leastsq, statsmodels

gk_analysis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ratio lsq with$0.773 x^{0.543}, R^2=0.880192$ and $3.26 x^{0.55}, R^2=0.964504$\n",
      "4.21348056996\n",
      "Ratio forcing sqrt: $0.852 x^{1/2}, R^2=0.883103$ and $3.65 x^{1/2}, R^2=0.968925$\n",
      "4.28509061504\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd131ba8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmEAAAFiCAYAAAC+iQ94AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nfCwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xcafb278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import xlwings as xw\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy.optimize import leastsq\n",
    "from scipy.stats import pearsonr\n",
    "from scipy.stats import t, norm, linregress\n",
    "from scipy.stats.mstats import theilslopes\n",
    "%matplotlib inline\n",
    "plt.set_cmap('viridis')\n",
    "plt.style.use('seaborn-deep')\n",
    "plt.rcParams['axes.grid']=True\n",
    "plt.rcParams['figure.figsize']=[10., 9/16.*10.]\n",
    "wb = xw.Book('Grease rem kinetics analysis.xlsx')\n",
    "sht = wb.sheets['ANALYSIS']\n",
    "column_names = sht.range('A18:D18').value\n",
    "column_names = [x.replace('Average of % ', '') for x in column_names]\n",
    "df = pd.DataFrame(\n",
    "    sht.range('A19:D38').value,\n",
    "    columns=column_names)\n",
    "grouped_df = df.groupby(u'Product')\n",
    "\n",
    "# Do pandas later...\n",
    "xrd = np.array(sht.range('B29:B38').value)\n",
    "yrd = np.array(sht.range('D29:D38').value)\n",
    "xup = np.array(sht.range('B19:B28').value)\n",
    "yup = np.array(sht.range('D19:D28').value)\n",
    "\n",
    "extendedx = np.arange(0,max(xrd)+1*200,(max(xrd)-0)/50.0) #for plots\n",
    "\n",
    "def residuals(p, y, x):\n",
    "    a, b = p\n",
    "    err = y - a*x**(b)\n",
    "    return err\n",
    "\n",
    "def residuals_sqrt(p, y, x):\n",
    "    a = p\n",
    "    err = y - a*x**(0.5)\n",
    "    return err\n",
    "\n",
    "p0 = [1.0, 1.0]\n",
    "plsq1 = leastsq(residuals, p0, args=(yrd, xrd))\n",
    "rsq1 = pearsonr(yrd, plsq1[0][0]*xrd**plsq1[0][1])[0]**2\n",
    "plsq2 = leastsq(residuals, p0, args=(yup, xup))\n",
    "rsq2 = pearsonr(yup, plsq1[0][0]*xup**plsq1[0][1])[0]**2\n",
    "\n",
    "# Force b=0.5 (sqrt)\n",
    "p0 = 1.0\n",
    "plsq3 = leastsq(residuals_sqrt, p0, args=(yrd, xrd))\n",
    "rsq3 = pearsonr(yrd, plsq3[0][0]*xrd**0.5)[0]**2\n",
    "plsq4 = leastsq(residuals_sqrt, p0, args=(yup, xup))\n",
    "rsq4 = pearsonr(yup, plsq4[0][0]*xup**0.5)[0]**2\n",
    "\n",
    "leg_str_1 = '$a x^{b}, R^2='.replace(\n",
    "    'a', '{0:1.3g}'.format(plsq1[0][0])\n",
    ").replace(\n",
    "    'b', '{0:1.3g}'.format(plsq1[0][1])\n",
    ") + '{0:g}'.format(rsq1) + '$'\n",
    "\n",
    "leg_str_2 = '$a x^{b}, R^2='.replace(\n",
    "    'a', '{0:1.3g}'.format(plsq2[0][0])\n",
    ").replace(\n",
    "    'b', '{0:1.3g}'.format(plsq2[0][1])\n",
    ") + '{0:g}'.format(rsq2) + '$'\n",
    "\n",
    "leg_str_3 = '$a x^{b}, R^2='.replace(\n",
    "    'a', '{0:1.3g}'.format(plsq3[0][0])\n",
    ").replace(\n",
    "    'b', '1/2'\n",
    ") + '{0:g}'.format(rsq3) + '$'\n",
    "\n",
    "leg_str_4 = '$a x^{b}, R^2='.replace(\n",
    "    'a', '{0:1.3g}'.format(plsq4[0][0])\n",
    ").replace(\n",
    "    'b', '1/2'\n",
    ") + '{0:g}'.format(rsq4) + '$'\n",
    "\n",
    "plt.subplots(1,2, figsize=plt.rcParams['figure.figsize'])\n",
    "plt.subplot(1,2,1)\n",
    "plt.plot(xrd, yrd, 'o', xup, yup, 's',\n",
    "        extendedx, plsq1[0][0]*extendedx**plsq1[0][1],\n",
    "        extendedx, plsq2[0][0]*extendedx**plsq2[0][1],\n",
    "        markeredgecolor='black')\n",
    "plt.legend(['rd','ud',\n",
    "            leg_str_1,\n",
    "            leg_str_2\n",
    "           ])\n",
    "plt.xlabel('soaking time, h')\n",
    "plt.ylabel('% Grease Rem')\n",
    "\n",
    "plt.subplot(1,2,2)\n",
    "plt.plot(xrd, yrd, 'o', xup, yup, 's',\n",
    "        extendedx, plsq3[0][0]*extendedx**0.5,\n",
    "        extendedx, plsq4[0][0]*extendedx**0.5,\n",
    "        markeredgecolor='black')\n",
    "plt.legend(['rd','ud',\n",
    "            leg_str_3,\n",
    "            leg_str_4\n",
    "           ])\n",
    "plt.xlabel('soaking time, h')\n",
    "plt.ylabel('% Grease Rem')\n",
    "\n",
    "print 'Ratio lsq with' + leg_str_1 + ' and ' + leg_str_2\n",
    "print plsq2[0][0]/plsq1[0][0]\n",
    "print 'Ratio forcing sqrt: ' + leg_str_3 + ' and ' + leg_str_4\n",
    "print plsq4[0][0]/plsq3[0][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ratio slopes direct linear lsq:\n",
      "4.44898\n",
      "Ratio slopes Theil-Sen median slope est.:\n",
      "4.60714\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmEAAAFiCAYAAAC+iQ94AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEdIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xdccbcf8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xrd_linear = np.array(sht.range('B29:B37').value)\n",
    "yrd_linear = np.array(sht.range('D29:D37').value)\n",
    "xup_linear = np.array(sht.range('B19:B27').value)\n",
    "yup_linear = np.array(sht.range('D19:D27').value)\n",
    "\n",
    "def line_residuals(p, y, x):\n",
    "    a, b = p\n",
    "    err = -y + a*x + b\n",
    "    return err\n",
    "\n",
    "p0 = [1.0, 1.0]\n",
    "linelsq1 = leastsq(line_residuals, p0, \n",
    "                   args=(yrd_linear, xrd_linear))[0]\n",
    "ycalc_rd = linelsq1[0] * xrd_linear + linelsq1[1]\n",
    "rsq5 = pearsonr(yrd_linear, ycalc_rd)[0]**2\n",
    "linelsq2 = leastsq(line_residuals, p0, \n",
    "                   args=(yup_linear, xup_linear))[0]\n",
    "ycalc_up = linelsq2[0] * xup_linear + linelsq2[1]\n",
    "rsq6 = pearsonr(yup_linear, ycalc_up)[0]**2\n",
    "\n",
    "# median slopes\n",
    "medslopesrd = theilslopes(yrd_linear, xrd_linear)\n",
    "medslopesup = theilslopes(yup_linear, xup_linear)\n",
    "\n",
    "ycalcmedsloperd = medslopesrd[0] * xrd_linear + medslopesrd[1]\n",
    "ycalcmedslopeup = medslopesup[0] * xup_linear + medslopesup[1]\n",
    "\n",
    "rsq7 = pearsonr(yrd_linear, ycalcmedsloperd)[0]**2\n",
    "rsq8 = pearsonr(yup_linear, ycalcmedslopeup)[0]**2\n",
    "\n",
    "leg_str_5 = '$a x+b, R^2='.replace(\n",
    "    'a', '{0:1.5g}'.format(linelsq1[0])\n",
    ").replace(\n",
    "    'b', '{0:1.5g}'.format(linelsq1[1])\n",
    ") + '{0:g}'.format(rsq5) + '$'\n",
    "leg_str_6 = '$a x+b, R^2='.replace(\n",
    "    'a', '{0:1.5g}'.format(linelsq2[0])\n",
    ").replace(\n",
    "    'b', '{0:1.5g}'.format(linelsq2[1])\n",
    ") + '{0:g}'.format(rsq6) + '$'\n",
    "leg_str_7 = '$a x+b, R^2='.replace(\n",
    "    'a', '{0:1.5g}'.format(medslopesrd[0])\n",
    ").replace(\n",
    "    'b', '{0:1.5g}'.format(medslopesrd[1])\n",
    ") + '{0:g}'.format(rsq7) + '$'\n",
    "leg_str_8 = '$a x+b, R^2='.replace(\n",
    "    'a', '{0:1.5g}'.format(medslopesup[0])\n",
    ").replace(\n",
    "    'b', '{0:1.5g}'.format(medslopesup[1])\n",
    ") + '{0:g}'.format(rsq8) + '$'\n",
    "\n",
    "unique_times = xrd_linear.reshape([3,3])[:,0]\n",
    "means_rd = np.array([np.mean(x) for x in yrd_linear.reshape([3,3])])\n",
    "means_up = np.array([np.mean(x) for x in yup_linear.reshape([3,3])])\n",
    "stdev_rd = np.array([np.std(x, ddof=1) for x in yrd_linear.reshape([3,3])])\n",
    "stdev_up = np.array([np.std(x, ddof=1) for x in yup_linear.reshape([3,3])])\n",
    "\n",
    "ci95rd = t.ppf((1-0.05/2), 3-1)/np.sqrt(3)*stdev_rd\n",
    "ci95up = t.ppf((1-0.05/2), 3-1)/np.sqrt(3)*stdev_up\n",
    "\n",
    "plt.plot(\n",
    "    xrd_linear, yrd_linear, 'o',\n",
    "    xrd_linear, ycalc_rd, '-',\n",
    "    xrd_linear, ycalcmedsloperd, '-.',\n",
    "    xup_linear, yup_linear, 'D',\n",
    "    xup_linear, ycalc_up, '-',\n",
    "    xup_linear, ycalcmedslopeup, '-.',\n",
    "    markeredgecolor='black'\n",
    ")\n",
    "plt.errorbar(unique_times, means_rd, yerr=ci95rd, capsize=5, elinewidth=None, fmt='none')\n",
    "plt.errorbar(unique_times, means_up, yerr=ci95up, capsize=5, elinewidth=None, fmt='none')\n",
    "plt.legend(['rd', leg_str_5, leg_str_7, 'ud', leg_str_6, leg_str_8])\n",
    "plt.xlabel('soaking time, h')\n",
    "plt.ylabel('% Grease Rem')\n",
    "print 'Ratio slopes direct linear lsq:'\n",
    "print '{0:g}'.format(linelsq2[0]/linelsq1[0])\n",
    "print 'Ratio slopes Theil-Sen median slope est.:'\n",
    "print '{0:g}'.format(medslopesup[0]/medslopesrd[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "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>   0.782</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.751</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   25.09</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 31 Jul 2017</td> <th>  Prob (F-statistic):</th>  <td>0.00155</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>20:44:18</td>     <th>  Log-Likelihood:    </th> <td> -4.5508</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>     9</td>      <th>  AIC:               </th> <td>   13.10</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>     7</td>      <th>  BIC:               </th> <td>   13.50</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>[95.0% Conf. Int.]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    0.2649</td> <td>    0.053</td> <td>    5.009</td> <td> 0.002</td> <td>    0.140     0.390</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    0.4523</td> <td>    0.275</td> <td>    1.646</td> <td> 0.144</td> <td>   -0.198     1.102</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 2.356</td> <th>  Durbin-Watson:     </th> <td>   2.849</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.308</td> <th>  Jarque-Bera (JB):  </th> <td>   0.196</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.217</td> <th>  Prob(JB):          </th> <td>   0.907</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 3.577</td> <th>  Cond. No.          </th> <td>    9.66</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.782\n",
       "Model:                            OLS   Adj. R-squared:                  0.751\n",
       "Method:                 Least Squares   F-statistic:                     25.09\n",
       "Date:                Mon, 31 Jul 2017   Prob (F-statistic):            0.00155\n",
       "Time:                        20:44:18   Log-Likelihood:                -4.5508\n",
       "No. Observations:                   9   AIC:                             13.10\n",
       "Df Residuals:                       7   BIC:                             13.50\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
       "------------------------------------------------------------------------------\n",
       "x1             0.2649      0.053      5.009      0.002         0.140     0.390\n",
       "const          0.4523      0.275      1.646      0.144        -0.198     1.102\n",
       "==============================================================================\n",
       "Omnibus:                        2.356   Durbin-Watson:                   2.849\n",
       "Prob(Omnibus):                  0.308   Jarque-Bera (JB):                0.196\n",
       "Skew:                           0.217   Prob(JB):                        0.907\n",
       "Kurtosis:                       3.577   Cond. No.                         9.66\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Confidence intervals for linear regressions\n",
    "import statsmodels.api as sm\n",
    "modrd = sm.OLS(\n",
    "    yrd_linear, \n",
    "    sm.add_constant(xrd_linear, prepend=False)\n",
    ")\n",
    "resrd = modrd.fit()\n",
    "resrd.conf_int(0.05)\n",
    "\n",
    "modup = sm.OLS(\n",
    "    yup_linear, \n",
    "    sm.add_constant(xup_linear, prepend=False)\n",
    ")\n",
    "resup = modup.fit()\n",
    "resup.conf_int(0.05)\n",
    "\n",
    "ci95_sloperd, ci95_interceptrd = resrd.conf_int(0.05)\n",
    "ci95_slopeup, ci95_interceptup = resup.conf_int(0.05)\n",
    "\n",
    "resrd.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "metadata": {
    "scrolled": false
   },
   "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>   0.939</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Model:</th>                   <td>OLS</td>       <th>  Adj. R-squared:    </th> <td>   0.930</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Method:</th>             <td>Least Squares</td>  <th>  F-statistic:       </th> <td>   107.6</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Date:</th>             <td>Mon, 31 Jul 2017</td> <th>  Prob (F-statistic):</th> <td>1.68e-05</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Time:</th>                 <td>20:43:35</td>     <th>  Log-Likelihood:    </th> <td> -11.433</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>No. Observations:</th>      <td>     9</td>      <th>  AIC:               </th> <td>   26.87</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Df Residuals:</th>          <td>     7</td>      <th>  BIC:               </th> <td>   27.26</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>[95.0% Conf. Int.]</th> \n",
       "</tr>\n",
       "<tr>\n",
       "  <th>x1</th>    <td>    1.1784</td> <td>    0.114</td> <td>   10.373</td> <td> 0.000</td> <td>    0.910     1.447</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>const</th> <td>    1.6937</td> <td>    0.590</td> <td>    2.869</td> <td> 0.024</td> <td>    0.298     3.090</td>\n",
       "</tr>\n",
       "</table>\n",
       "<table class=\"simpletable\">\n",
       "<tr>\n",
       "  <th>Omnibus:</th>       <td> 2.034</td> <th>  Durbin-Watson:     </th> <td>   1.861</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Prob(Omnibus):</th> <td> 0.362</td> <th>  Jarque-Bera (JB):  </th> <td>   0.958</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Skew:</th>          <td> 0.778</td> <th>  Prob(JB):          </th> <td>   0.619</td>\n",
       "</tr>\n",
       "<tr>\n",
       "  <th>Kurtosis:</th>      <td> 2.639</td> <th>  Cond. No.          </th> <td>    9.66</td>\n",
       "</tr>\n",
       "</table>"
      ],
      "text/plain": [
       "<class 'statsmodels.iolib.summary.Summary'>\n",
       "\"\"\"\n",
       "                            OLS Regression Results                            \n",
       "==============================================================================\n",
       "Dep. Variable:                      y   R-squared:                       0.939\n",
       "Model:                            OLS   Adj. R-squared:                  0.930\n",
       "Method:                 Least Squares   F-statistic:                     107.6\n",
       "Date:                Mon, 31 Jul 2017   Prob (F-statistic):           1.68e-05\n",
       "Time:                        20:43:35   Log-Likelihood:                -11.433\n",
       "No. Observations:                   9   AIC:                             26.87\n",
       "Df Residuals:                       7   BIC:                             27.26\n",
       "Df Model:                           1                                         \n",
       "Covariance Type:            nonrobust                                         \n",
       "==============================================================================\n",
       "                 coef    std err          t      P>|t|      [95.0% Conf. Int.]\n",
       "------------------------------------------------------------------------------\n",
       "x1             1.1784      0.114     10.373      0.000         0.910     1.447\n",
       "const          1.6937      0.590      2.869      0.024         0.298     3.090\n",
       "==============================================================================\n",
       "Omnibus:                        2.034   Durbin-Watson:                   1.861\n",
       "Prob(Omnibus):                  0.362   Jarque-Bera (JB):                0.958\n",
       "Skew:                           0.778   Prob(JB):                        0.619\n",
       "Kurtosis:                       2.639   Cond. No.                         9.66\n",
       "==============================================================================\n",
       "\n",
       "Warnings:\n",
       "[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
       "\"\"\""
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "resup.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 151,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rd params, stdev, se\n",
      "[ 0.26486486  0.45225225]\n",
      "[[ 0.15864921         nan]\n",
      " [        nan  0.82436547]]\n",
      "[[ 0.05288307         nan]\n",
      " [        nan  0.27478849]]\n",
      "up params, stdev, se\n",
      "[ 1.17837838  1.69369369]\n",
      "[[ 0.34081621         nan]\n",
      " [        nan  1.770933  ]]\n",
      "[[ 0.1136054        nan]\n",
      " [       nan  0.590311 ]]\n"
     ]
    }
   ],
   "source": [
    "print 'rd params, stdev, se'\n",
    "print resrd.params\n",
    "print np.sqrt(resrd.cov_params())*np.sqrt(9)\n",
    "print np.sqrt(resrd.cov_params())\n",
    "print 'up params, stdev, se'\n",
    "print resup.params\n",
    "print np.sqrt(resup.cov_params())*np.sqrt(9)\n",
    "print np.sqrt(resup.cov_params())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.48413771184\n",
      "0.368513775978\n",
      "0.396233691496\n"
     ]
    }
   ],
   "source": [
    "print t.ppf((1-0.05/2), 3-1)/np.sqrt(3)\n",
    "\n",
    "lreg1 = linregress(xrd_linear, yrd_linear)\n",
    "\n",
    "print lreg1.slope+lreg1.stderr*norm.ppf(1-0.05/2)\n",
    "print lreg1.slope+lreg1.stderr*t.ppf((1-0.05/2), 3-1)/np.sqrt(3)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}