{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "b117e8cf",
   "metadata": {},
   "source": [
    "# Least Squares\n",
    "We have developed the equation of the regression line that runs through a football shaped scatter plot. But not all scatter plots are football shaped, not even linear ones. Does every scatter plot have a \"best\" line that goes through it? If so, can we still use the formulas for the slope and intercept developed in the previous section, or do we need new ones?\n",
    "\n",
    "To address these questions, we need a reasonable definition of \"best\". Recall that the purpose of the line is to *predict* or *estimate* values of $y$, given values of $x$. Estimates typically aren't perfect. Each one is off the true value by an *error*. A reasonable criterion for a line to be the \"best\" is for it to have the smallest possible overall error among all straight lines.\n",
    "\n",
    "In this section we will make this criterion precise and see if we can identify the best straight line under the criterion."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2e866b15",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:08.380563Z",
     "iopub.status.busy": "2026-08-31T06:02:08.380213Z",
     "iopub.status.idle": "2026-08-31T06:02:08.753018Z",
     "shell.execute_reply": "2026-08-31T06:02:08.752721Z"
    },
    "tags": [
     "hide-input",
     "thebe-init",
     "runnable"
    ]
   },
   "outputs": [],
   "source": [
    "path_data = '../../data/'\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('fivethirtyeight')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81ee9b7f",
   "metadata": {},
   "source": [
    "```{contents}\n",
    ":local:\n",
    ":depth: 2\n",
    "```\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5725e396",
   "metadata": {},
   "source": [
    "For simple linear regression, we know that the formula is:\n",
    "\n",
    "**y = mx + b**, where\n",
    "\n",
    "* **m** = slope (coefficient)\n",
    "* **b** = intercept\n",
    "* **x** = independent variable\n",
    "* **y** = dependent variable (prediction)\n",
    "\n",
    "Computationally, we can define these regression formula elements as below:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "5fdaa335",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:08.754452Z",
     "iopub.status.busy": "2026-08-31T06:02:08.754348Z",
     "iopub.status.idle": "2026-08-31T06:02:08.756440Z",
     "shell.execute_reply": "2026-08-31T06:02:08.756257Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def standard_units(any_numbers):\n",
    "    \"Convert any array of numbers to standard units.\"\n",
    "    return (any_numbers - np.mean(any_numbers))/np.std(any_numbers)  \n",
    "\n",
    "def correlation(t, x, y):       # r, the average of the product of the standard units x and y\n",
    "    return np.mean(standard_units(t[x])*standard_units(t[y]))   \n",
    "\n",
    "def slope(table, x, y):         # the correlation multiplied by the ratio of the standard deviations\n",
    "    r = correlation(table, x, y)\n",
    "    return r * np.std(table[y])/np.std(table[x])\n",
    "\n",
    "def intercept(table, x, y):     # the mean of y minus the slope multiplied by the mean of x\n",
    "    a = slope(table, x, y)\n",
    "    return np.mean(table[y]) - a * np.mean(table[x])\n",
    "\n",
    "def fit(table, x, y):           # the PREDICTED height (y) of the regression line at each x value\n",
    "    \"\"\"Return the height of the regression line at each x value.\"\"\"\n",
    "    a = slope(table, x, y)\n",
    "    b = intercept(table, x, y)\n",
    "    return a * table[x] + b"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "395a2557",
   "metadata": {},
   "source": [
    "Our first example is a dataset that has one row for every chapter of the novel \"Little Women.\" The goal is to estimate the number of characters (that is, letters, spaces punctuation marks, and so on) based on the number of periods."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "ed040296",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:08.757412Z",
     "iopub.status.busy": "2026-08-31T06:02:08.757354Z",
     "iopub.status.idle": "2026-08-31T06:02:08.764283Z",
     "shell.execute_reply": "2026-08-31T06:02:08.764090Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Characters</th>\n",
       "      <th>Periods</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>21759</td>\n",
       "      <td>189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>22148</td>\n",
       "      <td>188</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>20558</td>\n",
       "      <td>231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>25526</td>\n",
       "      <td>195</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>23395</td>\n",
       "      <td>255</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Characters  Periods\n",
       "0       21759      189\n",
       "1       22148      188\n",
       "2       20558      231\n",
       "3       25526      195\n",
       "4       23395      255"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "little_women = pd.read_csv(path_data + 'little_women.csv')\n",
    "little_women.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "8d44e2f2",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:08.765212Z",
     "iopub.status.busy": "2026-08-31T06:02:08.765158Z",
     "iopub.status.idle": "2026-08-31T06:02:08.767744Z",
     "shell.execute_reply": "2026-08-31T06:02:08.767572Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Periods</th>\n",
       "      <th>Characters</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>189</td>\n",
       "      <td>21759</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>188</td>\n",
       "      <td>22148</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>231</td>\n",
       "      <td>20558</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>195</td>\n",
       "      <td>25526</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>255</td>\n",
       "      <td>23395</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Periods  Characters\n",
       "0      189       21759\n",
       "1      188       22148\n",
       "2      231       20558\n",
       "3      195       25526\n",
       "4      255       23395"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "periods = little_women['Periods']\n",
    "little_women.pop('Periods')\n",
    "little_women.insert(0, 'Periods', periods)\n",
    "little_women.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "7f4b4322",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:08.768685Z",
     "iopub.status.busy": "2026-08-31T06:02:08.768633Z",
     "iopub.status.idle": "2026-08-31T06:02:08.807174Z",
     "shell.execute_reply": "2026-08-31T06:02:08.806940Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "little_women.plot(       ### using pandas plot for visualization\n",
    "    'Periods', \n",
    "    'Characters', \n",
    "    kind='scatter', \n",
    "    figsize=(4,4), \n",
    "    fontsize=9, \n",
    "    s=10, \n",
    "    alpha=.8\n",
    ")\n",
    "\n",
    "plt.xlabel('Periods', fontsize=12)\n",
    "plt.ylabel('characters', fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2b4e92de",
   "metadata": {},
   "source": [
    "To explore the data, we will need to use the functions `correlation`, `slope`, `intercept`, and `fit` defined in the previous section."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b45cda2f",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:08.808349Z",
     "iopub.status.busy": "2026-08-31T06:02:08.808283Z",
     "iopub.status.idle": "2026-08-31T06:02:08.810363Z",
     "shell.execute_reply": "2026-08-31T06:02:08.810174Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9229576895854816"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(little_women, 'Periods', 'Characters').item()     ### corr == r"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9634345b",
   "metadata": {},
   "source": [
    "The scatter plot is remarkably close to linear, and the correlation is more than 0.92."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "33d8433b",
   "metadata": {},
   "source": [
    "## Error in Estimation\n",
    "\n",
    "The graph below shows the scatter plot and line that we developed in the previous section. We don't yet know if that's the best among all lines. We first have to say precisely what \"best\" means."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "9c1eec77",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:08.811367Z",
     "iopub.status.busy": "2026-08-31T06:02:08.811308Z",
     "iopub.status.idle": "2026-08-31T06:02:08.847964Z",
     "shell.execute_reply": "2026-08-31T06:02:08.847758Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lw_with_predictions = little_women.copy()\n",
    "lw_with_predictions['Linear Prediction'] = fit(little_women, 'Periods', 'Characters')\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8,4))\n",
    "\n",
    "ax.scatter(lw_with_predictions['Periods'], \n",
    "           lw_with_predictions['Characters'], \n",
    "           label='Characters', \n",
    "           color='darkblue')\n",
    "\n",
    "ax.scatter(lw_with_predictions['Periods'], \n",
    "           lw_with_predictions['Linear Prediction'], \n",
    "           label='Linear Prediction', \n",
    "           color='gold')\n",
    "\n",
    "x_label = 'Periods'\n",
    "y_label = ''\n",
    "y_vals = ax.get_yticks()\n",
    "plt.ylabel(y_label)\n",
    "plt.xlabel(x_label)\n",
    "ax.legend(bbox_to_anchor=(1.04,1), loc=\"upper left\", frameon=False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "021cd61b",
   "metadata": {},
   "source": [
    "Corresponding to each point on the scatter plot, there is an **error** of prediction calculated as the *actual value minus the predicted value*. It is the *vertical distance* between the point and the line, with a negative sign if the point is below the line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e1b37149",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:08.849067Z",
     "iopub.status.busy": "2026-08-31T06:02:08.849003Z",
     "iopub.status.idle": "2026-08-31T06:02:08.850511Z",
     "shell.execute_reply": "2026-08-31T06:02:08.850331Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "actual = lw_with_predictions['Characters']\n",
    "predicted = lw_with_predictions['Linear Prediction']\n",
    "errors = actual - predicted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "37f49997",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:08.851454Z",
     "iopub.status.busy": "2026-08-31T06:02:08.851404Z",
     "iopub.status.idle": "2026-08-31T06:02:08.854041Z",
     "shell.execute_reply": "2026-08-31T06:02:08.853860Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Periods</th>\n",
       "      <th>Characters</th>\n",
       "      <th>Linear Prediction</th>\n",
       "      <th>Error</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>189</td>\n",
       "      <td>21759</td>\n",
       "      <td>21183.596794</td>\n",
       "      <td>575.403206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>188</td>\n",
       "      <td>22148</td>\n",
       "      <td>21096.618953</td>\n",
       "      <td>1051.381047</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>231</td>\n",
       "      <td>20558</td>\n",
       "      <td>24836.666127</td>\n",
       "      <td>-4278.666127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>195</td>\n",
       "      <td>25526</td>\n",
       "      <td>21705.463842</td>\n",
       "      <td>3820.536158</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>255</td>\n",
       "      <td>23395</td>\n",
       "      <td>26924.134317</td>\n",
       "      <td>-3529.134317</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Periods  Characters  Linear Prediction        Error\n",
       "0      189       21759       21183.596794   575.403206\n",
       "1      188       22148       21096.618953  1051.381047\n",
       "2      231       20558       24836.666127 -4278.666127\n",
       "3      195       25526       21705.463842  3820.536158\n",
       "4      255       23395       26924.134317 -3529.134317"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lw_with_predictions['Error'] =  errors\n",
    "lw_with_predictions.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89960c40",
   "metadata": {},
   "source": [
    "We can use `slope` and `intercept` to calculate the slope and intercept of the fitted line. The graph below shows the line (in light blue). The errors corresponding to four of the points are shown in red. There is nothing special about those four points. They were just chosen for clarity of the display. The function `lw_errors` takes a slope and an intercept (in that order) as its arguments and draws the figure. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "7a025a29",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:08.854999Z",
     "iopub.status.busy": "2026-08-31T06:02:08.854945Z",
     "iopub.status.idle": "2026-08-31T06:02:08.856645Z",
     "shell.execute_reply": "2026-08-31T06:02:08.856457Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "lw_reg_slope = slope(little_women, 'Periods', 'Characters')\n",
    "lw_reg_intercept = intercept(little_women, 'Periods', 'Characters')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "48f7ed3b",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:08.857527Z",
     "iopub.status.busy": "2026-08-31T06:02:08.857474Z",
     "iopub.status.idle": "2026-08-31T06:02:08.859084Z",
     "shell.execute_reply": "2026-08-31T06:02:08.858899Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "sample = [[131, 14431], [231, 20558], [392, 40935], [157, 23524]]\n",
    "\n",
    "def lw_errors(slope, intercept):\n",
    "    little_women.plot('Periods', 'Characters', kind='scatter')\n",
    "    xlims = np.array([50, 450])\n",
    "    plt.plot(xlims, slope * xlims + intercept, lw=2)\n",
    "    for x, y in sample:\n",
    "        plt.plot([x, x], [y, slope * x + intercept], color='r', lw=2, )\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "d5f160ab",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:08.860010Z",
     "iopub.status.busy": "2026-08-31T06:02:08.859937Z",
     "iopub.status.idle": "2026-08-31T06:02:08.890530Z",
     "shell.execute_reply": "2026-08-31T06:02:08.890337Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Slope of Regression Line:     87.0 characters per period\n",
      "Intercept of Regression Line: 4745.0 characters\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plt.figure(figsize=(6,3))\n",
    "\n",
    "print('Slope of Regression Line:    ', np.round(lw_reg_slope), 'characters per period')\n",
    "print('Intercept of Regression Line:', np.round(lw_reg_intercept), 'characters')\n",
    "\n",
    "lw_errors(lw_reg_slope, lw_reg_intercept)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3d92df05",
   "metadata": {},
   "source": [
    "Had we used a different line to create our estimates, the errors would have been different. The graph below shows how big the errors would be if we were to use another line for estimation. The second graph shows large errors obtained by using a line that is downright silly."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "83fc5d8a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:08.891588Z",
     "iopub.status.busy": "2026-08-31T06:02:08.891526Z",
     "iopub.status.idle": "2026-08-31T06:02:08.922554Z",
     "shell.execute_reply": "2026-08-31T06:02:08.922315Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lw_errors(50, 10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "96336d35",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:08.923532Z",
     "iopub.status.busy": "2026-08-31T06:02:08.923473Z",
     "iopub.status.idle": "2026-08-31T06:02:08.956501Z",
     "shell.execute_reply": "2026-08-31T06:02:08.956264Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lw_errors(-100, 50000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d598383d",
   "metadata": {},
   "source": [
    "## Root Mean Squared Error\n",
    "\n",
    "What we need now is one overall measure of the rough size of the errors. You will recognize the approach to creating this – it's exactly the way we developed the SD.\n",
    "\n",
    "If you use any arbitrary line to calculate your estimates, then some of your errors are likely to be positive and others negative. To avoid cancellation when measuring the rough size of the errors, we will take the mean of the squared errors rather than the mean of the errors themselves. \n",
    "\n",
    "The mean squared error of estimation is a measure of roughly how big the squared errors are, but as we have noted earlier, its units are hard to interpret. Taking the square root yields the root mean square error (rmse), which is in the same units as the variable being predicted and therefore much easier to understand. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b5ba2736",
   "metadata": {},
   "source": [
    "## Minimizing the Root Mean Squared Error\n",
    "\n",
    "Our observations so far can be summarized as follows.\n",
    "\n",
    "- To get estimates of $y$ based on $x$, you can use any line you want.\n",
    "- Every line has a root mean squared error of estimation.\n",
    "- \"Better\" lines have smaller errors.\n",
    "\n",
    "Is there a \"best\" line? That is, is there a line that minimizes the root mean squared error among all lines? \n",
    "\n",
    "To answer this question, we will start by defining a function `lw_rmse` to compute the root mean squared error of any line through the Little Women scatter diagram. The function takes the slope and the intercept (in that order) as its arguments."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "aa98e94d",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:08.957813Z",
     "iopub.status.busy": "2026-08-31T06:02:08.957744Z",
     "iopub.status.idle": "2026-08-31T06:02:08.959551Z",
     "shell.execute_reply": "2026-08-31T06:02:08.959335Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def lw_rmse(slope, intercept):\n",
    "    lw_errors(slope, intercept)\n",
    "    x = little_women['Periods']\n",
    "    y = little_women['Characters']\n",
    "    fitted = slope * x + intercept\n",
    "    mse = np.mean((y - fitted) ** 2)\n",
    "    print(\"Root mean squared error:\", mse ** 0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "5793a5cb",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:08.960656Z",
     "iopub.status.busy": "2026-08-31T06:02:08.960592Z",
     "iopub.status.idle": "2026-08-31T06:02:08.993341Z",
     "shell.execute_reply": "2026-08-31T06:02:08.993127Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root mean squared error: 4322.167831766537\n"
     ]
    }
   ],
   "source": [
    "lw_rmse(50, 10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "e64c3d0a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:08.994425Z",
     "iopub.status.busy": "2026-08-31T06:02:08.994356Z",
     "iopub.status.idle": "2026-08-31T06:02:09.025501Z",
     "shell.execute_reply": "2026-08-31T06:02:09.025299Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root mean squared error: 16710.11983735375\n"
     ]
    }
   ],
   "source": [
    "lw_rmse(-100, 50000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "61971ebd",
   "metadata": {},
   "source": [
    "Bad lines have big values of rmse, as expected. But the rmse is much smaller if we choose a slope and intercept close to those of the regression line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "555e86a3",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:09.026642Z",
     "iopub.status.busy": "2026-08-31T06:02:09.026581Z",
     "iopub.status.idle": "2026-08-31T06:02:09.057007Z",
     "shell.execute_reply": "2026-08-31T06:02:09.056787Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root mean squared error: 2715.5391063834586\n"
     ]
    }
   ],
   "source": [
    "lw_rmse(90, 4000)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60d44e33",
   "metadata": {},
   "source": [
    "Here is the root mean squared error corresponding to the regression line. By a remarkable fact of mathematics, no other line can beat this one. \n",
    "\n",
    "- The regression line is the unique straight line that minimizes the mean squared error of estimation among all straight lines."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "55ab7088",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:09.058000Z",
     "iopub.status.busy": "2026-08-31T06:02:09.057936Z",
     "iopub.status.idle": "2026-08-31T06:02:09.088142Z",
     "shell.execute_reply": "2026-08-31T06:02:09.087937Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root mean squared error: 2701.690785311856\n"
     ]
    }
   ],
   "source": [
    "lw_rmse(lw_reg_slope, lw_reg_intercept)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0b23a28",
   "metadata": {},
   "source": [
    "The proof of this statement requires abstract mathematics that is beyond the scope of this course. On the other hand, we do have a powerful tool – Python – that performs large numerical computations with ease. So we can use Python to confirm that the regression line minimizes the mean squared error."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c20c03ae",
   "metadata": {},
   "source": [
    "### Numerical Optimization ###\n",
    "First note that a line that minimizes the root mean squared error is also a line that minimizes the squared error. The square root makes no difference to the minimization. So we will save ourselves a step of computation and just minimize the mean squared error (mse).\n",
    "\n",
    "We are trying to predict the number of characters ($y$) based on the number of periods ($x$) in chapters of Little Women. If we use the line\n",
    "\n",
    "$$\n",
    "\\mbox{prediction} ~=~ ax + b\n",
    "$$\n",
    "\n",
    "it will have an mse that depends on the slope $a$ and the intercept $b$. The function `lw_mse` takes the slope and intercept as its arguments and returns the corresponding mse."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "f96cf1a6",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:09.089326Z",
     "iopub.status.busy": "2026-08-31T06:02:09.089266Z",
     "iopub.status.idle": "2026-08-31T06:02:09.090788Z",
     "shell.execute_reply": "2026-08-31T06:02:09.090603Z"
    },
    "tags": []
   },
   "outputs": [],
   "source": [
    "def lw_mse(any_slope, any_intercept):\n",
    "    x = little_women['Periods']\n",
    "    y = little_women['Characters']\n",
    "    fitted = any_slope*x + any_intercept\n",
    "    return np.mean((y - fitted) ** 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e6998c52",
   "metadata": {},
   "source": [
    "Let's check that `lw_mse` gets the right answer for the root mean squared error of the regression line. Remember that `lw_mse` returns the mean squared error, so we have to take the square root to get the rmse."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "9ddfcbf1",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:09.091730Z",
     "iopub.status.busy": "2026-08-31T06:02:09.091676Z",
     "iopub.status.idle": "2026-08-31T06:02:09.093432Z",
     "shell.execute_reply": "2026-08-31T06:02:09.093229Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(2701.690785311856)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lw_mse(lw_reg_slope, lw_reg_intercept)**0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7957f778",
   "metadata": {},
   "source": [
    "That's the same as the value we got by using `lw_rmse` earlier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "62bfe764",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:09.094340Z",
     "iopub.status.busy": "2026-08-31T06:02:09.094286Z",
     "iopub.status.idle": "2026-08-31T06:02:09.124743Z",
     "shell.execute_reply": "2026-08-31T06:02:09.124543Z"
    },
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root mean squared error: 2701.690785311856\n"
     ]
    }
   ],
   "source": [
    "lw_rmse(lw_reg_slope, lw_reg_intercept)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b43b4e9",
   "metadata": {},
   "source": [
    "You can confirm that `lw_mse` returns the correct value for other slopes and intercepts too. For example, here is the rmse of the extremely bad line that we tried earlier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "16c7bb6b",
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    "execution": {
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     "shell.execute_reply": "2026-08-31T06:02:09.127500Z"
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "16710.11983735375"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(lw_mse(-100, 50000)**0.5).item()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98211c31",
   "metadata": {},
   "source": [
    "And here is the rmse for a line that is close to the regression line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "344fefde",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:09.128619Z",
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     "shell.execute_reply": "2026-08-31T06:02:09.130050Z"
    },
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2715.5391063834586"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(lw_mse(90, 4000)**0.5).item()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "d398bbfa",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:09.131160Z",
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   "outputs": [],
   "source": [
    "from scipy import optimize\n",
    "import functools\n",
    "           # f is the function to minimize, start is the starting point for optimization, smooth indicates whether to use a method that assumes smoothness, log is a logging function, array indicates whether the function takes an array of arguments, and vargs are other arguments passed to scipy.optimize.minimize\n",
    "def minimize(f, start=None, smooth=False, log=None, array=False, **vargs):\n",
    "    \"\"\"Minimize a function f of one or more arguments.\n",
    "    Args:\n",
    "        f: A function that takes numbers and returns a number\n",
    "        start: A starting value or list of starting values\n",
    "        smooth: Whether to assume that f is smooth and use first-order info\n",
    "        log: Logging function called on the result of optimization (e.g. print)\n",
    "        vargs: Other named arguments passed to scipy.optimize.minimize\n",
    "    Returns either:\n",
    "        (a) the minimizing argument of a one-argument function\n",
    "        (b) an array of minimizing arguments of a multi-argument function\n",
    "    \"\"\"\n",
    "    if start is None:\n",
    "        assert not array, \"Please pass starting values explicitly when array=True\"\n",
    "        arg_count = f.__code__.co_argcount\n",
    "        assert arg_count > 0, \"Please pass starting values explicitly for variadic functions\"\n",
    "        start = [0] * arg_count\n",
    "    if not hasattr(start, '__len__'):\n",
    "        start = [start]\n",
    "\n",
    "    if array:\n",
    "        objective = f\n",
    "    else:\n",
    "        @functools.wraps(f)\n",
    "        def objective(args):\n",
    "            return f(*args)\n",
    "\n",
    "    if not smooth and 'method' not in vargs:\n",
    "        vargs['method'] = 'Powell'\n",
    "    result = optimize.minimize(objective, start, **vargs)\n",
    "    if log is not None:\n",
    "        log(result)\n",
    "    if len(start) == 1:\n",
    "        return result.x.item(0)\n",
    "    else:\n",
    "        return result.x"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b0e2ffc6",
   "metadata": {},
   "source": [
    "If we experiment with different values, we can find a low-error slope and intercept through trial and error, but that would take a while. Fortunately, there is a Python function that does all the trial and error for us.\n",
    "\n",
    "The `minimize` function can be used to find the arguments of a function for which the function returns its minimum value. Python uses a similar trial-and-error approach, following the changes that lead to incrementally lower output values. \n",
    "\n",
    "The argument of `minimize` is a function that itself takes numerical arguments and returns a numerical value. For example, the function `lw_mse` takes a numerical slope and intercept as its arguments and returns the corresponding mse. \n",
    "\n",
    "The call `minimize(lw_mse)` returns an array consisting of the slope and the intercept that minimize the mse. These minimizing values are excellent approximations arrived at by intelligent trial-and-error, not exact values based on formulas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "c5ccc24e",
   "metadata": {
    "execution": {
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   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  86.97784117, 4744.78484535])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best = minimize(lw_mse)\n",
    "best"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c4782aa3",
   "metadata": {},
   "source": [
    "These values are the same as the values we calculated earlier by using the `slope` and `intercept` functions. We see small deviations due to the inexact nature of `minimize`, but the values are essentially the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "bd105718",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:09.361596Z",
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     "shell.execute_reply": "2026-08-31T06:02:09.362832Z"
    },
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "slope from formula:         86.97784125829821\n",
      "slope from minimize:        86.97784116615884\n",
      "intercept from formula:     4744.784796574928\n",
      "intercept from minimize:    4744.784845352655\n"
     ]
    }
   ],
   "source": [
    "print(\"slope from formula:        \", lw_reg_slope)\n",
    "print(\"slope from minimize:       \", best.item(0))\n",
    "print(\"intercept from formula:    \", lw_reg_intercept)\n",
    "print(\"intercept from minimize:   \", best.item(1))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d195a9bd",
   "metadata": {},
   "source": [
    "## The Least Squares Line\n",
    "\n",
    "Therefore, we have found not only that the regression line minimizes mean squared error, but also that minimizing mean squared error gives us the regression line. The regression line is the only line that minimizes mean squared error.\n",
    "\n",
    "That is why the regression line is sometimes called the \"least squares line.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "51221d76",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "cell-8e322ae2",
   "metadata": {},
   "source": [
    "\n",
    "## Section Practice\n",
    "\n",
    "Use this short exercise to check the main workflow from this section.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "cell-58b29811",
   "metadata": {
    "execution": {
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    },
    "tags": [
     "thebe-interactive"
    ]
   },
   "outputs": [],
   "source": [
    "### Exercise: Practice Least Squares\n",
    "# A manager proposes the line: sales = 4 * temperature - 120.\n",
    "#   1. Compute the RMSE of the manager's line on the coffee chain's data.\n",
    "#   2. Compute the RMSE of the regression line (slope and intercept as in 1202).\n",
    "#   3. Print both, rounded to 2 decimals. Which is smaller, and why must it be?\n",
    "import numpy as np\n",
    "\n",
    "temperature = np.array([58, 62, 66, 70, 75, 79, 83, 88])\n",
    "iced_sales = np.array([120, 135, 150, 148, 180, 205, 210, 240])\n",
    "### Your code starts here\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "### Your code ends here\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "cell-e2dbd34a",
   "metadata": {
    "execution": {
     "iopub.execute_input": "2026-08-31T06:02:09.366197Z",
     "iopub.status.busy": "2026-08-31T06:02:09.366132Z",
     "iopub.status.idle": "2026-08-31T06:02:09.367478Z",
     "shell.execute_reply": "2026-08-31T06:02:09.367303Z"
    },
    "tags": [
     "hide-input"
    ]
   },
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": "Manager's line RMSE: 7.43\nRegression line RMSE: 6.78\n"
    }
   ],
   "source": [
    "### Solution\n",
    "import numpy as np\n",
    "\n",
    "temperature = np.array([58, 62, 66, 70, 75, 79, 83, 88])\n",
    "iced_sales = np.array([120, 135, 150, 148, 180, 205, 210, 240])\n",
    "\n",
    "def rmse(predicted):\n",
    "    return np.sqrt(np.mean((iced_sales - predicted) ** 2))\n",
    "\n",
    "r = np.corrcoef(temperature, iced_sales)[0, 1]\n",
    "slope = r * np.std(iced_sales) / np.std(temperature)\n",
    "intercept = np.mean(iced_sales) - slope * np.mean(temperature)\n",
    "\n",
    "print(\"Manager's line RMSE:\", round(rmse(4 * temperature - 120), 2))\n",
    "print('Regression line RMSE:', round(rmse(slope * temperature + intercept), 2))\n",
    "# The regression line is the least squares line: no straight line has a smaller RMSE.\n"
   ]
  }
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