590246 0.339266738  0.409698501\n",
      "\r\n",
      "[291,] 1.305295e-02  0.234127225 0.339807360  0.413012465\n",
      "\r\n",
      "[292,] 1.052272e-02  0.209537858 0.343553196  0.436386223\n",
      "\r\n",
      "[293,] 1.019045e-02  0.205976854 0.344082980  0.439749714\n",
      "\r\n",
      "[294,] 9.758407e-03  0.201210697 0.344787351  0.444243545\n",
      "\r\n",
      "[295,] 9.442512e-03  0.197622629 0.345314142  0.447620717\n",
      "\r\n",
      "[296,] 9.338749e-03  0.196424070 0.345489458  0.448747723\n",
      "\r\n",
      "[297,] 8.342618e-03  0.184369893 0.347235036  0.460052453\n",
      "\r\n",
      "[298,] 7.509006e-03  0.173417177 0.348794558  0.470279258\n",
      "\r\n",
      "[299,] 4.470833e-03  0.123636566 0.355603895  0.516288706\n",
      "\r\n",
      "[300,] 3.479242e-03  0.101984644 0.358443096  0.536093018\n",
      "\r\n",
      "[301,] 2.782381e-03  0.083955767 0.360759375  0.552502478\n",
      "\r\n",
      "[302,] 2.736518e-03  0.082661523 0.360924108  0.553677851\n",
      "\r\n",
      "[303,] 2.558108e-03  0.077476219 0.361582119  0.558383554\n",
      "\r\n",
      "[304,] 2.146372e-03  0.064456292 0.363220881  0.570176455\n",
      "\r\n",
      "[305,] 1.747334e-03  0.050045348 0.365013672  0.583193646\n",
      "\r\n",
      "[306,] 1.401097e-03  0.035547145 0.366796812  0.596254945\n",
      "\r\n",
      "[307,] 5.748204e-04 -0.013778659 0.372732805  0.640471034\n",
      "\r\n",
      "[308,] 3.774241e-04 -0.032632934 0.374957791  0.657297718\n",
      "\r\n",
      "[309,] 3.307888e-04 -0.038036004 0.375591717  0.662113498\n",
      "\r\n",
      "[310,] 9.636889e-05 -0.078749647 0.380325077  0.698328202\n",
      "\r\n",
      "[311,] 6.985676e-05 -0.086926042 0.381268025  0.705588160\n",
      "\r\n",
      "[312,] 3.997043e-05 -0.099206964 0.382680641  0.716486352\n",
      "\r\n",
      "[313,] 2.376764e-05 -0.108770430 0.383778056  0.724968606\n",
      "\r\n",
      "[314,] 0.000000e+00 -0.159422431 0.389567366  0.769855065\n",
      "\r\n",
      "attr(,\"degree\")\n",
      "\r\n",
      "[1] 3\n",
      "\r\n",
      "attr(,\"knots\")\n",
      "\r\n",
      "[1] 0.9625 4.1000 8.2700\n",
      "\r\n",
      "attr(,\"Boundary.knots\")\n",
      "\r\n",
      "[1]  0.00 17.67\n",
      "\r\n",
      "attr(,\"intercept\")\n",
      "\r\n",
      "[1] FALSE\n",
      "\r\n",
      "attr(,\"class\")\n",
      "\r\n",
      "[1] \"ns\"     \"basis\"  \"matrix\"\n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(ns_design)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`ns` and `bs` return design matrices, not model objects! That's because they're meant to work with `lm`'s formula interface. To get a model object we populate a formula including `ns(<var>,<knots>)` and fit to data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "r_lm = robjects.r['lm']\n",
    "r_predict = robjects.r['predict']\n",
    "\n",
    "# populate the formula\n",
    "ns_formula = robjects.Formula(\"Gag ~ ns(Age, knots=r_quarts)\")\n",
    "ns_formula.environment['Gag'] = r_gag\n",
    "ns_formula.environment['Age'] = r_age\n",
    "ns_formula.environment['r_quarts'] = r_quarts\n",
    "         \n",
    "# fit the model\n",
    "ns_model = r_lm(ns_formula)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Predict like usual: build a dataframe to predict on and call `predict()`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "# predict\n",
    "predict_frame = robjects.DataFrame({\"Age\": robjects.FloatVector(np.linspace(0,20,100))})\n",
    "\n",
    "ns_out = r_predict(ns_model, predict_frame)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax32 = GAGurine.plot.scatter(x='Age',y='GAG',c='grey',title=\"GAG in urine of children\")\n",
    "ax32.set_xlabel(\"Age\")\n",
    "ax32.set_ylabel(\"GAG\")\n",
    "ax32.plot(predict_frame.rx2(\"Age\"),ns_out, color='red')\n",
    "ax32.legend([\"Natural spline, knots at quartiles\"]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div class=\"exercise\"><b>Exercise 4</b></div>\n",
    "\n",
    "1. Fit a basis spline model with the same knots, and add it to the plot above\n",
    "2. Fit a basis spline with 8 knots placed at [2,4,6...14,16] and add it to the plot above"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "bs_formula = robjects.Formula(\"Gag ~ bs(Age, knots=r_quarts)\")\n",
    "bs_formula.environment['Gag'] = r_gag\n",
    "bs_formula.environment['Age'] = r_age\n",
    "bs_formula.environment['r_quarts'] = r_quarts\n",
    "\n",
    "bs_model = r_lm(bs_formula)\n",
    "bs_out = r_predict(bs_model, predict_frame)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax32 = GAGurine.plot.scatter(x='Age',y='GAG',c='grey',title=\"GAG in urine of children\")\n",
    "ax32.set_xlabel(\"Age\")\n",
    "ax32.set_ylabel(\"GAG\")\n",
    "ax32.plot(predict_frame.rx2(\"Age\"),ns_out, color='red')\n",
    "ax32.plot(predict_frame.rx2(\"Age\"),bs_out, color='blue')\n",
    "ax32.legend([\"Natural spline, knots at quartiles\",\"B-spline, knots at quartiles\"]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "overfit_formula = robjects.Formula(\"Gag ~ bs(Age, knots=r_quarts)\")\n",
    "overfit_formula.environment['Gag'] = r_gag\n",
    "overfit_formula.environment['Age'] = r_age\n",
    "overfit_formula.environment['r_quarts'] = robjects.FloatVector(np.array([2,4,6,8,10,12,14,16]))\n",
    "\n",
    "overfit_model = r_lm(overfit_formula)\n",
    "overfit_out = r_predict(overfit_model, predict_frame)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax32 = GAGurine.plot.scatter(x='Age',y='GAG',c='grey',title=\"GAG in urine of children\")\n",
    "ax32.set_xlabel(\"Age\")\n",
    "ax32.set_ylabel(\"GAG\")\n",
    "ax32.plot(predict_frame.rx2(\"Age\"),ns_out, color='red')\n",
    "ax32.plot(predict_frame.rx2(\"Age\"),bs_out, color='blue')\n",
    "ax32.plot(predict_frame.rx2(\"Age\"),overfit_out, color='green')\n",
    "ax32.legend([\"Natural spline, knots at quartiles\", \"B-spline, knots at quartiles\", \"B-spline, lots of knots\"]);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## GAMs\n",
    "We come, at last, to our most advanced model. The coding here isn't any more complex than we've done before, though the behind-the-scenes is awesome.\n",
    "\n",
    "First, let's get our (multivariate!) data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "# kyphosis - wherther a particular deformation was present post-operation\n",
      "# age - patient's age in months\n",
      "# number - the number of vertebrae involved in the operation\n",
      "# start - the number of the topmost vertebrae operated on\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Kyphosis</th>\n",
       "      <th>Age</th>\n",
       "      <th>Number</th>\n",
       "      <th>Start</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>absent</td>\n",
       "      <td>71</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>absent</td>\n",
       "      <td>158</td>\n",
       "      <td>3</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>present</td>\n",
       "      <td>128</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>absent</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>absent</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Kyphosis  Age  Number  Start\n",
       "0   absent   71       3      5\n",
       "1   absent  158       3     14\n",
       "2  present  128       4      5\n",
       "3   absent    2       5      1\n",
       "4   absent    1       4     15"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
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       "\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>Kyphosis</th>\n",
       "      <th>Age</th>\n",
       "      <th>Number</th>\n",
       "      <th>Start</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>81</td>\n",
       "      <td>81.000000</td>\n",
       "      <td>81.000000</td>\n",
       "      <td>81.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>unique</th>\n",
       "      <td>2</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>top</th>\n",
       "      <td>absent</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>freq</th>\n",
       "      <td>64</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>NaN</td>\n",
       "      <td>83.654321</td>\n",
       "      <td>4.049383</td>\n",
       "      <td>11.493827</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>NaN</td>\n",
       "      <td>58.104251</td>\n",
       "      <td>1.619423</td>\n",
       "      <td>4.883962</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>NaN</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>NaN</td>\n",
       "      <td>26.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>9.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>NaN</td>\n",
       "      <td>87.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>13.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>NaN</td>\n",
       "      <td>130.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>16.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>NaN</td>\n",
       "      <td>206.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>18.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Kyphosis         Age     Number      Start\n",
       "count        81   81.000000  81.000000  81.000000\n",
       "unique        2         NaN        NaN        NaN\n",
       "top      absent         NaN        NaN        NaN\n",
       "freq         64         NaN        NaN        NaN\n",
       "mean        NaN   83.654321   4.049383  11.493827\n",
       "std         NaN   58.104251   1.619423   4.883962\n",
       "min         NaN    1.000000   2.000000   1.000000\n",
       "25%         NaN   26.000000   3.000000   9.000000\n",
       "50%         NaN   87.000000   4.000000  13.000000\n",
       "75%         NaN  130.000000   5.000000  16.000000\n",
       "max         NaN  206.000000  10.000000  18.000000"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "Kyphosis    object\n",
       "Age          int64\n",
       "Number       int64\n",
       "Start        int64\n",
       "dtype: object"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kyphosis = pd.read_csv(\"data/kyphosis.csv\")\n",
    "\n",
    "print(\"\"\"\n",
    "# kyphosis - wherther a particular deformation was present post-operation\n",
    "# age - patient's age in months\n",
    "# number - the number of vertebrae involved in the operation\n",
    "# start - the number of the topmost vertebrae operated on\n",
    "\n",
    "\"\"\")\n",
    "display(kyphosis.head())\n",
    "display(kyphosis.describe(include='all'))\n",
    "display(kyphosis.dtypes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "#If there are errors about missing R packages, run the code below:\n",
    "\n",
    "#r_utils = importr('utils')\n",
    "#r_utils.install_packages('codetools')\n",
    "#r_utils.install_packages('gam')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To fit a GAM, we\n",
    " - Import the `gam` library\n",
    " - Populate a formula including `s(<var>)` on variables we want to fit smooths for\n",
    " - Call `gam(formula, family=<string>)` where `family` is a string naming a probability distribution, chosen based on how the response variable is thought to occur. \n",
    " - Rough `family` guidelines:\n",
    "     - Response is binary or \"N occurances out of M tries\", e.g. number of lab rats (out of 10) developing disease: chooose `\"binomial\"`\n",
    "     - Response is a count with no logical upper bound, e.g. number of ice creams sold: choose `\"poisson\"`\n",
    "     - Response is real, with normally-distributed noise, e.g. person's height: choose `\"gaussian\"` (the default)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "#There is a Python library in development for using GAMs (https://github.com/dswah/pyGAM)\n",
    "# but it is not yet as comprehensive as the R GAM library, which we will use here instead.\n",
    "\n",
    "# R also has the mgcv library, which implements some more advanced/flexible fitting methods\n",
    "\n",
    "r_gam_lib = importr('gam')\n",
    "r_gam = r_gam_lib.gam\n",
    "\n",
    "r_kyph = robjects.FactorVector(kyphosis[[\"Kyphosis\"]].values)\n",
    "r_Age = robjects.FloatVector(kyphosis[[\"Age\"]].values)\n",
    "r_Number = robjects.FloatVector(kyphosis[[\"Number\"]].values)\n",
    "r_Start = robjects.FloatVector(kyphosis[[\"Start\"]].values)\n",
    "\n",
    "kyph1_fmla = robjects.Formula(\"Kyphosis ~ s(Age) + s(Number) + s(Start)\")\n",
    "kyph1_fmla.environment['Kyphosis']=r_kyph\n",
    "kyph1_fmla.environment['Age']=r_Age\n",
    "kyph1_fmla.environment['Number']=r_Number\n",
    "kyph1_fmla.environment['Start']=r_Start\n",
    "\n",
    "\n",
    "kyph1_gam = r_gam(kyph1_fmla, family=\"binomial\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The fitted gam model has a lot of interesting data within it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [1] \"smooth.frame\"        \"coefficients\"        \"residuals\"          \n",
      "\r\n",
      " [4] \"fitted.values\"       \"effects\"             \"weights\"            \n",
      "\r\n",
      " [7] \"rank\"                \"assign\"              \"qr\"                 \n",
      "\r\n",
      "[10] \"smooth\"              \"nl.df\"               \"df.residual\"        \n",
      "\r\n",
      "[13] \"iter\"                \"var\"                 \"additive.predictors\"\n",
      "\r\n",
      "[16] \"R\"                   \"rank\"                \"family\"             \n",
      "\r\n",
      "[19] \"deviance\"            \"aic\"                 \"null.deviance\"      \n",
      "\r\n",
      "[22] \"iter\"                \"bf.iter\"             \"prior.weights\"      \n",
      "\r\n",
      "[25] \"y\"                   \"df.null\"             \"nl.chisq\"           \n",
      "\r\n",
      "[28] \"model\"               \"call\"                \"formula\"            \n",
      "\r\n",
      "[31] \"terms\"               \"data\"                \"offset\"             \n",
      "\r\n",
      "[34] \"control\"             \"method\"              \"contrasts\"          \n",
      "\r\n",
      "[37] \"xlevels\"            \n",
      "\n"
     ]
    }
   ],
   "source": [
    "print(kyph1_gam.names)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remember plotting? Calling R's `plot()` on a gam model is the easiest way to view the fitted splines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n"
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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crE/w/uFt8fNBdPegyuHP9ts9NViJTb/s/F3p7u65fzAJwVJs/3jslT51TTOCpdj0jx893XdN9G3fNiNYin4Ufeh9P8y+1WUE69DNgw998P7h8vmlaf7x1/3bo4WMoqFGECwOgsVBsDgIFgfB4iBYHASLg2BxECwOgsVBsDgIFgfB4iBYHASLg2BxECzO/wEyuHbsgrT8KQAAAABJRU5ErkJggg==\n"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%R -i kyph1_gam plot(kyph1_gam, residuals=TRUE,se=TRUE, scale=20);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Prediction works like normal (build a data frame to predict on, if you don't already have one, and call `predict()`). However, predict always reports the sum of the individual variable effects. If `family` is non-default this can be different from the actual prediction for that point.\n",
    "\n",
    "For instance, we're doing a 'logistic regression' so the raw prediction is log odds, but we can get probability by using in `predict(..., type=\"response\")`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raw response (so, Log odds):\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <span>FloatVector with 3 elements.</span>\n",
       "    <table>\n",
       "      <tbody>\n",
       "      <tr>\n",
       "      \n",
       "      <td>\n",
       "        -2.369793\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        2.726143\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        0.363981\n",
       "      </td>\n",
       "      \n",
       "      </tr>\n",
       "      </tbody>\n",
       "    </table>\n",
       "    "
      ],
      "text/plain": [
       "R object with classes: ('numeric',) mapped to:\n",
       "<FloatVector - Python:0x0000023129BD6208 / R:0x000002312534DEC8>\n",
       "[-2.369793, 2.726143, 0.363981]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Scaled response (so, probabilty of kyphosis):\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "\n",
       "    <span>FloatVector with 3 elements.</span>\n",
       "    <table>\n",
       "      <tbody>\n",
       "      <tr>\n",
       "      \n",
       "      <td>\n",
       "        0.085505\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        0.938552\n",
       "      </td>\n",
       "      \n",
       "      <td>\n",
       "        0.590004\n",
       "      </td>\n",
       "      \n",
       "      </tr>\n",
       "      </tbody>\n",
       "    </table>\n",
       "    "
      ],
      "text/plain": [
       "R object with classes: ('numeric',) mapped to:\n",
       "<FloatVector - Python:0x0000023129BD6088 / R:0x0000023129B19398>\n",
       "[0.085505, 0.938552, 0.590004]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "kyph_new = robjects.DataFrame({'Age': robjects.IntVector((84,85,86)), \n",
    "                               'Start': robjects.IntVector((5,3,1)), \n",
    "                               'Number': robjects.IntVector((1,6,10))})\n",
    "\n",
    "print(\"Raw response (so, Log odds):\")\n",
    "display(r_predict(kyph1_gam, kyph_new))\n",
    "print(\"Scaled response (so, probabilty of kyphosis):\")\n",
    "display(r_predict(kyph1_gam, kyph_new, type=\"response\"))"
   ]
  }
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