{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": [
     "remove_input"
    ]
   },
   "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",
    "plt.style.use('fivethirtyeight')\n",
    "\n",
    "import functools\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": [
     "remove_input"
    ]
   },
   "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):\n",
    "    return np.mean(standard_units(t[x])*standard_units(t[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",
    "    a = slope(table, x, y)\n",
    "    return np.mean(table[y]) - a * np.mean(table[x])\n",
    "\n",
    "def fit(table, x, y):\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",
   "metadata": {},
   "source": [
    "# The Method of Least Squares\n",
    "We have retraced the steps that Galton and Pearson took to develop 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": "markdown",
   "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. Recall that we attempted to do this in the very first lecture of this course."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Periods  Characters\n",
       "0      189       21759\n",
       "1      188       22148\n",
       "2      231       20558"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "little_women = pd.read_csv(path_data + 'little_women.csv')\n",
    "\n",
    "periods = little_women['Periods']\n",
    "\n",
    "little_women.pop('Periods')\n",
    "\n",
    "little_women.insert(0, 'Periods', periods)\n",
    "\n",
    "little_women.head(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(6,6))\n",
    "\n",
    "ax.scatter(little_women['Periods'], \n",
    "           little_women['Characters'],  \n",
    "           color='darkblue')\n",
    "\n",
    "x_label = 'Periods'\n",
    "\n",
    "y_label = 'Characters'\n",
    "\n",
    "y_vals = ax.get_yticks()\n",
    "\n",
    "plt.ylabel(y_label)\n",
    "\n",
    "plt.xlabel(x_label)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "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": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9229576895854817"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "correlation(little_women, 'Periods', 'Characters')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The scatter plot is remarkably close to linear, and the correlation is more than 0.92."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Error in Estimation\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": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lw_with_predictions = little_women.copy()\n",
    "\n",
    "lw_with_predictions['Linear Prediction'] = fit(little_women, 'Periods', 'Characters')\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8,5))\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",
    "\n",
    "y_label = ''\n",
    "\n",
    "y_vals = ax.get_yticks()\n",
    "\n",
    "plt.ylabel(y_label)\n",
    "\n",
    "plt.xlabel(x_label)\n",
    "\n",
    "ax.legend(bbox_to_anchor=(1.04,1), loc=\"upper left\", frameon=False)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "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": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "actual = lw_with_predictions['Characters']\n",
    "predicted = lw_with_predictions['Linear Prediction']\n",
    "errors = actual - predicted"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>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",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>140</td>\n",
       "      <td>14622</td>\n",
       "      <td>16921.682573</td>\n",
       "      <td>-2299.682573</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>131</td>\n",
       "      <td>14431</td>\n",
       "      <td>16138.882001</td>\n",
       "      <td>-1707.882001</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>214</td>\n",
       "      <td>22476</td>\n",
       "      <td>23358.042826</td>\n",
       "      <td>-882.042826</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>337</td>\n",
       "      <td>33767</td>\n",
       "      <td>34056.317301</td>\n",
       "      <td>-289.317301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>185</td>\n",
       "      <td>18508</td>\n",
       "      <td>20835.685429</td>\n",
       "      <td>-2327.685429</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\n",
       "5      140       14622       16921.682573 -2299.682573\n",
       "6      131       14431       16138.882001 -1707.882001\n",
       "7      214       22476       23358.042826  -882.042826\n",
       "8      337       33767       34056.317301  -289.317301\n",
       "9      185       18508       20835.685429 -2327.685429"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lw_with_predictions['Error'] = errors\n",
    "lw_with_predictions.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "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": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lw_reg_slope = 86.97784125829823\n",
      "lw_reg_intercept = 4744.784796574924\n"
     ]
    }
   ],
   "source": [
    "lw_reg_slope = slope(little_women, 'Periods', 'Characters')\n",
    "\n",
    "lw_reg_intercept = intercept(little_women, 'Periods', 'Characters')\n",
    "\n",
    "print('lw_reg_slope =', lw_reg_slope )\n",
    "print('lw_reg_intercept =', lw_reg_intercept)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "tags": [
     "remove_input"
    ]
   },
   "outputs": [],
   "source": [
    "sample = [[131, 14431], [231, 20558], [392, 40935], [157, 23524]]\n",
    "\n",
    "def lw_errors(slope, intercept):\n",
    "    fig, ax = plt.subplots(figsize=(6,6))\n",
    "\n",
    "    ax.scatter(little_women['Periods'], \n",
    "               little_women['Characters'],  \n",
    "               color='darkblue')\n",
    "\n",
    "    x_label = 'Periods'\n",
    "\n",
    "    y_label = 'Characters'\n",
    "\n",
    "    y_vals = ax.get_yticks()\n",
    "\n",
    "    plt.ylabel(y_label)\n",
    "\n",
    "    plt.xlabel(x_label)\n",
    "    \n",
    "    xlims = np.array([50, 450])\n",
    "    \n",
    "    plt.plot(xlims, (slope * xlims) + intercept, lw=2)\n",
    "    \n",
    "    for x, y in sample:\n",
    "        plt.plot([x, x], [y, slope * x + intercept], color='r', lw=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "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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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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",
    "lw_errors(lw_reg_slope, lw_reg_intercept)"
   ]
  },
  {
   "cell_type": "markdown",
   "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": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lw_errors(50, 10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lw_errors(-100, 50000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Root Mean Squared Error\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",
   "metadata": {},
   "source": [
    "### Minimizing the Root Mean Squared Error\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": 14,
   "metadata": {},
   "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": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root mean squared error: 4322.167831766537\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lw_rmse(50, 10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root mean squared error: 16710.11983735375\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lw_rmse(-100, 50000)"
   ]
  },
  {
   "cell_type": "markdown",
   "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": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root mean squared error: 2715.5391063834586\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lw_rmse(90, 4000)"
   ]
  },
  {
   "cell_type": "markdown",
   "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": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root mean squared error: 2701.6907853118555\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lw_rmse(lw_reg_slope, lw_reg_intercept)"
   ]
  },
  {
   "cell_type": "markdown",
   "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",
   "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",
    "$$\n",
    "\\mbox{prediction} ~=~ ax + b\n",
    "$$\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": 19,
   "metadata": {},
   "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",
   "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": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2701.6907853118555"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lw_mse(lw_reg_slope, lw_reg_intercept)**0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That's the same as the value we got by using `lw_rmse` earlier:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Root mean squared error: 2701.6907853118555\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "lw_rmse(lw_reg_slope, lw_reg_intercept)"
   ]
  },
  {
   "cell_type": "markdown",
   "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": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "16710.11983735375"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lw_mse(-100, 50000)**0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here is the rmse for a line that is close to the regression line."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2715.5391063834586"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lw_mse(90, 4000)**0.5"
   ]
  },
  {
   "cell_type": "markdown",
   "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 (defined below) 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": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import optimize\n",
    "\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": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([  86.97784101, 4744.78484127])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "best = minimize(lw_mse)\n",
    "best"
   ]
  },
  {
   "cell_type": "markdown",
   "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": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "slope from formula:         86.97784125829823\n",
      "slope from minimize:        86.97784101391096\n",
      "intercept from formula:     4744.784796574924\n",
      "intercept from minimize:    4744.784841267639\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",
   "metadata": {},
   "source": [
    "### The Least Squares Line\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.\""
   ]
  }
 ],
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