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 "cells": [
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   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "import os\n",
    "if not any(path.endswith('textbook') for path in sys.path):\n",
    "    sys.path.append(os.path.abspath('../../..'))\n",
    "from textbook_utils import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "# Example: A Simple Linear Model for Air Quality"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "Recall from  {numref}`Chapter %s <ch:pa>` that our aim is to use air quality measurements from the accurate Air Quality System  (AQS) sensors operated by the US government to predict the measurements made by PurpleAir (PA) sensors.  The pairs of data values come from neighboring instruments that measure the average daily concentration of particulate matter in the air on the same day. (The unit of measurement is an average count of particles under 2.5 mm in size per cubic liter of air in a 24-hour period.) In this section, we focus on air quality measurements at one location in Georgia. These are a subset of the data we examined in the case study in {numref}`Chapter %s <ch:pa>`. The measurements are daily averages from August 2019 to mid-November 2019:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [],
   "source": [
    "csv_file = 'data/Full24hrdataset.csv'\n",
    "usecols = ['Date', 'ID', 'region', 'PM25FM', 'PM25cf1']\n",
    "\n",
    "full = (pd.read_csv(csv_file, usecols=usecols, parse_dates=['Date'])\n",
    "        .dropna())\n",
    "full.columns = ['date', 'id', 'region', 'pm25aqs', 'pm25pa']\n",
    "\n",
    "GA = full.loc[(full['id'] == 'GA1') , :]\n",
    "\n",
    "from sklearn.linear_model import LinearRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
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       "<div>\n",
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       "        text-align: right;\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>date</th>\n",
       "      <th>id</th>\n",
       "      <th>region</th>\n",
       "      <th>pm25aqs</th>\n",
       "      <th>pm25pa</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>5258</th>\n",
       "      <td>2019-08-02</td>\n",
       "      <td>GA1</td>\n",
       "      <td>Southeast</td>\n",
       "      <td>8.65</td>\n",
       "      <td>16.19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5259</th>\n",
       "      <td>2019-08-03</td>\n",
       "      <td>GA1</td>\n",
       "      <td>Southeast</td>\n",
       "      <td>7.70</td>\n",
       "      <td>13.59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5260</th>\n",
       "      <td>2019-08-04</td>\n",
       "      <td>GA1</td>\n",
       "      <td>Southeast</td>\n",
       "      <td>6.30</td>\n",
       "      <td>10.30</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5439</th>\n",
       "      <td>2019-10-18</td>\n",
       "      <td>GA1</td>\n",
       "      <td>Southeast</td>\n",
       "      <td>6.30</td>\n",
       "      <td>12.94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5440</th>\n",
       "      <td>2019-10-21</td>\n",
       "      <td>GA1</td>\n",
       "      <td>Southeast</td>\n",
       "      <td>7.50</td>\n",
       "      <td>13.62</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5441</th>\n",
       "      <td>2019-10-30</td>\n",
       "      <td>GA1</td>\n",
       "      <td>Southeast</td>\n",
       "      <td>5.20</td>\n",
       "      <td>14.55</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>184 rows × 5 columns</p>\n",
       "</div>"
      ],
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       "           date   id     region  pm25aqs  pm25pa\n",
       "5258 2019-08-02  GA1  Southeast     8.65   16.19\n",
       "5259 2019-08-03  GA1  Southeast     7.70   13.59\n",
       "5260 2019-08-04  GA1  Southeast     6.30   10.30\n",
       "...         ...  ...        ...      ...     ...\n",
       "5439 2019-10-18  GA1  Southeast     6.30   12.94\n",
       "5440 2019-10-21  GA1  Southeast     7.50   13.62\n",
       "5441 2019-10-30  GA1  Southeast     5.20   14.55\n",
       "\n",
       "[184 rows x 5 columns]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "The feature `pm25aqs` contains measurements from the AQS sensor and `pm25pa` from the PurpleAir monitor. Since we are interested in studying how well the AQS measurements predict the PurpleAir measurements, our scatter plot places PurpleAir readings on the y-axis and AQS readings on the x-axis. We also add a trend line: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": []
   },
   "outputs": [
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           "xanchor": "center"
          },
          "width": 350,
          "xaxis": {
           "automargin": true,
           "gridcolor": "rgb(232,232,232)",
           "linecolor": "rgb(36,36,36)",
           "showgrid": true,
           "showline": true,
           "ticks": "outside",
           "title": {
            "standoff": 15
           },
           "zeroline": false,
           "zerolinecolor": "rgb(36,36,36)"
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "rgb(232,232,232)",
           "linecolor": "rgb(36,36,36)",
           "showgrid": true,
           "showline": true,
           "ticks": "outside",
           "title": {
            "standoff": 15
           },
           "zeroline": false,
           "zerolinecolor": "rgb(36,36,36)"
          }
         }
        },
        "width": 350,
        "xaxis": {
         "anchor": "y",
         "autorange": true,
         "domain": [
          0,
          1
         ],
         "range": [
          2.0283171521035603,
          18.97168284789644
         ],
         "title": {
          "text": "AQS PM2.5"
         },
         "type": "linear"
        },
        "yaxis": {
         "anchor": "x",
         "autorange": true,
         "domain": [
          0,
          1
         ],
         "range": [
          1.362655522145745,
          37.47469634948399
         ],
         "title": {
          "text": "PurpleAir PM2.5"
         },
         "type": "linear"
        }
       }
      },
      "image/png": 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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "px.scatter(GA, x=\"pm25aqs\", y=\"pm25pa\", trendline='ols',\n",
    "           trendline_color_override=\"darkorange\",\n",
    "           labels={'pm25aqs':'AQS PM2.5', 'pm25pa':'PurpleAir PM2.5'},\n",
    "           width=350, height=250)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "This scatter plot shows a linear relationship between the measurements from these two kinds of instruments. The model that we want to fit has the following form:\n",
    "\n",
    "$$ PA \\approx \\theta_0 + \\theta_1 AQ$$\n",
    "\n",
    "where $PA$ refers to the  PurpleAir average daily measurement and $AQ$ to its partner AQS measurement."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "Since `pandas.Series` objects have built-in methods to compute SDs and correlation coefficients, we can quickly define functions that calculate the best-fitting line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def theta_1(x, y):\n",
    "    r = x.corr(y)\n",
    "    return r * y.std() / x.std()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def theta_0(x, y):\n",
    "    return y.mean() - theta_1(x, y) * x.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [],
    "user_expressions": []
   },
   "source": [
    "Now we can fit the model by computing\n",
    "$\\hat{\\theta}_0$ and $\\hat{\\theta}_1$ for these data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "t1 = theta_1(GA['pm25aqs'], GA['pm25pa'])\n",
    "t0 = theta_0(GA['pm25aqs'], GA['pm25pa'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Model: -3.36 + 2.10AQ\n"
     ]
    }
   ],
   "source": [
    "print(f'Model: {t0:.2f} + {t1:.2f}AQ')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "This model matches the trend line shown in the scatter plot. That's not by accident. The parameter value for `trendline` in the call to `scatter()` is `\"ols\"`, which stands for *ordinary least squares*, another name for fitting a linear model by minimizing squared error."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "Let's examine the errors. \n",
    "First, we find the predictions for PA measurements given the AQS measurements, and \n",
    "then we calculate the errors---the difference between the actual PA measurements and the predictions:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "prediction = t0 + t1 * GA[\"pm25aqs\"]\n",
    "error = GA[\"pm25pa\"] - prediction\n",
    "fit = pd.DataFrame(dict(prediction=prediction, error=error))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "Let's plot these errors against the predicted values:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
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   ],
   "source": [
    "fig = px.scatter(fit, y='error', x='prediction',\n",
    "                 labels={\"prediction\": \"Prediction\",\n",
    "                         \"error\": \"Error\"},\n",
    "                 width=350, height=250)\n",
    "\n",
    "fig.add_hline(0, line_width=2, line_dash='dash', opacity=1)\n",
    "fig.update_yaxes(range=[-12, 12])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "An error of 0 means that the actual measurement falls on the fitted line; we also call this line the *least squares line* or the *regression line*. A positive value means it is above the line, and negative means it's below. You might be wondering how good this model is and what it says about our data. We consider these topics next. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "## Interpreting Linear Models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "The original scatter plot of paired measurements shows that the PurpleAir recordings are often quite a bit higher than the more accurate AQS measurements. Indeed, the equation for our simple line model has a slope of about 2.1. We interpret the slope to mean that a change of 1 ppm measured by the AQS monitor is associated with a 2 ppm change in the PA measurement, on average. So, if on one day the AQS sensor measures 10 ppm and on the next day it is 5 ppm higher, namely 15 ppm, then our prediction for the PA measurement increases from one day to the next by $2 * 5 = 10$ ppm."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "Any change in the PurpleAir reading is not caused by the change in the AQS reading. Rather, they both reflect the air quality, and our model captures the relationship between the two devices. Oftentimes, the term *prediction* is taken to mean *causation*, but that is not the case here. Instead, the prediction just refers to our use of the *linear association* between PA and AQS measurements."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "As for the intercept in the model, we might expect it to be 0, since when there is no particulate matter in the air we would think that both instruments would measure 0 ppm. But for an AQS of 0, the model predicts $-3.4$ ppm for PurpleAir, which doesn't make sense. There can't be negative amounts of particles in the air. This highlights the problem of using the model outside the range where measurements were taken. We observed AQS recordings between 3 and 18 ppm, and in this range the model fits well. While it makes sense for the line to have an intercept of 0, such a model doesn't fit well in a practical sense and the predictions tend to be much worse.\n",
    "\n",
    "George Box, a renowned statistician, famously said, \"All models are wrong, but some are useful.\" Here is a case where despite the intercept of the line not passing through 0, the simple linear model is useful in predicting  air quality measurements for a PurpleAir sensor. Indeed, the correlation between our two features is very high:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>pm25aqs</th>\n",
       "      <th>pm25pa</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>pm25aqs</th>\n",
       "      <td>1.00</td>\n",
       "      <td>0.92</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>pm25pa</th>\n",
       "      <td>0.92</td>\n",
       "      <td>1.00</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      ],
      "text/plain": [
       "         pm25aqs  pm25pa\n",
       "pm25aqs     1.00    0.92\n",
       "pm25pa      0.92    1.00"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GA[['pm25aqs', 'pm25pa']].corr()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "Aside from looking at correlation coefficients, there are other ways to assess the quality of a linear model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "## Assessing the Fit\n",
    "\n",
    "The earlier plot of the errors against the fitted values gives a visual assessment of the quality of the fit. (This plot is called a  *residual plot* because the errors are sometimes referred to as *residuals*.) A good fit should show a cloud of points around the horizontal line at 0 with no clear pattern. When there is a pattern, we can usually conclude that the simple linear model doesn't entirely capture the signal. We saw earlier that there are no apparent patterns in the residual plot. \n",
    "\n",
    "Another type of residual plot that can be useful is a plot of the residuals against a feature that is not in the model. If we see a pattern, then we may want to include this feature in the model, in addition to the feature(s) already in the model. Also, when the data have a time component, we want to check for patterns in the residuals over time. For these particular data, since the measurements are daily averages over a four-month period, we plot the error against the date the measurement is recorded:   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [
    {
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stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,193v5\" transform=\"translate(244.68,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"xtick ticks crisp\" d=\"M0,193v5\" transform=\"translate(325.71,0)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"212.4\" transform=\"translate(85.24,0)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 12px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">Aug 2019</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"212.4\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 12px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\" transform=\"translate(166.26999999999998,0)\">Sep 2019</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"212.4\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 12px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\" transform=\"translate(244.68,0)\">Oct 2019</text></g><g class=\"xtick\"><text text-anchor=\"middle\" x=\"0\" y=\"212.4\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 12px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\" transform=\"translate(325.71,0)\">Nov 2019</text></g></g><g class=\"yaxislayer-above\"><path class=\"ytick ticks crisp\" d=\"M67,0h-5\" transform=\"translate(0,176.83)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M67,0h-5\" transform=\"translate(0,138.92)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M67,0h-5\" transform=\"translate(0,101)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M67,0h-5\" transform=\"translate(0,63.08)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><path class=\"ytick ticks crisp\" d=\"M67,0h-5\" transform=\"translate(0,25.17)\" style=\"stroke: rgb(68, 68, 68); stroke-opacity: 1; stroke-width: 1px;\"/><g class=\"ytick\"><text text-anchor=\"end\" x=\"59.6\" y=\"4.199999999999999\" transform=\"translate(0,176.83)\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 12px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\">−10</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"59.6\" y=\"4.199999999999999\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 12px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\" transform=\"translate(0,138.92)\">−5</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"59.6\" y=\"4.199999999999999\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 12px; fill: rgb(36, 36, 36); fill-opacity: 1; white-space: pre; opacity: 1;\" transform=\"translate(0,101)\">0</text></g><g class=\"ytick\"><text text-anchor=\"end\" x=\"59.6\" y=\"4.199999999999999\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; 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font-size: 14px; fill: rgb(36, 36, 36); opacity: 1; font-weight: normal; white-space: pre;\">Date</text></g><g class=\"g-ytitle\" transform=\"translate(3.7841796875,0)\"><text class=\"ytitle\" transform=\"rotate(-90,10.215625000000003,101)\" x=\"10.215625000000003\" y=\"101\" text-anchor=\"middle\" style=\"font-family: 'Open Sans', verdana, arial, sans-serif; font-size: 14px; fill: rgb(36, 36, 36); opacity: 1; font-weight: normal; white-space: pre;\">Error</text></g></g></svg>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = px.scatter(x= GA[\"date\"], y=error, \n",
    "                 labels={\"x\":\"Date\",\"y\":\"Error\"},\n",
    "                 width=400, height=250)\n",
    "\n",
    "fig.update_yaxes(range=[-12, 12])\n",
    "fig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "It looks like there are a few consecutive days near the end of August and again near the end of September where the data are far below what is expected. Looking back at the original scatter plot (and the first residual plot), we can see two small clusters of horizontal points below the main point cloud. The plot we just made indicates that we should check the original data and any available information about the equipment to determine whether it was properly functioning on those days."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "The residual plot can also give us a general sense of how accurate\n",
    "the model is in its predictions.\n",
    "Most of the errors lie between $\\pm 6 $ ppm of the line.\n",
    "And we find the standard deviation of the errors to be about 2.8 ppm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.796095864304746"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "error.std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "In comparison, the standard deviation of the PurpleAir measurements is quite a bit larger:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.947418231019876"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "GA['pm25pa'].std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "user_expressions": []
   },
   "source": [
    "The model error may be further reduced if we find the monitor wasn't working on those days in late August and September and exclude them from the dataset. In any event, for situations where the air is quite clean, the error is relatively large, but in absolute terms it is inconsequential. We are typically more concerned about the case when there is air pollution, and in that case, an error of 2.8 ppm seems reasonable.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [],
    "user_expressions": []
   },
   "source": [
    "Let's return to the process of how to find this line, the process of *model fitting*. In the next section, we derive the intercept and slope by minimizing the mean squared error. "
   ]
  }
 ],
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