{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "90d173f1",
   "metadata": {},
   "source": [
    "# Time Series Statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "93515dae",
   "metadata": {},
   "source": [
    ":::{admonition} Content\n",
    ":class: note, dropdown\n",
    "\n",
    "1. Load in your data\n",
    "2. Plotting a time series\n",
    "3. Cumulative Sum\n",
    "4. Kendall's Tau\n",
    "5. Theil Sen Estimator\n",
    "\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e959c42",
   "metadata": {},
   "source": [
    "## 1) Load in your data with `pandas`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2ac4b430",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b2d5df79",
   "metadata": {},
   "outputs": [],
   "source": [
    "gauge_data = pd.read_csv('englewood_3_21_21_usgs_modified.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "62788a44",
   "metadata": {},
   "outputs": [],
   "source": [
    "# If your file doesn't read in that easily you might also try using additional flags such as\n",
    "pd.read_csv('englewood_3_21_21_usgs_modified.csv', header=1) # specify header row\n",
    "pd.read_csv('englewood_3_21_21_usgs_modified.csv', skiprows=10) # ignore some rows at the top of the file\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d698e1d6",
   "metadata": {},
   "source": [
    "We see we have a pandas DataFrame with rows corresponding to 146 times and several data columns, the interesting ones being Discharge, Temperature, Dissolved oxygen and pH."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "68c859a1",
   "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>agency_cd</th>\n",
       "      <th>site_no</th>\n",
       "      <th>datetime</th>\n",
       "      <th>tz_cd</th>\n",
       "      <th>Discharge</th>\n",
       "      <th>Temperature</th>\n",
       "      <th>Dissolved oxygen</th>\n",
       "      <th>pH</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>USGS</td>\n",
       "      <td>6711565</td>\n",
       "      <td>2021-03-12 00:00</td>\n",
       "      <td>MST</td>\n",
       "      <td>44.5</td>\n",
       "      <td>8.1</td>\n",
       "      <td>8.3</td>\n",
       "      <td>8.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>USGS</td>\n",
       "      <td>6711565</td>\n",
       "      <td>2021-03-12 00:15</td>\n",
       "      <td>MST</td>\n",
       "      <td>44.5</td>\n",
       "      <td>8.1</td>\n",
       "      <td>8.2</td>\n",
       "      <td>8.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>USGS</td>\n",
       "      <td>6711565</td>\n",
       "      <td>2021-03-12 00:30</td>\n",
       "      <td>MST</td>\n",
       "      <td>44.5</td>\n",
       "      <td>8.1</td>\n",
       "      <td>8.2</td>\n",
       "      <td>8.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>USGS</td>\n",
       "      <td>6711565</td>\n",
       "      <td>2021-03-12 00:45</td>\n",
       "      <td>MST</td>\n",
       "      <td>44.5</td>\n",
       "      <td>8.1</td>\n",
       "      <td>8.1</td>\n",
       "      <td>8.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>USGS</td>\n",
       "      <td>6711565</td>\n",
       "      <td>2021-03-12 01:00</td>\n",
       "      <td>MST</td>\n",
       "      <td>44.5</td>\n",
       "      <td>8.1</td>\n",
       "      <td>8.1</td>\n",
       "      <td>8.1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>141</th>\n",
       "      <td>USGS</td>\n",
       "      <td>6711565</td>\n",
       "      <td>2021-03-13 11:15</td>\n",
       "      <td>MST</td>\n",
       "      <td>42.6</td>\n",
       "      <td>6.7</td>\n",
       "      <td>9.8</td>\n",
       "      <td>7.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>142</th>\n",
       "      <td>USGS</td>\n",
       "      <td>6711565</td>\n",
       "      <td>2021-03-13 11:30</td>\n",
       "      <td>MST</td>\n",
       "      <td>42.6</td>\n",
       "      <td>6.7</td>\n",
       "      <td>9.9</td>\n",
       "      <td>7.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>143</th>\n",
       "      <td>USGS</td>\n",
       "      <td>6711565</td>\n",
       "      <td>2021-03-13 11:45</td>\n",
       "      <td>MST</td>\n",
       "      <td>42.6</td>\n",
       "      <td>6.7</td>\n",
       "      <td>10.2</td>\n",
       "      <td>7.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>144</th>\n",
       "      <td>USGS</td>\n",
       "      <td>6711565</td>\n",
       "      <td>2021-03-13 12:00</td>\n",
       "      <td>MST</td>\n",
       "      <td>46.5</td>\n",
       "      <td>6.7</td>\n",
       "      <td>10.3</td>\n",
       "      <td>7.9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>145</th>\n",
       "      <td>USGS</td>\n",
       "      <td>6711565</td>\n",
       "      <td>2021-03-13 12:15</td>\n",
       "      <td>MST</td>\n",
       "      <td>NaN</td>\n",
       "      <td>6.6</td>\n",
       "      <td>10.3</td>\n",
       "      <td>7.9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>146 rows × 8 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    agency_cd  site_no          datetime tz_cd  Discharge  Temperature  \\\n",
       "0        USGS  6711565  2021-03-12 00:00   MST       44.5          8.1   \n",
       "1        USGS  6711565  2021-03-12 00:15   MST       44.5          8.1   \n",
       "2        USGS  6711565  2021-03-12 00:30   MST       44.5          8.1   \n",
       "3        USGS  6711565  2021-03-12 00:45   MST       44.5          8.1   \n",
       "4        USGS  6711565  2021-03-12 01:00   MST       44.5          8.1   \n",
       "..        ...      ...               ...   ...        ...          ...   \n",
       "141      USGS  6711565  2021-03-13 11:15   MST       42.6          6.7   \n",
       "142      USGS  6711565  2021-03-13 11:30   MST       42.6          6.7   \n",
       "143      USGS  6711565  2021-03-13 11:45   MST       42.6          6.7   \n",
       "144      USGS  6711565  2021-03-13 12:00   MST       46.5          6.7   \n",
       "145      USGS  6711565  2021-03-13 12:15   MST        NaN          6.6   \n",
       "\n",
       "     Dissolved oxygen   pH  \n",
       "0                 8.3  8.1  \n",
       "1                 8.2  8.1  \n",
       "2                 8.2  8.1  \n",
       "3                 8.1  8.1  \n",
       "4                 8.1  8.1  \n",
       "..                ...  ...  \n",
       "141               9.8  7.9  \n",
       "142               9.9  7.9  \n",
       "143              10.2  7.9  \n",
       "144              10.3  7.9  \n",
       "145              10.3  7.9  \n",
       "\n",
       "[146 rows x 8 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gauge_data"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22461798",
   "metadata": {},
   "source": [
    ":::{note} A Note about using `pandas`\n",
    "\n",
    "You get data from a single column using the following notation:\n",
    "\n",
    "`gauge_data['Discharge']`\n",
    "\n",
    "This will be helpful while plotting.\n",
    "\n",
    ":::"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "237bb865",
   "metadata": {},
   "source": [
    "## 2) Plotting a time series"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "18307e34",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6862017c",
   "metadata": {},
   "source": [
    "There are two plots below.  Plot 1 is the simpliest way to make a plot.  Because with my data I have a lot of x axis labels and they are over lapping eachother in plot 2 I add some code to format my x labels to make them nicer.  For your data I would start with the technique in Plot 1 and only use the Plot 2 axis labels code if your x axis labels are hard to read.\n",
    "\n",
    "The plotting methods will work for lots of types of python data (i.e. anything that is an `numpy` array)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "11457c2e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x28397dcb5b0>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot 1\n",
    "# inputs: x values, y values\n",
    "plt.plot(gauge_data['datetime'], gauge_data['Discharge'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "8020082f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot 2\n",
    "# inputs: x values, y values\n",
    "plt.plot(gauge_data['datetime'], gauge_data['Discharge'])\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.xaxis.set_major_locator(plt.MaxNLocator(5))  # Use only 4 labels\n",
    "ax.tick_params(axis='x', labelrotation = 80)  # Rotate the labels so the are more vertical"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd877fd0",
   "metadata": {},
   "source": [
    "### Optional Extra: A pandas-specific way to plot\n",
    "\n",
    "This plotting method is faster but only works for pandas dataframes.  The benefit is that you get the lagend automatically."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4d22aca8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='datetime'>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot 1\n",
    "# inputs: x column name, y column name\n",
    "gauge_data.plot('datetime', 'Discharge')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "954047b2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot 2\n",
    "# inputs: x column name, y column name\n",
    "gauge_data.plot('datetime', 'Discharge')\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.xaxis.set_major_locator(plt.MaxNLocator(5))  # Use only 4 labels\n",
    "ax.tick_params(axis='x', labelrotation = 80)  # Rotate the labels so the are more vertical"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "57ff586c",
   "metadata": {},
   "source": [
    "## 3) Cumulative sum"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9d7cacca",
   "metadata": {},
   "source": [
    "###  Subtracting the mean value as a baseline\n",
    "\n",
    "In Raphe's examples the mean value of a large value was used as the baseline and then used to compute the anomaly of each value.  Here we use the mean of our dataset (even though the record isn't that long, hopefully it conveys the idea)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "52c2cea3",
   "metadata": {},
   "outputs": [],
   "source": [
    "baseline_discharge = gauge_data['Discharge'].mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "394a02f7",
   "metadata": {},
   "outputs": [],
   "source": [
    "gauge_data['discharge_anomaly'] = gauge_data['Discharge'] - baseline_discharge"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "4ee9adb6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     -0.304138\n",
       "1     -0.304138\n",
       "2     -0.304138\n",
       "3     -0.304138\n",
       "4     -0.304138\n",
       "         ...   \n",
       "141   -2.204138\n",
       "142   -2.204138\n",
       "143   -2.204138\n",
       "144    1.695862\n",
       "145         NaN\n",
       "Name: discharge_anomaly, Length: 146, dtype: float64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gauge_data['discharge_anomaly']"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "05543be7",
   "metadata": {},
   "source": [
    "### Compute the cumulative sum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "95b7553d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "f88a5d3f",
   "metadata": {},
   "outputs": [],
   "source": [
    "# inputs: the data variable you want to sum\n",
    "discharge_csum = np.cumsum(gauge_data['discharge_anomaly'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "dbf5c8fe",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     -3.041379e-01\n",
       "1     -6.082759e-01\n",
       "2     -9.124138e-01\n",
       "3     -1.216552e+00\n",
       "4     -1.520690e+00\n",
       "           ...     \n",
       "141    2.712414e+00\n",
       "142    5.082759e-01\n",
       "143   -1.695862e+00\n",
       "144   -2.003731e-12\n",
       "145             NaN\n",
       "Name: discharge_anomaly, Length: 146, dtype: float64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "discharge_csum"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "475938c9",
   "metadata": {},
   "source": [
    "### Plot the cumulative sum"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "46e62184",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "e1f5d18c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.title('Cumulative Sum Discharge')\n",
    "# inputs: x values, y values\n",
    "plt.plot(gauge_data['datetime'], discharge_csum)\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.xaxis.set_major_locator(plt.MaxNLocator(5))  # Use only 4 labels\n",
    "ax.tick_params(axis='x', labelrotation = 80)  # Rotate the labels so the are more vertical"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d8c615fd",
   "metadata": {},
   "source": [
    "## Kendall's Tau\n",
    "\n",
    "[docs page](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.kendalltau.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "7d667cdb",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "1186364c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tau:  -0.5386593699749752  p_value:  1.19439882810134e-14\n"
     ]
    }
   ],
   "source": [
    "# inputs: variable 1, variable 2, (OPTIONAL nan_policy if your dataset has nan values)\n",
    "tau, p_value = stats.kendalltau(gauge_data['Discharge'], gauge_data['pH'], nan_policy='omit')\n",
    "print('tau: ', tau, ' p_value: ', p_value)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9df0386f",
   "metadata": {},
   "source": [
    "### Scatter plot of the Discharge and pH"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "e33c598c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'pH vs. Discharge')"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "gauge_data.plot.scatter('Discharge', 'pH')\n",
    "plt.title('pH vs. Discharge')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4ab8c5c",
   "metadata": {},
   "source": [
    "## Theil Sen Estimator\n",
    "\n",
    "\n",
    "[docs page](https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.theilslopes.html#scipy.stats.theilslopes)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "c6c60b2c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import stats"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11ac8483",
   "metadata": {},
   "source": [
    "**If needed** drop rows with nans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "531e7db0",
   "metadata": {},
   "outputs": [],
   "source": [
    "gauge_data = gauge_data.dropna(subset=['Discharge', 'pH'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14cac991",
   "metadata": {},
   "source": [
    "Compute the slope values for the best fit line and confidence interval lines.\n",
    "\n",
    "Output `res` returns four values:\n",
    "1. slope of the Theil line\n",
    "2. intercept of the Theil line\n",
    "3. slope of lower bound of confidence on the Theil line\n",
    "4. slope of upper bound of confidence on the Theil line"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "8465b8a6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(-0.02702702702702691, 9.202702702702698, -0.03636363636363624, -0.02564102564102556)\n"
     ]
    }
   ],
   "source": [
    "# inputs are: y variable, x variable, confidence interval (value between 0 and 1)\n",
    "res = stats.theilslopes(gauge_data['pH'], gauge_data['Discharge'], 0.90)\n",
    "# Here I used the index as a replacement for time\n",
    "print(res)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dfb01334",
   "metadata": {},
   "source": [
    "### Plot the lines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "4df8d9db",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "976dc188",
   "metadata": {},
   "source": [
    "Use the slope and y intercept values from the `stats.theilslopes()` method and plot the lines using the form _y = b + m*x_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "5ae2b448",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x28399fac250>]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Inputs for all plots: x values, y values, (optional color preferences)\n",
    "# base scatter plot\n",
    "plt.scatter(gauge_data['Discharge'], gauge_data['pH'])\n",
    "# Theil slope\n",
    "plt.plot(gauge_data['Discharge'], res[1] + res[0]*gauge_data['Discharge'], color='red')\n",
    "# lower confidence line\n",
    "plt.plot(gauge_data['Discharge'], res[1] + res[2]*gauge_data['Discharge'], '--k')\n",
    "# upper confidence line\n",
    "plt.plot(gauge_data['Discharge'], res[1] + res[3]*gauge_data['Discharge'], '--k')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "243861cf",
   "metadata": {},
   "source": [
    "More color preferences for the plot are listed in the \"Notes\" section of the [`plt.plot` docs](https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9f1d5995",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.9.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}