04_curve_fitting.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Acknowledgements\n",
    "\n",
    "## Polynomial fitting\n",
    "Amazing **notebooks** about curve fitting and confidence intervals\n",
    "\n",
    "https://nbviewer.ipython.org/github/demotu/BMC/blob/master/notebooks/CurveFitting.ipynb\n",
    "https://nbviewer.jupyter.org/github/demotu/BMC/blob/master/notebooks/ConfidencePredictionIntervals.ipynb\n",
    "\n",
    "Basic reminder about confidence intervals, prediction intervals and a common misconception:\n",
    "\n",
    "> The 95% CI means that if we randomly obtain 100 samples of a population and calculate the CI of each sample (i.e., we replicate the experiment 99 times in a independent way), 95% of these CIs should contain the population mean (the true mean). This is **different from the prediction interval**, which is larger, and gives the **probability that a new observation is inside this interval**. Note that the confidence interval **DOES NOT give the probability that the true mean (the mean of the population) is inside this interval**. The true mean is a parameter (fixed) and it is either inside the calculated interval or not; it is not a matter of chance (probability). >\n",
    "\n",
    "Code: Thank you Stackoverflow!!\n",
    "\n",
    "https://stackoverflow.com/questions/27164114/show-confidence-limits-and-prediction-limits-in-scatter-plot\n",
    "\n",
    "## Locally weighted running line smoother\n",
    "\n",
    "Code from João Paulo Figueira's github repo\n",
    "\n",
    "https://towardsdatascience.com/loess-373d43b03564\n",
    "https://github.com/joaofig/pyloess"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import scipy.stats as stats\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>ID</th>\n",
       "      <th>number_cells</th>\n",
       "      <th>somite_stage</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>18ss_1</td>\n",
       "      <td>80</td>\n",
       "      <td>18ss</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>18ss_10</td>\n",
       "      <td>40</td>\n",
       "      <td>18ss</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>18ss_11</td>\n",
       "      <td>77</td>\n",
       "      <td>18ss</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>18ss_12</td>\n",
       "      <td>63</td>\n",
       "      <td>18ss</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>18ss_13</td>\n",
       "      <td>35</td>\n",
       "      <td>18ss</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0       ID  number_cells somite_stage\n",
       "0           1   18ss_1            80         18ss\n",
       "1           2  18ss_10            40         18ss\n",
       "2           3  18ss_11            77         18ss\n",
       "3           4  18ss_12            63         18ss\n",
       "4           5  18ss_13            35         18ss"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv(\"files/csv/exported_counts_050421.csv\")\n",
    "data.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f5c82d9cf10>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "x = data.somite_stage.str.split(\"ss\").str[0].values\n",
    "x = [int(i) for i in x]\n",
    "y = data.number_cells.values\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "ax.plot(x,y,'ro')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fitting with second-order polynomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Code adapted from https://stackoverflow.com/questions/27164114/show-confidence-limits-and-prediction-limits-in-scatter-plot\n",
    "\n",
    "def plot_ci_manual(t, s_err, n, x, x2, y2, ax=None):\n",
    "    \"\"\"Return an axes of confidence bands using a simple approach.\n",
    "\n",
    "    Notes\n",
    "    -----\n",
    "    .. math:: \\left| \\: \\hat{\\mu}_{y|x0} - \\mu_{y|x0} \\: \\right| \\; \\leq \\; T_{n-2}^{.975} \\; \\hat{\\sigma} \\; \\sqrt{\\frac{1}{n}+\\frac{(x_0-\\bar{x})^2}{\\sum_{i=1}^n{(x_i-\\bar{x})^2}}}\n",
    "    .. math:: \\hat{\\sigma} = \\sqrt{\\sum_{i=1}^n{\\frac{(y_i-\\hat{y})^2}{n-2}}}\n",
    "\n",
    "    References\n",
    "    ----------\n",
    "    .. [1] M. Duarte.  \"Curve fitting,\" Jupyter Notebook.\n",
    "       http://nbviewer.ipython.org/github/demotu/BMC/blob/master/notebooks/CurveFitting.ipynb\n",
    "\n",
    "    \"\"\"\n",
    "    if ax is None:\n",
    "        ax = plt.gca()\n",
    "\n",
    "    ci = t * s_err * np.sqrt(1/n + (x2 - np.mean(x))**2 / np.sum((x - np.mean(x))**2))\n",
    "    #print(\"Confidence interval\", ci)\n",
    "    ax.fill_between(x2, y2 + ci, y2 - ci, color=\"#b9cfe7\", edgecolor=\"\")\n",
    "\n",
    "    return ax\n",
    "\n",
    "def plot_ci_bootstrap(xs, ys, resid, nboot=500, ax=None):\n",
    "    \"\"\"Return an axes of confidence bands using a bootstrap approach.\n",
    "\n",
    "    Notes\n",
    "    -----\n",
    "    The bootstrap approach iteratively resampling residuals.\n",
    "    It plots `nboot` number of straight lines and outlines the shape of a band.\n",
    "    The density of overlapping lines indicates improved confidence.\n",
    "\n",
    "    Returns\n",
    "    -------\n",
    "    ax : axes\n",
    "        - Cluster of lines\n",
    "        - Upper and Lower bounds (high and low) (optional)  Note: sensitive to outliers\n",
    "\n",
    "    References\n",
    "    ----------\n",
    "    .. [1] J. Stults. \"Visualizing Confidence Intervals\", Various Consequences.\n",
    "       http://www.variousconsequences.com/2010/02/visualizing-confidence-intervals.html\n",
    "\n",
    "    \"\"\" \n",
    "    if ax is None:\n",
    "        ax = plt.gca()\n",
    "\n",
    "    bootindex = sp.random.randint\n",
    "\n",
    "    for _ in range(nboot):\n",
    "        resamp_resid = resid[bootindex(0, len(resid) - 1, len(resid))]\n",
    "        # Make coeffs of for polys\n",
    "        pc = np.polyfit(xs, ys + resamp_resid, 1)                   \n",
    "        # Plot bootstrap cluster\n",
    "        ax.plot(xs, np.polyval(pc, xs), \"b-\", linewidth=2, alpha=3.0 / float(nboot))\n",
    "\n",
    "    return ax"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def equation(a, b):\n",
    "    \"\"\"Return a 1D polynomial.\"\"\"\n",
    "    return np.polyval(a, b) \n",
    "\n",
    "p, cov = np.polyfit(x, y, 2, cov=True)  # parameters and covariance from of the fit of 1-D polynom.\n",
    "model = np.poly1d(p)\n",
    "y_model = equation(p, x)                # model using the fit parameters; NOTE: parameters here are coefficients#\n",
    "\n",
    "# Statistics\n",
    "n = y.size                                           # number of observations\n",
    "m = p.size                                                 # number of parameters\n",
    "dof = n - m                                                # degrees of freedom\n",
    "t = stats.t.ppf(0.975, n - m)                              # used for CI and PI bands\n",
    "\n",
    "# Estimates of Error in Data/Model\n",
    "resid = y - y_model                           \n",
    "chi2 = np.sum((resid / y_model)**2)                        # chi-squared; estimates error in data\n",
    "chi2_red = chi2 / dof  # reduced chi-squared; measures goodness of fit\n",
    "#print(chi2_red)\n",
    "s_err = np.sqrt(np.sum(resid**2) / dof)                    # standard deviation of the error\n",
    "\n",
    "# Plotting --------------------------------------------------------------------\n",
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "# Data\n",
    "ax.plot(x, y, \"o\", color=\"#b9cfe7\", markersize=8, markeredgewidth=1, markeredgecolor=\"b\", markerfacecolor=\"None\")\n",
    "#ax.plot(x, y, \"o\", color=\"#b9cfe7\", markersize=8)\n",
    "# Fit\n",
    "ax.plot(x, y_model, \"-\", color=\"0.1\", linewidth=1.5, alpha=0.5, label=\"Fit\")  \n",
    "\n",
    "x2 = np.linspace(np.min(x), np.max(x), 100)\n",
    "y2 = equation(p, x2)\n",
    "\n",
    "# Confidence Interval (select one)\n",
    "plot_ci_manual(t, s_err, n, x, x2, y2, ax=ax)\n",
    "#plot_ci_bootstrap(x, y, resid, ax=ax)\n",
    "\n",
    "# Prediction Interval\n",
    "pi = t * s_err * np.sqrt(1 + 1/n + (x2 - np.mean(x))**2 / np.sum((x - np.mean(x))**2))   \n",
    "ax.fill_between(x2, y2 + pi, y2 - pi, color=\"None\", linestyle=\"--\")\n",
    "ax.plot(x2, y2 - pi, \"--\", color=\"0.5\", label=\"95% Prediction Limits\")\n",
    "ax.plot(x2, y2 + pi, \"--\", color=\"0.5\")\n",
    "\n",
    "\n",
    "# Figure Modifications --------------------------------------------------------\n",
    "# Borders\n",
    "ax.spines[\"top\"].set_color(\"0.5\")\n",
    "ax.spines[\"bottom\"].set_color(\"0.5\")\n",
    "ax.spines[\"left\"].set_color(\"0.5\")\n",
    "ax.spines[\"right\"].set_color(\"0.5\")\n",
    "ax.get_xaxis().set_tick_params(direction=\"out\")\n",
    "ax.get_yaxis().set_tick_params(direction=\"out\")\n",
    "ax.xaxis.tick_bottom()\n",
    "ax.yaxis.tick_left() \n",
    "\n",
    "# Labels\n",
    "plt.title(\"Depletion of NMps over somitogenesis\", fontsize=\"14\")\n",
    "plt.xlabel(\"Stage(ss)\")\n",
    "plt.ylabel(\"NMp number\")\n",
    "plt.xlim(np.min(x) - 1, np.max(x) + 1)\n",
    "plt.ylim(np.min(y) - 10, np.max(y) + 10)\n",
    "\n",
    "unique_x_vals = [i for i in set(x)]\n",
    "plt.xticks(unique_x_vals)\n",
    "\n",
    "# Custom legend\n",
    "handles, labels = ax.get_legend_handles_labels()\n",
    "display = (0, 1)\n",
    "anyArtist = plt.Line2D((0, 1), (0, 0), color=\"#b9cfe7\")    # create custom artists\n",
    "legend = plt.legend(\n",
    "    [handle for i, handle in enumerate(handles) if i in display] + [anyArtist],\n",
    "    [label for i, label in enumerate(labels) if i in display] + [\"95% Confidence Limits\"],\n",
    "    loc=9, bbox_to_anchor=(0, -0.21, 1., 0.102), ncol=3, mode=\"expand\"\n",
    ")  \n",
    "frame = legend.get_frame().set_edgecolor(\"0.5\")\n",
    "\n",
    "# Save Figure\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"images/fitted_curve_nmpcounts.png\", bbox_extra_artists=(legend,), bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Statistics"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table class=\"simpletable\">\n",
       "<caption>OLS Regression Results</caption>\n",
       "<tr>\n",
       "  <th>Dep. Variable:</th>            <td>y</td>        <th>  R-squared:         </th> <td>   0.320</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.312</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   41.44</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 05 Apr 2021</td> <th>  Prob (F-statistic):</th> <td>6.19e-09</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>14:26:01</td>     <th>  Log-Likelihood:    </th> <td> -492.31</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>    90</td>      <th>  AIC:               </th> <td>   988.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>    88</td>      <th>  BIC:               </th> <td>   993.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Model:</th>              <td>     1</td>      <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Covariance Type:</th>      <td>nonrobust</td>    <th>                     </th>     <td> </td>   \n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "      <td></td>         <th>coef</th>     <th>std err</th>      <th>t</th>      <th>P>|t|</th>  <th>[0.025</th>    <th>0.975]</th>  \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Intercept</th> <td>-1.134e-12</td> <td>   15.358</td> <td>-7.38e-14</td> <td> 1.000</td> <td>  -30.522</td> <td>   30.522</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>model(x)</th>  <td>    1.0000</td> <td>    0.155</td> <td>    6.438</td> <td> 0.000</td> <td>    0.691</td> <td>    1.309</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td>14.085</td> <th>  Durbin-Watson:     </th> <td>   1.438</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.001</td> <th>  Jarque-Bera (JB):  </th> <td>  15.324</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.934</td> <th>  Prob(JB):          </th> <td>0.000470</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.773</td> <th>  Cond. No.          </th> <td>    248.</td>\n",
       "</tr>\n",
       "</table><br/><br/>Warnings:<br/>[1] Standard Errors assume that the covariance matrix of the errors is correctly specified."
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.320\n",
       "Model:                            OLS   Adj. R-squared:                  0.312\n",
       "Method:                 Least Squares   F-statistic:                     41.44\n",
       "Date:                Mon, 05 Apr 2021   Prob (F-statistic):           6.19e-09\n",
       "Time:                        14:26:01   Log-Likelihood:                -492.31\n",
       "No. Observations:                  90   AIC:                             988.6\n",
       "Df Residuals:                      88   BIC:                             993.6\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [0.025      0.975]\n",
       "------------------------------------------------------------------------------\n",
       "Intercept  -1.134e-12     15.358  -7.38e-14      1.000     -30.522      30.522\n",
       "model(x)       1.0000      0.155      6.438      0.000       0.691       1.309\n",
       "==============================================================================\n",
       "Omnibus:                       14.085   Durbin-Watson:                   1.438\n",
       "Prob(Omnibus):                  0.001   Jarque-Bera (JB):               15.324\n",
       "Skew:                           0.934   Prob(JB):                     0.000470\n",
       "Kurtosis:                       3.773   Cond. No.                         248.\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import statsmodels.formula.api as smf\n",
    "results = smf.ols(formula='y ~ model(x)', data=data).fit()\n",
    "results.summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Checking normality of residuals"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Checking assumption that residuals are normally distributed. This is important as we are fitting the parameters by minimizing the chi-squared statistic, which assumes normality.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 936x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(13, 5))\n",
    "ax[0].plot(x, resid, 'ro')\n",
    "ax[0].plot([x[0], x[-1]], [0, 0], 'k')\n",
    "ax[0].set_xlabel('x', fontsize=12)\n",
    "ax[0].set_ylabel('Residuals', fontsize=12)\n",
    "stats.probplot(resid, dist=\"norm\", plot=plt)\n",
    "ax[1].set_xlabel('Quantiles', fontsize=12)\n",
    "ax[1].set_ylabel('Ordered values', fontsize=12)\n",
    "ax[1].set_title('Probability Plot of the residuals')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.savefig(\"images/residuals.png\",bbox_inches=\"tight\")\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fitting with LOESS"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/porcupine/miniconda3/envs/toggleSwitch/lib/python3.8/site-packages/sklearn/utils/deprecation.py:143: FutureWarning: The sklearn.neighbors.kde module is  deprecated in version 0.22 and will be removed in version 0.24. The corresponding classes / functions should instead be imported from sklearn.neighbors. Anything that cannot be imported from sklearn.neighbors is now part of the private API.\n",
      "  warnings.warn(message, FutureWarning)\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "from pyloess.pyloess.Loess import Loess\n",
    "from sklearn.neighbors.kde import KernelDensity\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "xx = np.linspace(np.min(x), np.max(x), 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "yy = np.zeros_like(xx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "loess = Loess(x, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 60"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(len(xx)):\n",
    "    yy[i] = loess.estimate(xx[i], window=k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "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": [
    "unique_x_vals = [i for i in set(x)]\n",
    "plt.xticks(unique_x_vals)\n",
    "#plt.plot(x_noise, y_signal, \"r\")\n",
    "plt.plot(x, y, \"o\", color=\"#b9cfe7\", markersize=8, markeredgewidth=1, markeredgecolor=\"b\", markerfacecolor=\"None\", label = \"embryo\")\n",
    "plt.plot(xx, yy, \"r\", label = \"loess fit\")\n",
    "plt.title(\"Depletion of NMps over somitogenesis\", fontsize=\"14\")\n",
    "plt.xlabel(\"Stage(ss)\")\n",
    "plt.ylabel(\"NMp number\")\n",
    "plt.legend(loc=\"upper right\")\n",
    "plt.savefig(\"images/loess_fit.png\",bbox_inches=\"tight\")\n",
    "#plt.plot(x2, y2, \"r\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.save('loess_fit_vals_050421', yy)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}