{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "eaad80af",
   "metadata": {},
   "source": [
    "# Diagnostics and Inference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "063ed3f8",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:08.710239Z",
     "iopub.status.busy": "2026-11-14T11:08:08.710006Z",
     "iopub.status.idle": "2026-11-14T11:08:09.024453Z",
     "shell.execute_reply": "2026-11-14T11:08:09.024036Z"
    },
    "tags": [
     "hide-input",
     "thebe-init",
     "runnable"
    ]
   },
   "outputs": [],
   "source": [
    "path_data = '../../data/'\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Regression functions from 1201 and 1202 (columns given by name)\n",
    "def standard_units(values):\n",
    "    return (values - np.mean(values)) / np.std(values)\n",
    "\n",
    "def correlation(table, x, y):\n",
    "    return np.mean(standard_units(table[x]) * standard_units(table[y]))\n",
    "\n",
    "def slope(table, x, y):\n",
    "    r = correlation(table, x, y)\n",
    "    return r * np.std(table[y]) / np.std(table[x])\n",
    "\n",
    "def intercept(table, x, y):\n",
    "    return np.mean(table[y]) - slope(table, x, y) * np.mean(table[x])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d1e0a7c",
   "metadata": {},
   "source": [
    "```{index} diagnostics; regression\n",
    "```\n",
    "\n",
    "```{index} inference; regression slope\n",
    "```\n",
    "\n",
    "A least squares line can be fitted to any scatter plot. The formulas from {doc}`1202-regression-line` return a slope and an intercept even when the points follow a curve, and the computer does not warn you. A manager who trusts the line without checking may order the wrong amount of stock or promise a budget result that never arrives.\n",
    "\n",
    "This section asks two questions before you rely on a line. First, is a straight line the right description? **Diagnostics** answer that, mainly with plots of the **residuals**. Second, how much could the slope change with a different sample? The bootstrap from Chapter 11 gives a confidence interval for the slope and a test of whether it could be 0."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2165ea79",
   "metadata": {},
   "source": [
    "```{contents}\n",
    ":local:\n",
    ":depth: 2\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7a8f489",
   "metadata": {},
   "source": [
    "## Residual Plots\n",
    "\n",
    "```{index} residual plot\n",
    "```\n",
    "\n",
    "Recall from {doc}`1202-regression-line` that the **residual** for an observation is the observed value minus the fitted value:\n",
    "\n",
    "$$\n",
    "\\text{residual} = \\text{observed } y - \\text{fitted } y.\n",
    "$$\n",
    "\n",
    "A positive residual means the line predicted too low; a negative residual means it predicted too high. A **residual plot** is a scatter plot of the residuals against the feature (or against the fitted values). A horizontal line at 0 marks a perfect prediction.\n",
    "\n",
    "Start with the 40 stores. The file `store_ad_sales.csv` is a simulated teaching data set, not real store records. Each row has the weekly ad spend and weekly sales, both in thousands of dollars."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "9bb63dee",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.025780Z",
     "iopub.status.busy": "2026-11-14T11:08:09.025694Z",
     "iopub.status.idle": "2026-11-14T11:08:09.032444Z",
     "shell.execute_reply": "2026-11-14T11:08:09.032042Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope:     3.87\n",
      "Intercept: 57.54\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>store</th>\n",
       "      <th>ad_spend</th>\n",
       "      <th>sales</th>\n",
       "      <th>fitted</th>\n",
       "      <th>residual</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>S01</td>\n",
       "      <td>6.0</td>\n",
       "      <td>77.3</td>\n",
       "      <td>80.75</td>\n",
       "      <td>-3.45</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>S02</td>\n",
       "      <td>7.2</td>\n",
       "      <td>85.3</td>\n",
       "      <td>85.39</td>\n",
       "      <td>-0.09</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>S03</td>\n",
       "      <td>2.0</td>\n",
       "      <td>50.2</td>\n",
       "      <td>65.27</td>\n",
       "      <td>-15.07</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>S04</td>\n",
       "      <td>3.4</td>\n",
       "      <td>69.8</td>\n",
       "      <td>70.69</td>\n",
       "      <td>-0.89</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>S05</td>\n",
       "      <td>10.0</td>\n",
       "      <td>91.4</td>\n",
       "      <td>96.23</td>\n",
       "      <td>-4.83</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  store  ad_spend  sales  fitted  residual\n",
       "0   S01       6.0   77.3   80.75     -3.45\n",
       "1   S02       7.2   85.3   85.39     -0.09\n",
       "2   S03       2.0   50.2   65.27    -15.07\n",
       "3   S04       3.4   69.8   70.69     -0.89\n",
       "4   S05      10.0   91.4   96.23     -4.83"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stores = pd.read_csv(path_data + 'store_ad_sales.csv')\n",
    "\n",
    "store_slope = slope(stores, 'ad_spend', 'sales')\n",
    "store_intercept = intercept(stores, 'ad_spend', 'sales')\n",
    "\n",
    "stores['fitted'] = store_slope * stores['ad_spend'] + store_intercept\n",
    "stores['residual'] = stores['sales'] - stores['fitted']\n",
    "\n",
    "print('Slope:    ', round(store_slope, 2))\n",
    "print('Intercept:', round(store_intercept, 2))\n",
    "stores[['store', 'ad_spend', 'sales', 'fitted', 'residual']].head().round(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "309d6ec5",
   "metadata": {},
   "source": [
    "Here is the scatter plot with the line, and next to it the residual plot. Each point on the right is the vertical distance from a point on the left to the line, so the line in the left plot becomes the flat line at 0 in the right plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ff2d2e4b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.033516Z",
     "iopub.status.busy": "2026-11-14T11:08:09.033448Z",
     "iopub.status.idle": "2026-11-14T11:08:09.106470Z",
     "shell.execute_reply": "2026-11-14T11:08:09.106081Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x380 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 3.8))\n",
    "\n",
    "ax1.scatter(stores['ad_spend'], stores['sales'], s=20)\n",
    "xs = np.array([stores['ad_spend'].min(), stores['ad_spend'].max()])\n",
    "ax1.plot(xs, store_slope * xs + store_intercept, color='gold', lw=3)\n",
    "ax1.set_xlabel('Weekly ad spend ($1,000s)')\n",
    "ax1.set_ylabel('Weekly sales ($1,000s)')\n",
    "ax1.set_title('Sales and the fitted line')\n",
    "\n",
    "ax2.scatter(stores['ad_spend'], stores['residual'], s=20)\n",
    "ax2.axhline(0, color='gold', lw=3)\n",
    "ax2.set_xlabel('Weekly ad spend ($1,000s)')\n",
    "ax2.set_ylabel('Residual ($1,000s)')\n",
    "ax2.set_title('Residuals show no pattern')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c33cc8c5",
   "metadata": {},
   "source": [
    "```{index} healthy residual plot\n",
    "```\n",
    "\n",
    "This is what a **healthy residual plot** looks like. Look for three things:\n",
    "\n",
    "1. **No pattern.** The points form a shapeless cloud. There is no curve, no tilt, and no clump of points on one side of 0 at some range of ad spend.\n",
    "2. **Centered on 0.** In every range of ad spend, the residuals average out near 0. (Equal counts are not the test: many small negative residuals can balance a few large positive ones.)\n",
    "3. **Even spread.** The cloud is about as tall at the left end as at the right end.\n",
    "\n",
    "When all three hold, the straight line has captured the main trend, and what is left over looks like random noise. In the store data the line is a reasonable model.\n",
    "\n",
    "The plot is centered on 0 for a reason that is not a coincidence. For the least squares line, the residuals always average to zero. You can check this directly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "acca688f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.107551Z",
     "iopub.status.busy": "2026-11-14T11:08:09.107490Z",
     "iopub.status.idle": "2026-11-14T11:08:09.109542Z",
     "shell.execute_reply": "2026-11-14T11:08:09.109265Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average residual: 0.0\n",
      "Smallest residual: -25.37\n",
      "Largest residual:  24.04\n",
      "Residual SD:       11.11\n"
     ]
    }
   ],
   "source": [
    "print('Average residual:', round(stores['residual'].mean(), 10))\n",
    "print('Smallest residual:', round(stores['residual'].min(), 2))\n",
    "print('Largest residual: ', round(stores['residual'].max(), 2))\n",
    "print('Residual SD:      ', round(stores['residual'].std(ddof=0), 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8cc5f594",
   "metadata": {},
   "source": [
    "The average residual is 0 (to rounding error). This holds for every least squares line, however poor, so the average cannot tell you whether a line is good. That is why you look at the **shape** of the residual plot, not just its center.\n",
    "\n",
    "The residual SD of about 11.1 (\\$11,100) is the typical size of a miss. Individual misses run from about -25 to 24, but they show no pattern."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e880613a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.110477Z",
     "iopub.status.busy": "2026-11-14T11:08:09.110423Z",
     "iopub.status.idle": "2026-11-14T11:08:09.111844Z",
     "shell.execute_reply": "2026-11-14T11:08:09.111545Z"
    },
    "tags": [
     "thebe-interactive"
    ]
   },
   "outputs": [],
   "source": [
    "### Exercise: Residuals of Sales on Staff\n",
    "#   1. Fit the least squares line of sales on staff (number of employees), using the\n",
    "#      slope and intercept functions.\n",
    "#   2. Compute the residuals: sales minus the fitted values.\n",
    "#   3. Print the average residual, rounded to 6 decimals.\n",
    "#   4. Print the smallest and largest residuals, rounded to 2 decimals.\n",
    "# Print exactly:\n",
    "#   Average residual: <value>\n",
    "#   Smallest residual: <value>\n",
    "#   Largest residual: <value>\n",
    "### Your code starts here.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "### Your code ends here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "121025af",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.112647Z",
     "iopub.status.busy": "2026-11-14T11:08:09.112591Z",
     "iopub.status.idle": "2026-11-14T11:08:09.115499Z",
     "shell.execute_reply": "2026-11-14T11:08:09.115189Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average residual: 0.0\n",
      "Smallest residual: -30.99\n",
      "Largest residual: 23.76\n"
     ]
    }
   ],
   "source": [
    "### Solution\n",
    "ex_stores = pd.read_csv(path_data + 'store_ad_sales.csv')\n",
    "\n",
    "ex_slope = slope(ex_stores, 'staff', 'sales')\n",
    "ex_intercept = intercept(ex_stores, 'staff', 'sales')\n",
    "ex_resid = ex_stores['sales'] - (ex_slope * ex_stores['staff'] + ex_intercept)\n",
    "\n",
    "print('Average residual:', round(ex_resid.mean(), 6))\n",
    "print('Smallest residual:', round(ex_resid.min(), 2))\n",
    "print('Largest residual:', round(ex_resid.max(), 2))\n",
    "# The average is 0 for any least squares line, even a weaker one."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5743ad2d",
   "metadata": {},
   "source": [
    "## Detecting Nonlinearity\n",
    "\n",
    "```{index} linearity\n",
    "```\n",
    "\n",
    "```{index} nonlinearity\n",
    "```\n",
    "\n",
    "```{index} curved pattern; residuals\n",
    "```\n",
    "\n",
    "Suppose a retailer records, for 104 weeks (the file `price_demand.csv` is another simulated teaching data set), the price of one product and the number of units sold that week. The prices were changed regularly. In {doc}`1201-correlation` you saw that price and units are strongly related. What happens when you fit a straight line? **Linearity** is the assumption that the average outcome changes by a constant amount per unit of the predictor, so that a straight line describes the pattern. A residual plot is the standard check."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "26677a45",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.116361Z",
     "iopub.status.busy": "2026-11-14T11:08:09.116311Z",
     "iopub.status.idle": "2026-11-14T11:08:09.120140Z",
     "shell.execute_reply": "2026-11-14T11:08:09.119763Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Correlation: -0.951\n",
      "Slope:       -27.94\n",
      "Intercept:   458.57\n"
     ]
    }
   ],
   "source": [
    "pd_data = pd.read_csv(path_data + 'price_demand.csv')\n",
    "\n",
    "pd_slope = slope(pd_data, 'price', 'units')\n",
    "pd_intercept = intercept(pd_data, 'price', 'units')\n",
    "pd_data['fitted'] = pd_slope * pd_data['price'] + pd_intercept\n",
    "pd_data['residual'] = pd_data['units'] - pd_data['fitted']\n",
    "\n",
    "print('Correlation:', round(correlation(pd_data, 'price', 'units'), 3))\n",
    "print('Slope:      ', round(pd_slope, 2))\n",
    "print('Intercept:  ', round(pd_intercept, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "379bb81b",
   "metadata": {},
   "source": [
    "The correlation is about -0.95, which is strong. The slope says that each \\$1 increase in price goes with about 28 fewer units sold per week. Now look at the scatter plot and at the residuals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "a192e46d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.121074Z",
     "iopub.status.busy": "2026-11-14T11:08:09.121025Z",
     "iopub.status.idle": "2026-11-14T11:08:09.184512Z",
     "shell.execute_reply": "2026-11-14T11:08:09.184136Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x380 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 3.8))\n",
    "\n",
    "ax1.scatter(pd_data['price'], pd_data['units'], s=20)\n",
    "xs = np.array([pd_data['price'].min(), pd_data['price'].max()])\n",
    "ax1.plot(xs, pd_slope * xs + pd_intercept, color='gold', lw=3)\n",
    "ax1.set_xlabel('Price ($)')\n",
    "ax1.set_ylabel('Units sold per week')\n",
    "ax1.set_title('The points bend away from the line')\n",
    "\n",
    "ax2.scatter(pd_data['price'], pd_data['residual'], s=20)\n",
    "ax2.axhline(0, color='gold', lw=3)\n",
    "ax2.set_xlabel('Price ($)')\n",
    "ax2.set_ylabel('Residual (units)')\n",
    "ax2.set_title('Residuals form a U shape')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7668620e",
   "metadata": {},
   "source": [
    "In the left plot the points sag below the line in the middle and rise above it at both ends. The residual plot shows the same thing more clearly: the residuals are positive at low prices, negative at middle prices, and positive again at high prices. This **U shape** is the signature of a **nonlinear** relationship. The residuals still average 0, as they must, but they are not random. At a given price, the line is wrong in a predictable direction.\n",
    "\n",
    "The correlation of -0.95 hid this. A high |r| says the points are close to *a* line, but the residual plot shows that a curve would do better. You can see the cost by comparing predictions for particular prices with the weeks' actual sales."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "3755a14d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.185520Z",
     "iopub.status.busy": "2026-11-14T11:08:09.185456Z",
     "iopub.status.idle": "2026-11-14T11:08:09.188262Z",
     "shell.execute_reply": "2026-11-14T11:08:09.187945Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average residual, prices under $6:    47.3 units\n",
      "Average residual, prices $9 to $12:   -27.7 units\n",
      "Average residual, prices over $14:    18.9 units\n"
     ]
    }
   ],
   "source": [
    "low = pd_data[pd_data['price'] < 6]\n",
    "mid = pd_data[(pd_data['price'] > 9) & (pd_data['price'] < 12)]\n",
    "high = pd_data[pd_data['price'] > 14]\n",
    "\n",
    "print('Average residual, prices under $6:   ', round(low['residual'].mean(), 1), 'units')\n",
    "print('Average residual, prices $9 to $12:  ', round(mid['residual'].mean(), 1), 'units')\n",
    "print('Average residual, prices over $14:   ', round(high['residual'].mean(), 1), 'units')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0473f1e",
   "metadata": {},
   "source": [
    "At prices under \\$6 the line under-predicts sales by about 47 units a week on average, and at prices over \\$14 by about 19 units. In the middle of the price range (\\$9 to \\$12) it over-predicts by about 28 units. A manager using this line to plan inventory would stock too few units at the lowest prices and too many at mid-range prices.\n",
    "\n",
    "What can be done when residuals are curved? There are three common responses.\n",
    "\n",
    "1. **Transform the data.** Demand often falls by a constant *percentage* for each extra dollar of price, not by a constant number of units. Taking the logarithm of units, and keeping price in dollars, turns such a relationship into a straight line. The example below shows this.\n",
    "2. **Fit a curve.** Choose the curve that minimizes the root mean squared error, just as least squares does for the line ({doc}`1202-regression-line`). Chapter 13 develops this further ({doc}`../13-multiple-regression/1300-multiple-regression`).\n",
    "3. **Use the line only over a narrow range.** Over a short stretch of prices the curve is nearly straight, so a line can serve as a local approximation. It should then not be used outside that range.\n",
    "\n",
    "Here is the first response. Fit a line to the logarithm of units against price, and draw the residuals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "ecadcc94",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.189260Z",
     "iopub.status.busy": "2026-11-14T11:08:09.189202Z",
     "iopub.status.idle": "2026-11-14T11:08:09.221999Z",
     "shell.execute_reply": "2026-11-14T11:08:09.221683Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 600x380 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope on the log scale: -0.184\n",
      "Change in units per extra $1: -16.8 %\n"
     ]
    }
   ],
   "source": [
    "pd_data['log_units'] = np.log(pd_data['units'])\n",
    "\n",
    "log_slope = slope(pd_data, 'price', 'log_units')\n",
    "log_intercept = intercept(pd_data, 'price', 'log_units')\n",
    "pd_data['log_residual'] = pd_data['log_units'] - (log_slope * pd_data['price'] + log_intercept)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(6, 3.8))\n",
    "ax.scatter(pd_data['price'], pd_data['log_residual'], s=20)\n",
    "ax.axhline(0, color='gold', lw=3)\n",
    "ax.set_xlabel('Price ($)')\n",
    "ax.set_ylabel('Residual (log units)')\n",
    "ax.set_title('After taking the log of units, the U shape is gone')\n",
    "plt.show()\n",
    "\n",
    "print('Slope on the log scale:', round(log_slope, 3))\n",
    "print('Change in units per extra $1:', round(100 * (np.exp(log_slope) - 1), 1), '%')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd3b4c03",
   "metadata": {},
   "source": [
    "The residuals no longer curve; they center on 0 across the price range. (They do spread out at high prices, where sales are small: uneven spread, the next topic.) The slope on the log scale is about -0.18: each extra \\$1 of price goes with about 17% fewer units sold. That is about 34 units where the product sells 200 a week but only about 9 where it sells 50, which is why a straight line in units missed in a U shape."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "c17487d4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.222981Z",
     "iopub.status.busy": "2026-11-14T11:08:09.222926Z",
     "iopub.status.idle": "2026-11-14T11:08:09.225653Z",
     "shell.execute_reply": "2026-11-14T11:08:09.225296Z"
    },
    "tags": [
     "thebe-interactive"
    ]
   },
   "outputs": [],
   "source": [
    "### Exercise: Curved Residuals in Two Price Ranges\n",
    "#   1. Using the data below, fit a line of units on price with the slope and\n",
    "#      intercept functions.\n",
    "#   2. Compute the residuals: units minus the fitted values.\n",
    "#   3. Print the average residual for the three cheapest prices and for the\n",
    "#      three prices in the middle (items 4 to 6), rounded to 1 decimal.\n",
    "#      Are the two averages on opposite sides of 0, as in a U shape?\n",
    "# Print exactly:\n",
    "#   Average residual, cheapest 3: <value>\n",
    "#   Average residual, middle 3: <value>\n",
    "ex_demand = pd.DataFrame({\n",
    "    'price': [4, 5, 6, 8, 10, 12, 14, 15],\n",
    "    'units': [300, 220, 170, 120, 90, 75, 60, 55],\n",
    "})\n",
    "### Your code starts here.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "### Your code ends here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "fc8344f2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.226461Z",
     "iopub.status.busy": "2026-11-14T11:08:09.226410Z",
     "iopub.status.idle": "2026-11-14T11:08:09.229161Z",
     "shell.execute_reply": "2026-11-14T11:08:09.228892Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average residual, cheapest 3: 12.0\n",
      "Average residual, middle 3: -26.8\n"
     ]
    }
   ],
   "source": [
    "### Solution\n",
    "ex_demand = pd.DataFrame({\n",
    "    'price': [4, 5, 6, 8, 10, 12, 14, 15],\n",
    "    'units': [300, 220, 170, 120, 90, 75, 60, 55],\n",
    "})\n",
    "\n",
    "ex_slope = slope(ex_demand, 'price', 'units')\n",
    "ex_intercept = intercept(ex_demand, 'price', 'units')\n",
    "ex_demand['residual'] = ex_demand['units'] - (ex_slope * ex_demand['price'] + ex_intercept)\n",
    "\n",
    "print('Average residual, cheapest 3:', round(ex_demand['residual'].iloc[:3].mean(), 1))\n",
    "print('Average residual, middle 3:', round(ex_demand['residual'].iloc[3:6].mean(), 1))\n",
    "# Positive at the cheap end, negative in the middle: the line misses in a\n",
    "# systematic way, so a straight line is the wrong shape for these data."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "837ee637",
   "metadata": {},
   "source": [
    "## Detecting Uneven Spread\n",
    "\n",
    "```{index} heteroscedasticity\n",
    "```\n",
    "\n",
    "```{index} uneven spread\n",
    "```\n",
    "\n",
    "A line can also be wrong in a different way. Even if the trend is straight, the points may be much more spread out in one part of the plot than in another.\n",
    "\n",
    "Here is a real example. The data are 5,000 yellow-taxi trips in New York City from March 4 to 10, 2019, taken from the 2019 Yellow Taxi Trip Data published by the NYC Taxi and Limousine Commission on NYC Open Data. Each trip has the pickup time, the trip distance in miles, and the metered fare in dollars (before tips, tolls, and surcharges). The extract takes trips spread over every hour of the week, drops trips with zero or negative distance or fare, fares above \\$150, and trips longer than 40 miles (likely data-entry errors), and keeps a random 5,000. No values were changed. Fit the line of fare on distance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "05983184",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.230030Z",
     "iopub.status.busy": "2026-11-14T11:08:09.229977Z",
     "iopub.status.idle": "2026-11-14T11:08:09.234386Z",
     "shell.execute_reply": "2026-11-14T11:08:09.234039Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trips:       5000\n",
      "Correlation: 0.947\n",
      "Slope:       2.72 dollars per mile\n",
      "Intercept:   4.84 dollars\n"
     ]
    }
   ],
   "source": [
    "taxi = pd.read_csv(path_data + 'nyc_taxi_fares.csv')\n",
    "\n",
    "taxi_slope = slope(taxi, 'distance_miles', 'fare')\n",
    "taxi_intercept = intercept(taxi, 'distance_miles', 'fare')\n",
    "taxi['fitted'] = taxi_slope * taxi['distance_miles'] + taxi_intercept\n",
    "taxi['residual'] = taxi['fare'] - taxi['fitted']\n",
    "\n",
    "print('Trips:      ', len(taxi))\n",
    "print('Correlation:', round(correlation(taxi, 'distance_miles', 'fare'), 3))\n",
    "print('Slope:      ', round(taxi_slope, 2), 'dollars per mile')\n",
    "print('Intercept:  ', round(taxi_intercept, 2), 'dollars')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebb5f580",
   "metadata": {},
   "source": [
    "The correlation is about 0.95, so the line looks excellent: each extra mile adds about \\$2.72 to the fare. Now the pictures. With 5,000 points, the plots use small, partly transparent markers so that dense areas look darker."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "25eb6547",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.235257Z",
     "iopub.status.busy": "2026-11-14T11:08:09.235208Z",
     "iopub.status.idle": "2026-11-14T11:08:09.324391Z",
     "shell.execute_reply": "2026-11-14T11:08:09.324036Z"
    },
    "tags": []
   },
   "outputs": [
    {
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",
      "text/plain": [
       "<Figure size 1000x380 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 3.8))\n",
    "\n",
    "ax1.scatter(taxi['distance_miles'], taxi['fare'], s=6, alpha=0.3)\n",
    "xs = np.array([0, 40])\n",
    "ax1.plot(xs, taxi_slope * xs + taxi_intercept, color='gold', lw=3)\n",
    "ax1.set_xlabel('Trip distance (miles)')\n",
    "ax1.set_ylabel('Fare ($)')\n",
    "ax1.set_title('Fares scatter more on long trips')\n",
    "\n",
    "ax2.scatter(taxi['distance_miles'], taxi['residual'], s=6, alpha=0.3)\n",
    "ax2.axhline(0, color='gold', lw=3)\n",
    "ax2.set_xlabel('Trip distance (miles)')\n",
    "ax2.set_ylabel('Residual ($)')\n",
    "ax2.set_title('Residuals fan out as distance grows')\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "563955e1",
   "metadata": {},
   "source": [
    "```{index} fan shape; residuals\n",
    "```\n",
    "\n",
    "The residuals spread out like a fan: narrow on the left and wide on the right. This is **heteroscedasticity** (uneven spread); equal spread everywhere is *homoscedasticity*. A short trip is almost all distance on the meter, while a long trip adds traffic time, route choices, and tolls. The horizontal band at \\$52 is consistent with the flat fare between Manhattan and JFK, but the data do not record locations, so the extract cannot confirm which \\$52 fares were JFK trips.\n",
    "\n",
    "You can measure the change in spread with the residual SD in distance bands."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d962bac7",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.325499Z",
     "iopub.status.busy": "2026-11-14T11:08:09.325434Z",
     "iopub.status.idle": "2026-11-14T11:08:09.328921Z",
     "shell.execute_reply": "2026-11-14T11:08:09.328575Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Trips with a recorded fare of $52: 125\n",
      "\n",
      "Under 2 miles:  2971 trips, residual SD: $ 2.77\n",
      "2 to 10 miles:  1723 trips, residual SD: $ 3.45\n",
      "Over 10 miles:  306 trips, residual SD: $ 7.31\n",
      "All trips:      5000 trips, residual SD: $ 3.52\n",
      "\n",
      "Over 20 miles:  33 trips, average residual: $ -5.2\n"
     ]
    }
   ],
   "source": [
    "print('Trips with a recorded fare of $52:', (taxi['fare'] == 52).sum())\n",
    "print()\n",
    "\n",
    "short = taxi[taxi['distance_miles'] < 2]\n",
    "medium = taxi[(taxi['distance_miles'] >= 2) & (taxi['distance_miles'] <= 10)]\n",
    "long_trips = taxi[taxi['distance_miles'] > 10]\n",
    "\n",
    "print('Under 2 miles: ', len(short), 'trips, residual SD: $', round(short['residual'].std(ddof=0), 2))\n",
    "print('2 to 10 miles: ', len(medium), 'trips, residual SD: $', round(medium['residual'].std(ddof=0), 2))\n",
    "print('Over 10 miles: ', len(long_trips), 'trips, residual SD: $', round(long_trips['residual'].std(ddof=0), 2))\n",
    "print('All trips:     ', len(taxi), 'trips, residual SD: $', round(taxi['residual'].std(ddof=0), 2))\n",
    "print()\n",
    "\n",
    "very_long = taxi[taxi['distance_miles'] > 20]\n",
    "print('Over 20 miles: ', len(very_long), 'trips, average residual: $', round(very_long['residual'].mean(), 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "75ec1ec3",
   "metadata": {},
   "source": [
    "The residual SD is about \\$2.8 for trips under 2 miles and about \\$7.3 for trips over 10 miles, 2.6 times as large. The overall \\$3.5 describes neither group well.\n",
    "\n",
    "The practical consequence is about **precision**. Up to about 20 miles, the line is a fair guide to the *average* fare. Beyond 20 miles it over-predicts those 33 trips by about \\$5 on average, possibly because of flat fares (the data cannot confirm this). And even where the average is right, a prediction for one 15-mile trip can miss by many dollars, while one for a 1-mile trip rarely does. A company forecasting the cost of employee rides should allow a wider margin as distance grows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "51344d54",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.329797Z",
     "iopub.status.busy": "2026-11-14T11:08:09.329745Z",
     "iopub.status.idle": "2026-11-14T11:08:09.331250Z",
     "shell.execute_reply": "2026-11-14T11:08:09.330888Z"
    },
    "tags": [
     "thebe-interactive"
    ]
   },
   "outputs": [],
   "source": [
    "### Exercise: Spread by Distance\n",
    "#   1. Read the taxi data and fit the line of fare on distance with the slope\n",
    "#      and intercept functions (all 5,000 trips). Compute the residuals.\n",
    "#   2. Find the residual SD (np.std) for trips of 5 miles or less\n",
    "#      and for trips over 15 miles, rounded to 2 decimals.\n",
    "#   3. Print the ratio of the long-trip SD to the short-trip SD, rounded to 1 decimal.\n",
    "# Print exactly:\n",
    "#   Up to 5 miles residual SD: <value>\n",
    "#   Over 15 miles residual SD: <value>\n",
    "#   Ratio: <value>\n",
    "### Your code starts here.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "### Your code ends here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "0a9eff5d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.332041Z",
     "iopub.status.busy": "2026-11-14T11:08:09.331973Z",
     "iopub.status.idle": "2026-11-14T11:08:09.336306Z",
     "shell.execute_reply": "2026-11-14T11:08:09.335998Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Up to 5 miles residual SD: 3.05\n",
      "Over 15 miles residual SD: 8.22\n",
      "Ratio: 2.7\n"
     ]
    }
   ],
   "source": [
    "### Solution\n",
    "ex_taxi = pd.read_csv(path_data + 'nyc_taxi_fares.csv')\n",
    "\n",
    "ex_slope = slope(ex_taxi, 'distance_miles', 'fare')\n",
    "ex_intercept = intercept(ex_taxi, 'distance_miles', 'fare')\n",
    "ex_taxi['residual'] = ex_taxi['fare'] - (ex_slope * ex_taxi['distance_miles'] + ex_intercept)\n",
    "\n",
    "band1 = ex_taxi[ex_taxi['distance_miles'] <= 5]\n",
    "band2 = ex_taxi[ex_taxi['distance_miles'] > 15]\n",
    "\n",
    "sd1 = np.std(band1['residual'])\n",
    "sd2 = np.std(band2['residual'])\n",
    "\n",
    "print('Up to 5 miles residual SD:', round(sd1, 2))\n",
    "print('Over 15 miles residual SD:', round(sd2, 2))\n",
    "print('Ratio:', round(sd2 / sd1, 1))\n",
    "# Trips over 15 miles have much more spread than trips of 5 miles or less:\n",
    "# uneven spread."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fdf64020",
   "metadata": {},
   "source": [
    "## Using Diagnostics in Practice\n",
    "\n",
    "```{index} diagnostic checklist\n",
    "```\n",
    "\n",
    "```{index} influential point\n",
    "```\n",
    "\n",
    "Before you trust a regression line, run through this short checklist.\n",
    "\n",
    "1. **Plot the data.** Draw the scatter plot. A single number such as r or the slope can look the same for very different pictures.\n",
    "2. **Plot the residuals.** Look for a curve (nonlinearity), a fan (uneven spread), and clumps. A healthy plot is a shapeless cloud centered on 0.\n",
    "3. **Check the range.** A line is a description of the data you have. Use it only for feature values within the range of the data, and avoid **extrapolation**, which means predicting far outside that range. In the price data, for example, the line would predict negative sales at a price of about \\$16.40, which is impossible.\n",
    "4. **Look for influential points.** A point far from the others in the feature direction can pull the line toward itself. Refit the line without it. If the slope changes a lot, the line depends on one observation, and you should find out whether that observation is correct."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3f9a6b21",
   "metadata": {},
   "source": [
    "### Influential Points\n",
    "\n",
    "In {doc}`1201-correlation` you added an invented new store to the 40: it spends \\$9,500 a week on ads but sells only \\$40,000, because it has not yet built a customer base. That one store pulled r from about 0.69 down to about 0.54. Here is what it does to the line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "8c2d5e47",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.337204Z",
     "iopub.status.busy": "2026-11-14T11:08:09.337148Z",
     "iopub.status.idle": "2026-11-14T11:08:09.387425Z",
     "shell.execute_reply": "2026-11-14T11:08:09.386947Z"
    }
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope without the new store: 3.87\n",
      "Slope with the new store:    3.19\n"
     ]
    }
   ],
   "source": [
    "new_store = pd.DataFrame({'store': ['S41'], 'region': ['North'], 'ad_spend': [9.5],\n",
    "                          'staff': [10], 'store_age': [0], 'sales': [40.0]})\n",
    "with_new = pd.concat([stores[new_store.columns], new_store], ignore_index=True)\n",
    "\n",
    "xs = np.array([1, 10])\n",
    "fig, ax = plt.subplots(figsize=(6, 4))\n",
    "ax.scatter(stores['ad_spend'], stores['sales'], s=25, label='40 stores')\n",
    "ax.scatter([9.5], [40.0], s=60, color='red', label='New store')\n",
    "for data, color, label in [(stores, 'gold', 'Line without the new store'),\n",
    "                           (with_new, 'tab:red', 'Line with the new store')]:\n",
    "    ax.plot(xs, slope(data, 'ad_spend', 'sales') * xs + intercept(data, 'ad_spend', 'sales'),\n",
    "            color=color, lw=2.5, label=label)\n",
    "ax.set_xlabel('Weekly ad spend ($1,000s)')\n",
    "ax.set_ylabel('Weekly sales ($1,000s)')\n",
    "ax.set_title('One store pulls the line down at the right')\n",
    "ax.legend(fontsize=9)\n",
    "plt.show()\n",
    "\n",
    "print('Slope without the new store:', round(slope(stores, 'ad_spend', 'sales'), 2))\n",
    "print('Slope with the new store:   ', round(slope(with_new, 'ad_spend', 'sales'), 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a4b7c0d9",
   "metadata": {},
   "source": [
    "One store out of 41 lowers the slope from about 3.87 to about 3.19, a drop of almost a fifth in the estimated sales per \\$1,000 of ads. The store sits near the right edge of the ad-spend range, far below the line, so it tilts the whole line toward itself. A manager deciding whether ads pay for themselves would read the two slopes very differently. The lesson is the one in the checklist: refit without the point, report both lines, and find out whether the store is typical of the stores the decision is about."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e2f8a1b3",
   "metadata": {},
   "source": [
    "```{index} Anscombe's quartet\n",
    "```\n",
    "\n",
    "### Anscombe's Quartet Revisited\n",
    "\n",
    "The quartet from {doc}`1201-correlation` shows all four checks at once. The four data sets share nearly the same r and the same least squares line. Their residual plots, in the bottom row, tell them apart."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "a3cd181e",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.388506Z",
     "iopub.status.busy": "2026-11-14T11:08:09.388435Z",
     "iopub.status.idle": "2026-11-14T11:08:09.543504Z",
     "shell.execute_reply": "2026-11-14T11:08:09.543171Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dataset I  slope: 0.5  intercept: 3.0  r: 0.82\n",
      "Dataset II  slope: 0.5  intercept: 3.0  r: 0.82\n",
      "Dataset III  slope: 0.5  intercept: 3.0  r: 0.82\n",
      "Dataset IV  slope: 0.5  intercept: 3.0  r: 0.82\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1100x500 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "quartet = pd.read_csv(path_data + 'anscombe_quartet.csv')\n",
    "\n",
    "fig, axes = plt.subplots(2, 4, figsize=(11, 5), sharex=True)\n",
    "for k, name in enumerate(['I', 'II', 'III', 'IV']):\n",
    "    part = quartet[quartet['dataset'] == name].copy()\n",
    "    a_slope = slope(part, 'x', 'y')\n",
    "    a_intercept = intercept(part, 'x', 'y')\n",
    "    part['residual'] = part['y'] - (a_slope * part['x'] + a_intercept)\n",
    "    xs = np.array([3, 20])\n",
    "\n",
    "    axes[0, k].scatter(part['x'], part['y'], s=25)\n",
    "    axes[0, k].plot(xs, a_slope * xs + a_intercept, color='gold', lw=3)\n",
    "    axes[0, k].set_title('Dataset ' + name)\n",
    "    axes[0, k].set_xlabel('x')\n",
    "\n",
    "    axes[1, k].scatter(part['x'], part['residual'], s=25)\n",
    "    axes[1, k].axhline(0, color='gold', lw=3)\n",
    "    axes[1, k].set_xlabel('x')\n",
    "    if k == 0:\n",
    "        axes[0, k].set_ylabel('y')\n",
    "        axes[1, k].set_ylabel('Residual')\n",
    "\n",
    "    print('Dataset', name, ' slope:', round(a_slope, 2), ' intercept:', round(a_intercept, 2),\n",
    "          ' r:', round(correlation(part, 'x', 'y'), 2))\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "da355d3d",
   "metadata": {},
   "source": [
    "The four lines are essentially the same, but the residual plots tell four different stories: **I** is a healthy, shapeless cloud; **II** curves, so the relationship is nonlinear; **III** is a straight line with one outlier that shows up as one huge residual; and in **IV** a single point far to the right determines the slope by itself, an influential point. Summary numbers cannot tell these data sets apart. Pictures can."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d434c2d4",
   "metadata": {},
   "source": [
    "When a check fails, you do not give up on the data. You transform the variables, fit a curve, restrict the range, or report that the predictions are less precise in some region. The checks also show what is still unsettled. A healthy diagnostic does not prove that a line is the true relationship, and it does not show that one variable causes the other ({doc}`../10-two-samples/1002-observational-comparisons`)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b0c9d1e",
   "metadata": {},
   "source": [
    "## Inference for the Slope\n",
    "\n",
    "```{index} sampling variability; slope\n",
    "```\n",
    "\n",
    "```{index} true slope\n",
    "```\n",
    "\n",
    "The store data passed the shape checks. Now the manager wants to know whether advertising pays off, and the slope of about 3.87 says that in these 40 stores each extra \\$1,000 of weekly ad spend goes with about \\$3,870 more in weekly sales. But the 40 stores are a **sample**. Imagine the line from **all** stores like these, observed under conditions like this month's. Its slope is the **true slope**, an unknown population parameter, and the sample slope estimates it, as a sample median estimated a population median in {doc}`../11-estimation/1102-bootstrap`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "cb36077c",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.544713Z",
     "iopub.status.busy": "2026-11-14T11:08:09.544650Z",
     "iopub.status.idle": "2026-11-14T11:08:09.571344Z",
     "shell.execute_reply": "2026-11-14T11:08:09.571027Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope:     3.87\n",
      "Intercept: 57.54\n"
     ]
    }
   ],
   "source": [
    "observed_slope = slope(stores, 'ad_spend', 'sales')\n",
    "observed_intercept = intercept(stores, 'ad_spend', 'sales')\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(5, 4))\n",
    "ax.scatter(stores['ad_spend'], stores['sales'], s=20)\n",
    "xs = np.array([1, 10])\n",
    "ax.plot(xs, observed_slope * xs + observed_intercept, color='gold', lw=3)\n",
    "ax.set_xlabel('Weekly ad spend ($1,000s)', fontsize=12)\n",
    "ax.set_ylabel('Weekly sales ($1,000s)', fontsize=12)\n",
    "plt.show()\n",
    "\n",
    "print('Slope:    ', round(observed_slope, 2))\n",
    "print('Intercept:', round(observed_intercept, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e9018fd",
   "metadata": {},
   "source": [
    "To see that the estimate depends on which stores happen to be in the sample, split the 40 stores into two groups of 20 and fit a line to each."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "66906a9d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.572357Z",
     "iopub.status.busy": "2026-11-14T11:08:09.572294Z",
     "iopub.status.idle": "2026-11-14T11:08:09.574679Z",
     "shell.execute_reply": "2026-11-14T11:08:09.574421Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope from the first 20 stores: 5.04\n",
      "Slope from the last 20 stores:  3.39\n"
     ]
    }
   ],
   "source": [
    "first_20 = stores.iloc[:20]\n",
    "last_20 = stores.iloc[20:]\n",
    "\n",
    "print('Slope from the first 20 stores:', round(slope(first_20, 'ad_spend', 'sales'), 2))\n",
    "print('Slope from the last 20 stores: ', round(slope(last_20, 'ad_spend', 'sales'), 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d55adf9d",
   "metadata": {},
   "source": [
    "The two halves give slopes of about 5.04 and 3.39. Neither is wrong; each is a fair estimate from a smaller sample. A fitted slope has **sampling variability**, and a manager who reads only one slope does not know whether the true slope might be 3, 4, or 5."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dab2a620",
   "metadata": {},
   "source": [
    "### Bootstrapping the Slope\n",
    "\n",
    "```{index} bootstrap; slope\n",
    "```\n",
    "\n",
    "```{index} bootstrap slope\n",
    "```\n",
    "\n",
    "You cannot go back and collect many new samples of stores. As in {doc}`../11-estimation/1102-bootstrap`, **resample the sample**: draw 40 rows from `stores` at random **with replacement**, and fit a line to the resample. The slope of that line is a **bootstrap slope**.\n",
    "\n",
    "One detail matters for regression: resample whole **rows**. Each row keeps a store's ad spend and sales together, so the resample keeps the relationship between the two variables. Resampling the two columns separately would break every pair and destroy the association you want to measure."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "daef1875",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.575593Z",
     "iopub.status.busy": "2026-11-14T11:08:09.575538Z",
     "iopub.status.idle": "2026-11-14T11:08:09.576924Z",
     "shell.execute_reply": "2026-11-14T11:08:09.576663Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def one_bootstrap_slope():\n",
    "    resample = stores.sample(len(stores), replace=True)\n",
    "    return slope(resample, 'ad_spend', 'sales')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5ee76f8",
   "metadata": {},
   "source": [
    "Run the cell below a few times. Each run gives a slightly different slope."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "bd7d7c3f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.577692Z",
     "iopub.status.busy": "2026-11-14T11:08:09.577641Z",
     "iopub.status.idle": "2026-11-14T11:08:09.581436Z",
     "shell.execute_reply": "2026-11-14T11:08:09.581092Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4.137821204412851"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "one_bootstrap_slope().item()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "856c7205",
   "metadata": {},
   "source": [
    "Now repeat the process 5,000 times and collect the slopes, as you collected medians and means in Chapter 11."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "97be1d59",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:09.582347Z",
     "iopub.status.busy": "2026-11-14T11:08:09.582290Z",
     "iopub.status.idle": "2026-11-14T11:08:10.811830Z",
     "shell.execute_reply": "2026-11-14T11:08:10.811458Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5000"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Seed once so the example is reproducible; do not reset inside the loop.\n",
    "np.random.seed(42)\n",
    "\n",
    "num_repetitions = 5000\n",
    "bstrap_slopes = np.array([])\n",
    "for i in np.arange(num_repetitions):\n",
    "    bstrap_slopes = np.append(bstrap_slopes, one_bootstrap_slope())\n",
    "\n",
    "len(bstrap_slopes)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7b1886af",
   "metadata": {},
   "source": [
    "The 5,000 bootstrap slopes form the **empirical distribution** of the slope. The histogram shows how much the slope moves from resample to resample; the red line marks the slope of the original sample."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "bd4bd05d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:10.812939Z",
     "iopub.status.busy": "2026-11-14T11:08:10.812879Z",
     "iopub.status.idle": "2026-11-14T11:08:10.919286Z",
     "shell.execute_reply": "2026-11-14T11:08:10.918963Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(5, 4))\n",
    "ax.hist(bstrap_slopes, bins=25, density=True, ec='white')\n",
    "ax.axvline(observed_slope, color='red', lw=2)\n",
    "ax.set_xlabel('Bootstrap slope ($ sales per $ ad)', fontsize=12)\n",
    "ax.set_ylabel('Density', fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "ee3f3f90",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:10.920469Z",
     "iopub.status.busy": "2026-11-14T11:08:10.920406Z",
     "iopub.status.idle": "2026-11-14T11:08:10.921989Z",
     "shell.execute_reply": "2026-11-14T11:08:10.921702Z"
    },
    "tags": [
     "thebe-interactive"
    ]
   },
   "outputs": [],
   "source": [
    "### Exercise: Bootstrap the Staffing Slope\n",
    "# Does sales rise with the number of staff?\n",
    "#   1. Write a function that resamples the rows of stores with replacement,\n",
    "#      using stores.sample(len(stores), replace=True, random_state=seed),\n",
    "#      and returns the slope of sales on staff.\n",
    "#   2. Collect 1,000 bootstrap slopes with seed = 0, 1, ..., 999.\n",
    "#   3. Print the observed slope, the number of bootstrap slopes, and the smallest\n",
    "#      and largest bootstrap slopes, rounded to 2 decimals.\n",
    "### Your code starts here.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "### Your code ends here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "71340555",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:10.922753Z",
     "iopub.status.busy": "2026-11-14T11:08:10.922700Z",
     "iopub.status.idle": "2026-11-14T11:08:11.212504Z",
     "shell.execute_reply": "2026-11-14T11:08:11.212239Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Observed slope: 1.95\n",
      "Number of bootstrap slopes: 1000\n",
      "Smallest and largest: -0.04 3.98\n"
     ]
    }
   ],
   "source": [
    "### Solution\n",
    "ex_stores = pd.read_csv(path_data + 'store_ad_sales.csv')\n",
    "\n",
    "def one_bootstrap_staff_slope(seed):\n",
    "    resample = ex_stores.sample(len(ex_stores), replace=True, random_state=seed)\n",
    "    return slope(resample, 'staff', 'sales')\n",
    "\n",
    "staff_slopes = np.array([one_bootstrap_staff_slope(i) for i in range(1000)])\n",
    "\n",
    "print('Observed slope:', round(slope(ex_stores, 'staff', 'sales'), 2))\n",
    "print('Number of bootstrap slopes:', len(staff_slopes))\n",
    "print('Smallest and largest:', round(staff_slopes.min(), 2), round(staff_slopes.max(), 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "25085ab1",
   "metadata": {},
   "source": [
    "### A Confidence Interval and a Test\n",
    "\n",
    "```{index} confidence interval; for a slope\n",
    "```\n",
    "\n",
    "```{index} slope confidence interval\n",
    "```\n",
    "\n",
    "The **bootstrap percentile method** from {doc}`../11-estimation/1103-confidence-intervals` works for slopes exactly as it did for medians and means. For a 95% confidence interval, take the 2.5th and 97.5th percentiles of the bootstrap slopes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "afdd0f99",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:11.213683Z",
     "iopub.status.busy": "2026-11-14T11:08:11.213619Z",
     "iopub.status.idle": "2026-11-14T11:08:11.215723Z",
     "shell.execute_reply": "2026-11-14T11:08:11.215468Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.79, 4.98])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "left = np.percentile(bstrap_slopes, 2.5, method='nearest')\n",
    "right = np.percentile(bstrap_slopes, 97.5, method='nearest')\n",
    "\n",
    "np.array([left, right]).round(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "eb8e3731",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:11.216581Z",
     "iopub.status.busy": "2026-11-14T11:08:11.216518Z",
     "iopub.status.idle": "2026-11-14T11:08:11.251260Z",
     "shell.execute_reply": "2026-11-14T11:08:11.250903Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(5, 4))\n",
    "ax.hist(bstrap_slopes, bins=25, density=True, ec='white')\n",
    "ax.plot([left, right], [0, 0], color='yellow', lw=8)\n",
    "ax.set_xlabel('Bootstrap slope ($ sales per $ ad)', fontsize=12)\n",
    "ax.set_ylabel('Density', fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce62b347",
   "metadata": {},
   "source": [
    "The approximate 95% confidence interval for the true slope runs from about 2.79 to 4.98.\n",
    "\n",
    "**Business interpretation.** Across the chain's stores, each extra \\$1,000 of weekly ad spend is associated with between about \\$2,790 and \\$4,980 more in weekly sales, at 95% confidence. As in Chapter 11, the 95% describes the method: intervals built this way would contain the true slope about 95% of the time.\n",
    "\n",
    "The interval describes an **association**: stores that spend more on ads may also differ in location or size ({doc}`1201-correlation`). That matters for the manager's real question. Suppose each dollar of sales brings 30 cents of gross profit. Then advertising pays for itself only if one extra dollar of ads *causes* more than $1/0.30 \\approx 3.33$ dollars of sales. An interval for an association cannot answer that causal question, and even if the slope were causal, the interval reaches below 3.33. To decide, the manager needs evidence about cause, such as an experiment that randomly assigns ad budgets to stores ({doc}`../10-two-samples/1003-causality`)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0872da7",
   "metadata": {},
   "source": [
    "```{index} hypothesis test; slope\n",
    "```\n",
    "\n",
    "```{index} no linear association\n",
    "```\n",
    "\n",
    "A slope of 0 means the best-fitting straight line is flat: $x$ has no *linear* association with $y$ (the average of $y$ could still change along a curve, as in the profit example of {doc}`1201-correlation`). In the language of {doc}`../09-test-hypothesis/0903-decisions-uncertainty`:\n",
    "\n",
    "- **Null hypothesis:** the true slope is 0; the sample slope differs from 0 only by chance.\n",
    "- **Alternative hypothesis:** the true slope is not 0.\n",
    "\n",
    "If 0 is **outside** the 95% confidence interval, reject the null hypothesis at about the 5% cutoff (the bootstrap interval is approximate, so the test is too). If 0 is **inside**, the data are consistent with no linear association. For ad spend, 0 is far outside 2.79 to 4.98, so you reject the null hypothesis.\n",
    "\n",
    "Now a different question: do older stores sell more? Here is the slope of sales on `store_age`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "e9e47e08",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:11.252245Z",
     "iopub.status.busy": "2026-11-14T11:08:11.252189Z",
     "iopub.status.idle": "2026-11-14T11:08:11.254225Z",
     "shell.execute_reply": "2026-11-14T11:08:11.253969Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.28"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "age_slope = slope(stores, 'store_age', 'sales')\n",
    "round(age_slope.item(), 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4527f8bd",
   "metadata": {},
   "source": [
    "In the sample, each extra year open goes with about \\$280 *less* in weekly sales. Is that a real pattern, or chance? Bootstrap the slope and check whether 0 is in the interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "ef7995b4",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:11.255483Z",
     "iopub.status.busy": "2026-11-14T11:08:11.255422Z",
     "iopub.status.idle": "2026-11-14T11:08:12.448138Z",
     "shell.execute_reply": "2026-11-14T11:08:12.447817Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.97,  0.37])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def one_bootstrap_age_slope():\n",
    "    resample = stores.sample(len(stores), replace=True)\n",
    "    return slope(resample, 'store_age', 'sales')\n",
    "\n",
    "np.random.seed(42)\n",
    "age_slopes = np.array([])\n",
    "for i in np.arange(5000):\n",
    "    age_slopes = np.append(age_slopes, one_bootstrap_age_slope())\n",
    "\n",
    "age_left = np.percentile(age_slopes, 2.5, method='nearest')\n",
    "age_right = np.percentile(age_slopes, 97.5, method='nearest')\n",
    "np.array([age_left, age_right]).round(2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "0b82c8b0",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:12.449179Z",
     "iopub.status.busy": "2026-11-14T11:08:12.449123Z",
     "iopub.status.idle": "2026-11-14T11:08:12.480136Z",
     "shell.execute_reply": "2026-11-14T11:08:12.479774Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(5, 4))\n",
    "ax.hist(age_slopes, bins=25, density=True, ec='white')\n",
    "ax.plot([age_left, age_right], [0, 0], color='yellow', lw=8)\n",
    "ax.axvline(0, color='red', lw=2)\n",
    "ax.set_xlabel('Bootstrap slope (sales on store age)', fontsize=12)\n",
    "ax.set_ylabel('Density', fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d34bb4a9",
   "metadata": {},
   "source": [
    "The interval runs from about -0.97 to 0.37 and contains 0 (the red line), so you do **not** reject the null hypothesis: the manager should not conclude that older stores sell less. Not rejecting is not proving, though. The interval also includes slopes such as -0.8, a loss of \\$800 a week per year open, and 40 stores cannot rule that out."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "eba879db",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:12.481126Z",
     "iopub.status.busy": "2026-11-14T11:08:12.481074Z",
     "iopub.status.idle": "2026-11-14T11:08:12.482603Z",
     "shell.execute_reply": "2026-11-14T11:08:12.482289Z"
    },
    "tags": [
     "thebe-interactive"
    ]
   },
   "outputs": [],
   "source": [
    "### Exercise: Is Staffing Associated with Sales?\n",
    "#   1. Collect 1,000 bootstrap slopes of sales on staff, using\n",
    "#      stores.sample(len(stores), replace=True, random_state=i) for i = 0, ..., 999.\n",
    "#   2. Compute the 95% confidence interval with np.percentile(..., method='nearest').\n",
    "#   3. Print the interval rounded to 2 decimals and whether 0 is inside it.\n",
    "# Print exactly:\n",
    "#   95% interval: 0.86 to 3.05\n",
    "#   0 inside the interval: False\n",
    "### Your code starts here.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "### Your code ends here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "id": "3bbabac6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:12.483392Z",
     "iopub.status.busy": "2026-11-14T11:08:12.483345Z",
     "iopub.status.idle": "2026-11-14T11:08:12.777644Z",
     "shell.execute_reply": "2026-11-14T11:08:12.777235Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "95% interval: 0.86 to 3.05\n",
      "0 inside the interval: False\n"
     ]
    }
   ],
   "source": [
    "### Solution\n",
    "ex_stores = pd.read_csv(path_data + 'store_ad_sales.csv')\n",
    "\n",
    "staff_slopes = np.array([\n",
    "    slope(ex_stores.sample(len(ex_stores), replace=True, random_state=i), 'staff', 'sales')\n",
    "    for i in range(1000)\n",
    "])\n",
    "\n",
    "staff_left = np.percentile(staff_slopes, 2.5, method='nearest')\n",
    "staff_right = np.percentile(staff_slopes, 97.5, method='nearest')\n",
    "print('95% interval:', round(staff_left, 2), 'to', round(staff_right, 2))\n",
    "print('0 inside the interval:', staff_left <= 0 <= staff_right)\n",
    "# 0 is outside the interval, so reject the null hypothesis at the 5% cutoff:\n",
    "# ex_stores with more staff tend to have higher sales (an association, not proof of cause)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5d6e7f8",
   "metadata": {},
   "source": [
    "### Cautions\n",
    "\n",
    "```{index} bootstrap; limitations\n",
    "```\n",
    "\n",
    "The bootstrap interval is only as good as the sample and the line.\n",
    "\n",
    "- **Shape and influential points.** Run the diagnostics first. If the residuals curve, the slope summarizes the wrong shape; if one store pulls the line, the interval reflects that store more than the chain. A fan does not spoil the interval for the slope, but it makes predictions for single stores less certain in parts of the range.\n",
    "- **How the data were collected.** The bootstrap assumes the rows are independent draws that represent the population ({doc}`../11-estimation/1103-confidence-intervals`). Resampling these 40 stores mimics drawing other stores under this month's conditions, not other months, and no plot can check this.\n",
    "- **Range and sample size.** The interval applies to ad spend between about \\$1,000 and \\$10,000 a week. With only a handful of rows, the interval can mislead, and more bootstrap repetitions do not help; only more data does."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aad2e9d2",
   "metadata": {},
   "source": [
    "## Section Practice"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "581be6ee",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:12.778812Z",
     "iopub.status.busy": "2026-11-14T11:08:12.778749Z",
     "iopub.status.idle": "2026-11-14T11:08:12.780578Z",
     "shell.execute_reply": "2026-11-14T11:08:12.780246Z"
    },
    "tags": [
     "thebe-interactive"
    ]
   },
   "outputs": [],
   "source": [
    "### Exercise: Practice Visual Diagnostics\n",
    "# A delivery company fits a regression line of delivery cost on distance.\n",
    "#   1. Fit the line (slope and intercept from r and the SDs) and compute the residuals.\n",
    "#   2. Draw a residual plot: distance on the x-axis, residual on the y-axis, with a\n",
    "#      horizontal line at 0.\n",
    "#   3. Describe the pattern: is it curved, or does the spread change?\n",
    "# Print exactly:\n",
    "#   Residuals: [<the 10 residuals, rounded to 1 decimal, as a NumPy array>]\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "distance = np.array([2, 4, 6, 8, 10, 12, 14, 16, 18, 20])\n",
    "cost = np.array([9, 11, 12, 16, 15, 22, 18, 30, 21, 36])\n",
    "### Your code starts here.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "### Your code ends here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "9e213daa",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-11-14T11:08:12.781411Z",
     "iopub.status.busy": "2026-11-14T11:08:12.781362Z",
     "iopub.status.idle": "2026-11-14T11:08:12.810482Z",
     "shell.execute_reply": "2026-11-14T11:08:12.810114Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 500x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Residuals: [ 1.3  0.8 -0.7  0.8 -2.7  1.7 -4.8  4.7 -6.8  5.7]\n"
     ]
    }
   ],
   "source": [
    "### Solution\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "distance = np.array([2, 4, 6, 8, 10, 12, 14, 16, 18, 20])\n",
    "cost = np.array([9, 11, 12, 16, 15, 22, 18, 30, 21, 36])\n",
    "\n",
    "r = np.corrcoef(distance, cost)[0, 1]\n",
    "delivery_slope = r * np.std(cost) / np.std(distance)\n",
    "delivery_intercept = np.mean(cost) - delivery_slope * np.mean(distance)\n",
    "residuals = cost - (delivery_slope * distance + delivery_intercept)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(5, 3))\n",
    "ax.scatter(distance, residuals)\n",
    "ax.axhline(0, color='gray')\n",
    "ax.set_xlabel('Distance (km)')\n",
    "ax.set_ylabel('Residual ($)')\n",
    "plt.show()\n",
    "\n",
    "print('Residuals:', residuals.round(1))\n",
    "# The residuals fan out as distance grows (heteroscedasticity): predictions for\n",
    "# long deliveries are much less precise than for short ones."
   ]
  }
 ],
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